Exponential and logarithmic function approximations for floating-point numbers

Abstract

The approaches presented herein provide the efficient approximation of exponential or logarithmic functions using values ​​in semi-precision, floating-point format. In at least one embodiment, an activation function of a neural network can perform tasks such as converting raw values ​​from the network into probabilities using the exponential of each output. A fixed-point representation of each raw value, incorporating a bias factor, can be generated and used to create an intermediate representation with a specified number of bits. The intermediate representation can be incremented so that its mantissa matches the fixed-point representation. The decimal coitus can be shifted to obtain a value that is an exponential approximation of the raw value and used to determine the probability (or any other such value) for a given arithmetic operation.At least some of these operations can be reversed to obtain a similar approximation for a logarithmic function.

Description

BACKGROUND There are several situations that can benefit from the use of exponential or logarithmic functions. These can include, for example, determining the growth or decay of a parameter value over time, or using them in SoftMax activation layers in neural networks to determine probabilities of derived values ​​or classifications, among other such options. Unfortunately, evaluating exponential values ​​can be computationally expensive, especially for operations involving calculating and summing multiple exponential values. Previous approaches could approximate an exponential function to try to reduce the computational effort, but such approximations often required conversion to and from integer values.While such integer-based operations can be relatively efficient, they are usually implemented for specific formats, such as individual precision formats. Approaches that require integer conversion may not perform as efficiently for other formats or, in some cases, may not be feasible using specific hardware. For example, it is difficult to perform such conversions for semi-precision formats on certain graphics processing units (GPUs). Certain approaches have been used to try to improve performance when using exponential functions, including direct numerical methods (e.g., polynomial interpolation, rational approximations, and iterative techniques that exploit the different algebraic properties of exponential and logarithmic functions).This includes exploiting the IEEE floating-point representation and the efficiency of hardware performing these operations, including bit manipulation. These approaches have not proven to be successful alternatives or implementation options for exponential functions on at least certain types of hardware. BRIEF DESCRIPTION OF THE DRAWINGS Various embodiments according to the present disclosure are described with reference to the drawings, in which: Fig. 1 illustrates components of an exemplary system that can infer classifications of input data according to at least one embodiment; Fig. 2A illustrates an exemplary architecture of a classification network according to at least one embodiment; Fig. 2B illustrates an exemplary SoftMax activation function that can be used with at least one embodiment; Fig. 3A and Fig. 3B illustrate an exemplary approach for approximating an exponentiation of raw values ​​inferred by a machine learning network according to at least one embodiment; Fig. 4A illustrates a plot of relative error for a semi-precision approximation according to at least one embodiment; Fig.4B illustrates an exemplary semi-precision floating-point format according to at least one embodiment; Fig. 5A illustrates an exemplary process that can be executed to infer one or more classifications according to at least one embodiment; Fig. 5B illustrates an exemplary process that can be executed to approximate an exponential function according to at least one embodiment; Fig. 6 illustrates components of a distributed system that can be used to generate and provide image content using object and scene models, including textures, according to at least one embodiment; Fig. 7A illustrates inference and / or training logic according to at least one embodiment; Fig. 7B illustrates inference and / or training logic according to at least one embodiment; Fig.Figure 8 illustrates an exemplary data center system according to at least one embodiment; Figure 9 illustrates a computer system according to at least one embodiment; Figure 10 illustrates a computer system according to at least one embodiment; Figure 11 illustrates at least portions of a graphics processor according to one or more embodiments; Figure 12 illustrates at least portions of a graphics processor according to one or more embodiments; Figure 13 is an exemplary data flow diagram for an advanced computing pipeline according to at least one embodiment; Figure 14 is a system diagram for an exemplary system for training, adapting, instantiating, and deploying machine learning models in an advanced computing pipeline according to at least one embodiment; and Figures 15A and 16A illustrate the following:Figure 15B illustrates a data flow diagram for a process for training a machine learning model and a client-server architecture for improving annotation tools with pre-trained annotation models according to at least one embodiment. DETAILED DESCRIPTION The following description details various embodiments. For explanatory purposes, specific configurations and details are presented to provide a thorough understanding of the embodiments. However, it will also be obvious to a person skilled in the art that the embodiments can be implemented without these specific details. Furthermore, well-known features may be omitted or simplified so as not to obscure the described embodiment. The systems and procedures described herein may be used by, without limitation, non-autonomous vehicles or machines, semi-autonomous or autonomous vehicles or machines (e.g., in one or more advanced driver assistance systems (ADAS), one or more in-vehicle infotainment systems, one or more emergency vehicle detection systems), piloted and unpiloted robots or robotic platforms, storage vehicles, all-terrain vehicles, vehicles coupled to one or more trailers, flying ships, boats, shuttles, emergency response vehicles, motorcycles, electric or motorized bicycles, aircraft, construction vehicles, trains, underwater vehicles, remotely controlled vehicles such as drones, and / or other types of vehicles.Furthermore, the systems and methods described herein can be used for a wide variety of purposes, including but not limited to machine control, machine locomotion, machine driving, synthetic data generation, generative AI, model training or updating, perception, augmented reality, virtual reality, mixed reality, robotics, security and monitoring, simulation and digital twinning, autonomous or semi-autonomous machine applications, deep learning, environmental simulation, data center processing, conversational AI, light transport simulation (e.g., ray tracing, path tracing, etc.), collaborative content creation for 3D assets, generative AI, cloud computing, and / or any other suitable applications. Disclosed embodiments can be found in a variety of different systems, such as automotive systems (e.g.,an in-vehicle infotainment system for an autonomous or semi-autonomous machine, a perception system for an autonomous or semi-autonomous machine, systems implemented using a robot, air systems, medical systems, boat systems, intelligent area monitoring systems, systems for performing deep learning operations, systems for performing simulation operations, systems for performing digital twin operations, systems implemented using an edge device, systems that include one or more virtual machines (VMs), systems for performing synthetic data generation operations, systems that are at least partially implemented in a data center, systems for performing conversational AI operations, systems that implement one or more language models - such as large language models (LLMs), vision language models (VLMs), multimodal language models, etc., systems for performing generative AI operations (e.g., using one or more language models, transformer models, etc.), systems for performing light transport simulation, systems for performing collaborative content creation for 3D assets, systems that are implemented at least partially using cloud computing resources, and / or other types of systems. Approaches according to various embodiments can be used to generate one or more parameters for a content generation environment. In at least one embodiment, a trained machine learning (ML) and / or artificial intelligence (AI) system, such as a large language model (LLM) or a vision language model (VLM), can be used to generate parameters for the content generation environment, such as, but not limited to, camera settings, scene lighting, video parameters, and / or the like, used to display objects within a scene. The parameters can be based on input provided by a user or a user proxy to a trained language model (e.g., LLM, VLM, etc.), which can then generate one or more settings according to the input.Various embodiments can be used to generate settings in two-dimensional (2D) or three-dimensional (3D) environments. For embodiments that include one or more language models—that is, one or more LLMs, one or more VLMs, or a combination of LLMs and VLMs—the language model(s) can receive input (e.g., a prompt, a request, a query, etc.) that is parsed or otherwise formatted to produce deterministic output. For example, the input provided to the language model can include a single format for the output results, an example of desired output results, a single list of parameters and their respective formatting, and the like. An input generator (e.g.,A prompt generator, which can be driven or otherwise guided by one or more AI and / or ML systems, can be used to generate this input based on an initial input received from a user, device, proxy, and / or the like. A modified input generated by the prompt generator can then be provided to the language model, which produces an output set of parameters. This output can further be evaluated by a validator or other system to ensure its appropriateness. Subsequently, a configuration file can be generated, and / or the parameters can be directly provided to an environment to configure various components (e.g., camera settings, lighting, etc.) based on the parameters generated by the language model. In some examples, the machine learning model(s) (e.g., deep neural networks, language models, LLMs, VLMs, multimodal language models, perceptual models, tracking models, fusion models, transformer models, diffusion models, encoder-only models, decoder-only models, encoder-decoder models, neural rendering field (NERF) models, etc.) described herein may be packaged as a microservice—such as an inference microservice (e.g., NVIDIA NIMs)—which may contain a container (e.g., an operating system (OS)-level virtualization package) that may include an application programming interface (API) layer, a server layer, a runtime layer, and / or at least one model engine. For example, the inference microservice may contain the container itself and the model(s) (e.g., weights and biases). In some cases, such as when the machine learning model(s) is small enough (e.g.In some examples (where the model has a small number of parameters), the model(s) can be contained within the container itself. In other examples—such as when the model(s) is large—the model(s) can be hosted in the cloud (e.g., in a data center) and / or on-premises and / or at the edge (e.g., on a local server or computing device, but outside the container). In such embodiments, the model(s) can be accessed via one or more APIs, such as REST APIs. Thus, in some embodiments, the machine learning model(s) described herein can be used as an inference microservice to accelerate the deployment of a model(s) on any cloud, data center, or edge computing system while ensuring data security.For example, the inference microservice may include one or more APIs, a pre-configured container for simplified deployment, an optimized inference engine (e.g., built using a standardized AI model deployment, execution software such as NVIDIA's Triton Inference Server, and / or one or more APIs for high-performance deep learning inference, which may include inference runtime and model optimizations that deliver low latency and high throughput for production applications - such as NVIDIA's TensorRT), and / or enterprise management data for telemetry (e.g., including identity, metrics, health checks, and / or monitoring). The machine learning model(s) described herein may be included as part of the microservice, along with accelerated infrastructure capable of single-command deployment and / or orchestration and automatic scaling using a container orchestration system on accelerated infrastructure (e.g., from a single device to data center scale). Thus, the inference microservice may include the machine learning model(s) (optimized, for example, for high-performance inference), inference runtime software for executing the machine learning model(s) and providing outputs / responses to inputs (e.g., user queries, prompts, etc.), and enterprise management software for providing integrity checks, identity verification, and / or other monitoring.In some embodiments, the inference microservice may include software for performing on-site exchange and / or updates of the machine learning model(s). During exchange or update, the software performing the exchange / update may maintain user configurations of the inference runtime software and the enterprise management software. Approaches according to various illustrative embodiments can provide efficient approximations for various functions, such as exponential and / or logarithmic functions, which can be useful for operations performed in layers of a neural network. In at least one embodiment, a SoftMax function can be used to perform tasks such as converting raw output values ​​from a network into probabilities using the exponential of each output value. The output may be received as semi-precision numbers or floating-point numbers, which cannot be converted to higher precision, partly due to register boundaries or other such factors. Approaches according to at least one embodiment can manipulate the bits of a number so that integer exponentiation is achieved through IEEE floating-point representation with linear interpolation by shifting bits into the mantissa.In one example, an output value can be received in floating-point format, and a fixed-point representation of this value can be generated, incorporating a bias factor. An intermediate representation of this value can be created, containing a specific number of bits, and a value of 1 can be added to increment this intermediate representation so that the mantissa represents the fixed-point representation. The decimal point of this value can then be shifted by the appropriate number of bits to obtain a value that is an exponential approximation of the original output value. Any sign bit that may have remained from the shift can then be cleared. This exponential value can then be used to determine the probability (or any other such value) for a particular arithmetic operation using floating-point precision values.At least some of these operations can be reversed to obtain a similar approximation for a logarithmic function, also using floating-point precision values. Variations of this and other such functionality may also be used within the scope of the various embodiments, as would be obvious to an average person skilled in the art in view of the teachings and suggestions contained herein. Fig. 1 illustrates an exemplary system 100 that can be used to train one or more machine learning models and to perform inference according to at least one embodiment. In this example, a machine learning model can be a classification model trained to infer one or more classifications with associated probabilities for different instances of input data. An untrained classifier model 104, such as a convolutional neural network (CNN) or another such model, can be provided for training using a model training system 106.The model training system 106 can use a set of labeled and / or unlabeled classification data 102 (partially depending on the type of training performed) to train the untrained classifier model 104 to produce a trained classifier 114 capable of inferring classifications for unidentified objects, at least within the scope of classifications represented in the classification data 102. One or more instances of the trained classifier 114 can then be used to perform inference operations, such as by being hosted on a server 108 or other computing resource in a data center or other computing environment.In an exemplary use case, a user can use a client device 118, such as a desktop or notebook computer, to submit a user query to a server 108 to perform a classification by the trained classifier 114. The query can include data with one or more objects to be classified, such as words in a text query or objects represented in an image query, among other options. The trained classifier 114 can process the query and output one or more classifications, each with a corresponding probability value representing a calculated certainty that the classification is correct.In this example, the trained classifier 114 includes a SoftMax activation layer as a final layer that can accept raw values ​​generated by the intermediate layers of the trained classifier and convert these values ​​into probabilities. The trained classifier 114 can then output the inferred classifications 120 with probability values, which can be returned to the client device 118 in response to the user query, stored in the classification data repository 102 for use in further training of classifier models, and / or directed to another suitable recipient. As mentioned above, however, operations such as those performed in a SoftMax activation layer can be computationally intensive. A Server 108 may have certain processing hardware, such as at least one central processing unit (CPU) 110 and one or more graphics processing units (GPUs) 112, as well as data processing units (DPUs) or other such options. In an example where inference operations are to be performed using one or more GPUs, there may be limitations on the capacity of the individual GPUs or on certain types of operations that are more expensive to perform on those GPUs. For example, generating probabilities in a SoftMax layer requires evaluating exponential functions, which can be computationally intensive. Various approximations of an exponential (or logarithmic, etc.) function can be computationally intensive.Functions can be executed, but often require converting floating-point values ​​to integer values, which is computationally intensive and can be relatively slow, undesirably increasing inference latency. Attempting to avoid using exponential functions would require retraining or training a different model to implement this alternative approach. Even using semi-precision values ​​instead of full-precision ones can make certain operations prohibitively expensive, at least for some hardware. Approaches according to various embodiments can perform approximations for exponential, logarithmic, and other such functions in floating-point format. The values ​​can be received with semi-precision and can remain with semi-precision during computations without requiring conversion to individual precision or integer values, etc. Such use can be advantageous for any application or operation where, for example, exponential or logarithmic functions need to be performed efficiently, such as for a variety of inference and training operations performed using machine learning models. Fig. 2A illustrates an example of a classification module architecture 200 that can be used according to at least one embodiment. In this example, the model includes several layers of nodes, including an input layer 202, several intermediate layers 204, and an output layer 206 (which can also be called an end layer or SoftMax layer, the end layer being used with a SoftMax activation function). In such a model, the nodes of adjacent layers are typically fully connected. It is understood that an actual model will have many more intermediate layers with many more nodes per layer, each node representing a computation to be performed.In one example, a SoftMax output layer might receive 64 raw values ​​from nodes of a final intermediate layer 204 and would need to exponentiate and sum each of these 64 values ​​as part of a SoftMax activation operation to generate one or more corresponding probability values. Fig. 2B illustrates an exemplary plot 250 for an approximation of a SoftMax activation function according to at least one embodiment. The SoftMax function is a type of normalized exponential function that can be used to convert a set (or vector, etc.) or real numbers into a probability distribution over a number of potential outcomes. In a classifier network, the SoftMax function is used to normalize the network's output to a probability distribution over a number of predicted output classifications. Figure 3A illustrates an example of a SoftMax function 308, including a view of the values ​​of node 302 (including a bias node 304) of an example neural network, which can be used when performing a computation with the function. As mentioned, the SoftMax function 308 is frequently used in the final layer of a neural network, such as a network trained to generate classification inferences. A SoftMax function 308 can be used to convert values ​​produced by such a network into a set of probabilities. As illustrated in Figure 3B, the final value for x can be determined using the individual values ​​352 of x from the final network layer, where the individual x values ​​352 are a function of the z values ​​356 from the previous layer of nodes multiplied by the respective network weights 354 for the corresponding nodes.The conversion of raw values ​​into probabilities can be partially accomplished by taking the exponential of each output value and normalizing these values. Normalization can be achieved, for example, by dividing these individual exponential values ​​by the sum of all exponential values, as illustrated in the exemplary mathematical expression 308 in Fig. 3A. Such normalization can help ensure that the output values ​​are, for example, in a range from 0 to 1, and also sum to a total value of 1, so that the output values ​​effectively correspond to probabilities. In the exemplary mathematical expression 308 for the SoftMax function, xi represents the input to the SoftMax function for a given class i. As mentioned, the denominator of this mathematical expression 308 represents the sum of the exponentials of all class values ​​in the output layer 306 of the network. In one example, a network could be tasked with classifying a set of images. The network's final layer could output a vector containing a set of values ​​corresponding to the respective classifications. A softmax function can be used to convert these values ​​into a probability distribution for each class. A softmax function can take as input a vector (or a column matrix, etc.) x of real numbers representing the outputs from the neural network's final layer 306. Each element in the vector x can be exponentiated to ensure that all values ​​are positive. The exponentiation is illustrated in the numerator of mathematical expression 308, shown in Fig. 3A.The exponential values ​​can then be divided by the sum of all exponential values, which guarantees that the generated probability distribution sums to a value of 1.0, as discussed. While other functions can be used, a softmax function can provide several advantages for at least some operations or use cases. One such advantage is the normalization of probability values, ensuring that all output values ​​are between 0 and 1. As mentioned earlier, the sum of all outputs from the softmax function will always equal 1. A softmax function can also convert raw outputs into probabilities, potentially making the predictions of a classification (or other similar) network easier to understand and analyze. As mentioned, such an approach can experience performance issues when run on certain hardware. For example, evaluating a softmax function on values ​​of an activation layer can lead to performance problems, at least in part due to the computationally intensive nature of evaluating exponential values. As mentioned, for a value x, the exponential function is evaluated, which has a number as the exponent with a base e (i.e., Euler's number 2.718). Approaches according to various embodiments can provide an efficient approximation for an exponential function, which can reduce the computational effort required to evaluate a function such as a softmax function. In at least one embodiment, an approximation for floating-point numbers in an exponential and / or logarithmic function can be provided. This can involve manipulating the bits of a number to obtain integer exponentiation. This can be done using the IEEE linear interpolation representation of a floating-point number by transferring bits to the mantissa, or the portion of the floating-point number representing the significant digits, and multiplying this by the base, which is raised to the exponent to obtain the actual value of the number. In this example, a value x is provided that is semi-precise and is to be exponentiated in a given computation. A first step in an approximation process can be adding an exponentiation bias. A bias constant can also be subtracted from this value to improve the accuracy of the approximation.The chosen constant can be one that is determined to minimize a maximum relative error, as can be given by:. In this exemplary approach, the integer f is chosen to ensure the value is in a fixed-point format. The length of the fixed-point number may depend partly on the number of bits that can be granted for a given implementation. For semi-precision, and to try to obtain the maximum range of possible results, this might be a value of f = 5. Log 2 is used in the denominator to convert the value to a natural base. Shifting by five bits in this example results in five bits of integer values, followed by a decimal point, followed by five fractional bits, which is appropriate since, for a semi-precision representation, the exponent is defined as comprising five bits, with the total mantissa comprising ten bits. At this stage, the intermediate representation y is not yet exponential but is a fixed-point number with a value of zero to the left of the decimal point and all the bits to the right of the decimal point. A next step in this exemplary process is adding a value of 1 to y. After adding this value, the mantissa of the number will then contain a fixed-point representation of the numerator part of y with an exponent of one. A shift in bits can then be performed, such as shifting by the number of bits in the exponent (e.g., 5 for half-precision). The sign bit, as it may be left over from the shift, can then be cleared. The result for half-precision in this exemplary embodiment can then be obtained by: and outputting -ashalf(asint16(y) << 5. The relative error will then be approximately in the range of [-0.04,0.04] for all x for which the exponent result can be stored in half-precision, as illustrated in Fig. 4A on the carrier [-2,2].The logarithmic implementation can perform these operations in reverse, using an "OR" mask with a floating-point value of 1 instead of a bitmask. Such an approximation can have a relative error of up to about 4% of the true value of the exponential in semi-precision. It can be noted that in semi-precision, the achievable precision that can be guaranteed with more accurate approximations is about 2%. Such an approach can exploit a floating-point representation, such as the IEEE floating-point representation, in addition to bit manipulation. This avoids the need to convert to and from integer values, as well as the need to perform integer operations in 16 bits as in previous approaches, which can significantly reduce the computational and resource costs of these operations. Performing these operations at a semi-precision level can also help to significantly reduce the computation time per operation. Furthermore, performing these operations using floating-point values, along with some minor bit operations, allows these operations to be performed in a wide variety of formats. In at least some embodiments, the semi-precision or floating-point numbers received as input cannot be converted to higher-precision values, partly due to memory or memory register limitations.Evaluation of exponential values ​​(and sums of exponential values) can be performed using arbitrary inputs in semi-precision or using floating-point values. Fig. 4B illustrates the IEEE 754 semi-precision floating-point format 450, which can be used according to at least one embodiment. This format 450 involves a 16-bit word, which is subdivided into a 1-bit sign indicator s 452, a 5-bit biased exponent e 454, and a 10-bit fraction f 456. The IEEE representation of a floating-point number, as discussed previously, includes both an exponent and a mantissa, as may be given by: The first part corresponds to the mantissa, which defines the non-zero part of the number. The second part corresponds to the exponent, which defines the number of positions the decimal point must move. The exponent is positive when the decimal point is moved to the right and negative when the decimal point is moved to the left. Because half-type numbers are stored using 16 bits in this approach, they typically require less memory than single-type numbers (which use 32 bits) or double-type numbers (which use 64 bits). However, because these numbers are stored with fewer bits, half-type numbers are represented with less precision than single-type or double-type numbers. When an algorithm contains large or unknown dynamic ranges, such as for integrators in feedback loops, or when an algorithm uses operations that are difficult to design in fixed-point representation, it can be advantageous to use floating-point representations. The semi-precision data type, as mentioned, occupies only 16 bits of memory, but its floating-point representation allows it to handle wider dynamic ranges than integer or fixed-point data types of the same size. This makes semi-precision particularly suitable for some image processing and graphics applications. For example, when used with deep neural networks, semi-precision can significantly reduce the time required for training and inference. By using semi-precision as a memory location for lookup tables, the lookup table's memory footprint can be further reduced.Approximations can avoid conversion to integers and convert directly to a floating-point, semi-precision format, followed by bit manipulations that can be performed very quickly, providing much faster and lightweight computations. In another example, x can represent a semi-precise input value that needs to be exponentiated. If there is a value of 100, this could be given by e100, but this cannot be represented semi-precisely because it could overflow the register and represent an "illegal" number in at least some hardware. The value y in the equation above is a fixed-point representation of this value of x, with an applied bias. The value of y can be derived to obtain an intermediate representation that is not yet exponentiated. The intermediate representation of y is a fixed-point number with zero on the left and all significant bits to the right of the decimal point. A value of 1 is added to this intermediate representation, and the bits are then shifted to the left to obtain the exponent of that value.If x in this example is not an integer, it can be converted to a fixed-point value, which acts as a generalization of an integer. For a fixed-point value, the format would be zero followed by a decimal point and ten bits, whereas before division, it would be only ten bits of data. Such an approach avoids converting x to an integer representation when x comes as a floating-point number and needs to be converted to a fixed-point number. As mentioned, a manual conversion can be performed, but in at least some embodiments, the conversion will be limited in range, partly due to the limitations of the hardware used to perform the operation. Instead, an approximation can be used, generating a fixed-point representation of x with a bias factor, and this representation can be used to generate an intermediate representation in the specified number of bits.A value of 1 can then be added to this intermediate representation, so that the mantissa represents the fixed-point representation (where the value ranges from 0,bits to 1,bits). The format '1,bits' forces the mantissa to be exactly those bits as required. In at least some hardware, there is a match between floating-point and fixed-point values ​​only for a format such as 1,bits. Such an approach can be used with hardware that employs floating-point standardization, where the bits can be shifted as desired, since the values ​​are otherwise correctly positioned. Fig. 5A illustrates an exemplary process 500 that can be executed to generate inferred classifications for one or more objects or elements represented in input data, according to at least one embodiment. It should be understood that for this and other processes presented here, additional, fewer, or alternative steps may be performed in similar or alternative sequences, or at least partially in parallel, within the scope of the various embodiments, unless specifically stated otherwise. Although this example is discussed in terms of classification, other types of inference may also be performed, which may benefit from exponential, logarithmic, or other such approximations, likewise within the scope of various embodiments.This can be particularly true where it is advantageous to perform fast exponentiation, such as for computations useful in SoftMax activation determinations, among other such options. In this exemplary process, input data is provided to a neural classification network. The input data may include representations of one or more objects or elements for which classification is to be performed. Individual operations may be performed on the input data at various layers of the network, including a number of hidden or intermediate layers with nodes of network weights determined during a training process. A set of raw output values ​​may be received at a final output layer of nodes, such as a SoftMax activation layer of a classification network.Exponential approximations of these raw values ​​can be generated in this layer using semi-precision values ​​as received from the intermediate layers. The neural classification network can then generate as output probabilities for one or more classifications, as determined using the exponential approximations in semi-precision floating-point values. The one or more classifications and probabilities can be provided in response to the supplied input data or otherwise stored or transmitted to a target receiver or destination. Fig. 5B illustrates an exemplary process 550 that can be executed to generate an exponential approximation according to at least one embodiment. Although discussed in relation to its use in an activation layer of a classifier network, as described, for example, in relation to the process of Fig. 5A, such an approximation can be useful for any machine learning (or other) operation where efficient exponentiation or other such computation is to be performed on one or more input values. In this example, a value 552 is received (or otherwise obtained or generated) which is to be exponentiated in a floating-point format. A fixed-point representation of the value 554 can be generated, the fixed-point representation incorporating an exponentiation bias factor.Using this fixed-point representation, an intermediate representation of the value can be generated, where the intermediate representation has a target or a specific number of bits (e.g., 10 or 16 bits). The intermediate representation can be incremented (i.e., it can have a value of 1 added) so that one mantissa of the intermediate representation corresponds to the fixed-point representation. A decimal point of the incremented intermediate representation can be shifted (e.g., shifted to the rightmost five positions) to produce an exponential approximation of the received value. The exponential approximation can then be provided for use in a specific operation, such as determining and / or providing a probability for one or more inferences generated by a trained neural network. Such an approach can be used not only for linear approximations but also for higher-order approximations.Such an approach allows exponential, logarithmic, or other approximations using semi-precision floating-point values. For a value with 10 bits in the mantissa, proper placement of the decimal point can result in five bits to the left of the decimal point representing the exponent, and the five bits to the right of the decimal point representing the fractional bits, which can be used with the IEEE floating-point representation of a value. Such an approach allows linear interpolation between two exponent values. The addition of the value 1, as discussed, allows the mantissa to represent a fixed-point representation, after which the bits can be shifted as needed. There is a correspondence between the fixed-point and floating-point values ​​only where a value of 1 precedes the decimal point and the value bits follow the decimal point.The performance of such an operation can be relatively fast, as it involves a relatively lightweight fused multiply-add operation followed by a bit shift. The quality of the approximation is also relatively high, as the result falls within about 4% of the result for semi-precision without such an approximation. As mentioned, performing such an operation with steps in reverse order can also produce a logarithmic approximation. Aspects of various approaches presented herein may be lightweight enough to be performed in near real-time at different locations, such as on a client device or a cloud server. Such processing may be performed on or for content that is created or received on a client device or client server, or received from an external source, such as content received over at least one network from a cloud server 620 or third-party service 660, among other such options. In some cases, at least part of the processing, creation, compositing, and / or determination of such content may be performed by one of these other devices, systems, or entities, which are then made available to the client device 602 (or other such receiver) for presentation or other such use. As an example, Fig. 6 illustrates an exemplary network configuration 600 that can be used to provide, generate, modify, encode, process, and / or transmit various types of data or content. In at least one embodiment, a client device 602 can generate or receive data for a session using components of a content manager 604 and / or a content application 612 on the client device 602 and data stored locally on that client device. In at least one embodiment, a content application 624 running on a server 620 (e.g., a cloud server or edge server) can initiate a session associated with at least one client device 602, such as a session manager, and using user data stored in a user database 636, and can cause content, such as one or more digital assets (e.g.,Implicit and / or explicit object representations) from an asset repository 634 are determined by a content manager 626. A content manager 626 can work with at least one machine learning module 628 to generate inferences, which may be partially based on the assets in the asset repository 634. In other embodiments, the machine learning models 630 can be trained by a training module 628 using at least the assets in an asset repository 634, among other potential sources of training data. In at least one embodiment, one or more machine learning models 630 can be trained to perform an exponential or logarithmic approximation during inference.In at least one embodiment, the content application 624 can operate with one or more encoders, transcoders, and / or compressors that can perform tasks such as encoding, decoding, compressing, and / or decompressing a texture, image, or other such asset or instance of content, wherein different compressions or encodings may be advantageous for different operations, such as storage versus processing. At least a portion of the content can be transmitted to the client device 602 using a suitable transmission manager 622 for sending by downloading, streaming, or another such transmission channel. An encoder can be used to encode and / or compress at least some of this data before it is transmitted to the client device 602.In at least one embodiment, the client device 602, which receives such content, can provide this content to a corresponding content application 604, which may also or alternatively include a graphical user interface 610, a content application 612, and a machine learning module 614 for use in inferring, providing, synthesizing, rendering, assembling, modifying, or using content for presentation (or other purposes) on or by the client device 602. A decoder can also be used to decode data received over the network(s) 640 for presentation via the client device 602, such as image or video content through a display 606 and audio, such as sounds and music, through at least one audio playback device 608, such as a loudspeaker or headphones.In at least one embodiment, at least part of this content may already be stored, rendered, or accessible on the client device 602, so that transmission over the network 640 is not necessary for at least this portion of the content, for example, if this content may have been previously downloaded or stored locally on a hard disk or optical disk. In at least one embodiment, a transmission mechanism such as data streaming may be used to transfer this content from server 620 or user database 636 to client device 602. In at least one embodiment, at least part of this content may be obtained, enhanced, and / or streamed from another source, such as a third-party service 660 or another client device 650, which may also include a content application 662 for generating, enhancing, or providing content.In at least one embodiment, parts of this functionality can be performed using multiple computing devices or multiple processors within one or more computing devices, such as a combination of CPUs and GPUs. In this example, these client devices can include any suitable computing devices, such as a desktop computer, notebook computer, set-top box, streaming device, game console, smartphone, tablet computer, VR headset, AR glasses, portable computer, or smart TV. Each client device can submit a request over at least one wired or wireless network, such as the internet, Ethernet, a local area network (LAN), or a cellular network, among other such options. In this example, these requests can be sent to an address associated with a cloud provider, which may operate or control one or more electronic resources in a cloud provider environment, such as a data center or server farm.In at least one embodiment, the request can be received or processed by at least one edge server located at a network edge and outside at least one security layer associated with the cloud provider environment. This reduces latency by allowing client devices to interact with servers located closer to the network, while also improving the security of resources within the cloud provider environment. In at least one embodiment, such a system can be used to perform graphical rendering operations. In other embodiments, such a system can be used for other purposes, such as providing image or video content for testing or validating autonomous machine applications or for performing deep learning operations. In at least one embodiment, such a system can be implemented using an edge device or can include one or more virtual machines (VMs). In at least one embodiment, such a system can be implemented at least partially in a data center or at least partially using cloud computing resources. INFERENCE AND TRAINING LOGIC Fig. 7A illustrates inference and / or training logic 715, which is used to perform inference and / or training operations associated with one or more embodiments. Details regarding inference and / or training logic 715 are provided below in conjunction with Fig. 7A and / or 7B. In at least one embodiment, inference and / or training logic 715 can, without limitation, include code and / or data storage 701 for storing forward and / or output weights and / or input / output data and / or other parameters for configuring neurons or layers of a neural network that are trained and / or used for inference in aspects of one or more embodiments. In at least one embodiment, training logic 715 can include or be coupled to code and / or data storage 701 to store graph code or other software for controlling timing and / or sequencing, into which weight and / or other parameter information is to be loaded to configure logic, including integer and / or floating-point units (collectively, arithmetic logic units (ALUs)).In at least one embodiment, code, such as graph code, loads weight or other parameter information into processor ALUs based on a neural network architecture to which the code corresponds. In at least one embodiment, code and / or data memory 701 stores weight parameters and / or input / output data of each layer of a neural network, which, in conjunction with one or more embodiments, is trained or used during forward propagation of input / output data and / or weight parameters during training and / or inference using aspects of one or more embodiments. In at least one embodiment, any portion of code and / or data memory 701 may be included in another on-chip or off-chip data memory, including L1, L2, or L3 cache or system memory of a processor. In at least one embodiment, any portion of the code and / or data memory 701 can be internal or external to one or more processors or other hardware logic devices or circuits. In at least one embodiment, the code and / or data memory 701 can be cache memory, dynamic direct addressable memory (“DRAM”), static direct addressable memory (“SRAM”), non-volatile memory (e.g., flash memory), or other memory. In at least one embodiment, the choice of whether the code and / or data memory 701 is, for example, internal or external to a processor, or whether it consists of DRAM, SRAM, flash, or another type of memory, can depend on available on-chip memory versus off-chip memory, the latency requirements of training and / or inference functions being executed, the batch size of data used in inference and / or training of a neural network, or a combination of these factors.In at least one embodiment, inference and / or training logic 715 can, without limitation, include a code and / or data store 705 for storing backward and / or output weights and / or input / output data corresponding to neurons or layers of a neural network that are trained and / or used for inference in aspects of one or more embodiments. In at least one embodiment, code and / or data store 705 stores weight parameters and / or input / output data of each layer of a neural network that are trained or used in conjunction with one or more embodiments during backward propagation of input / output data and / or weight parameters during training and / or inference using aspects of one or more embodiments.In at least one embodiment, training logic 715 can include or be coupled to code and / or data memory 705 to store graph code or other software for controlling timing and / or sequencing, into which weight and / or other parameter information is to be loaded to configure logic, including integer and / or floating-point units (collectively, arithmetic logic units (ALUs)). In at least one embodiment, code, such as graph code, loads weight or other parameter information into processor ALUs based on a neural network architecture to which the code corresponds. In at least one embodiment, any portion of code and / or data memory 705 can be included in another on-chip or off-chip data memory, including L1, L2, or L3 cache or system memory of a processor.In at least one embodiment, any proportion of the code and / or data memory 705 can be internal or external to one or more processors or other hardware logic devices or circuits. In at least one embodiment, the code and / or data memory 705 can be cache memory, DRAM, SRAM, non-volatile memory (e.g., flash memory), or other memory. In at least one embodiment, the choice of whether the code and / or data memory 705 is, for example, internal or external to a processor, or whether it consists of DRAM, SRAM, flash, or another type of memory, can depend on available on-chip memory versus off-chip memory, the latency requirements of training and / or inference functions being executed, the batch size of data used in inference and / or training of a neural network, or a combination of these factors. In at least one embodiment, code and / or data memory 701 and code and / or data memory 705 can be separate memory structures. In at least one embodiment, code and / or data memory 701 and code and / or data memory 705 can be the same memory structure. In at least one embodiment, code and / or data memory 701 and code and / or data memory 705 can be partially the same memory structure and partially separate memory structures. In at least one embodiment, any portion of code and / or data memory 701 and code and / or data memory 705 can be included in another on-chip or off-chip data memory, including L1, L2, or L3 cache or system memory of a processor. In at least one embodiment, inference and / or training logic 715 can, without limitation, include one or more arithmetic logic unit(s) (“ALU(s)”) 710, including integer and / or floating-point units, to perform logical and / or mathematical operations that are at least partially based on or specified by training and / or inference code (e.g., graph code), wherein a result thereof can produce activations (e.g., output values ​​of layers or neurons within a neural network) that are stored in an activation memory 720, which are functions of input / output and / or weight parameter data that are stored in code and / or data memory 701 and / or code and / or data memory 705.In at least one embodiment, activations stored in activation memory 720 are generated according to linear algebraic and / or matrix-based mathematics, which is executed by ALU(s) 710 in response to the execution of instructions or other code, wherein weight values ​​stored in code and / or data memory 705 and / or code and / or data memory 701 are used as operands together with other values, such as bias values, gradient information, pulse values ​​or other parameters or hyperparameters, any or all of which may be stored in code and / or data memory 705 or code and / or data memory 701 or other memory on or off the chip. In at least one embodiment, ALU(s) 710 are included within one or more processors or other hardware logic devices or circuits, whereas in another embodiment, ALU(s) 710 may be external to a processor or other hardware logic device or circuit that uses them (e.g., a coprocessor). In at least one embodiment, ALU(s) 710 may be included within execution units of a processor or otherwise within a bank of ALUs accessible by execution units of a processor, either within the same processor or distributed among different processors of different types (e.g., central processing units, graphics processing units, fixed functional units, etc.).In at least one embodiment, code and / or data memory 701, code and / or data memory 705, and activation memory 720 can be located on the same processor or other hardware logic device or circuit, whereas in another embodiment, they can be located on different processors or other hardware logic devices or circuits, or a combination of the same and different processors or other hardware logic devices or circuits. In at least one embodiment, any portion of activation memory 720 can be included in other on-chip or off-chip data memory, including L1, L2, or L3 cache or system memory of a processor.Furthermore, inference and / or training code can be stored with other code that a processor or other hardware logic or circuitry can access and that is retrieved and / or processed using a processor's retrieval, decoding, scheduling, execution, shutdown, and / or other logic circuitry. In at least one embodiment, activation memory 720 can be cache memory, DRAM, SRAM, non-volatile memory (e.g., flash memory), or other memory. In at least one embodiment, activation memory 720 can be located wholly or partially inside or external to one or more processors or other logic circuits. In at least one embodiment, the choice of whether activation memory 720 is, for example, internal or external to a processor, or whether it consists of DRAM, SRAM, flash, or another type of memory, can depend on available on-chip memory versus off-chip memory, latency requirements of training and / or inference functions being executed, batch size of data used in inference and / or training of a neural network, or a combination of these factors. In at least one embodiment, the inference and / or training logic 715 shown in Fig.Figure 7A illustrates the inference and / or training logic 715 being used in conjunction with an application-specific integrated circuit (“ASIC”), such as Google’s Tensorflow® Processing Unit, a Graphcore™ Inference Processing Unit (IPU), or an Intel Corp. Nervana® Processor (e.g., “Lake Crest”). In at least one embodiment, the inference and / or training logic 715 illustrated in Figure 7A can be used in conjunction with central processing unit (“CPU”) hardware, graphics processing unit (“GPU”) hardware, or other hardware, such as field-programmable gate arrays (“FPGAs”). Fig. 7B illustrates inference and / or training logic 715 according to at least one or more embodiments. In at least one embodiment, inference and / or training logic 715 can, without limitation, include hardware logic in which computing resources are dedicated or otherwise used exclusively in connection with weight values ​​or other information corresponding to one or more layers of neurons within a neural network. In at least one embodiment, inference and / or training logic 715 illustrated in Fig. 7B can be used in conjunction with an application-specific integrated circuit (ASIC), such as Google's TensorFlow® Processing Unit, a Graphcore™ Inference Processing Unit (IPU), or an Intel Corp. Nervana® Processor (e.g., "Lake Crest"). In at least one embodiment, inference and / or training logic 715, illustrated in Fig.Figure 7B illustrates the inference and / or training logic 715, which can be used in conjunction with central processing unit (CPU) hardware, graphics processing unit (GPU) hardware, or other hardware, such as field-programmable gate arrays (FPGAs). In at least one embodiment, the inference and / or training logic 715 includes, without limitation, code and / or data memory 701 and code and / or data memory 705, which can be used to store code (e.g., graph code), weight values, and / or other information, including bias values, gradient information, pulse values, and / or other parameter or hyperparameter information. In at least one embodiment, illustrated in Figure 7B, each code and / or data memory 701 and code and / or data memory 705 is associated with a dedicated computational resource, such as computational hardware 702 and computational hardware 706, respectively.In at least one embodiment, each of the computing hardware 702 and computing hardware 706 has one or more ALUs that execute mathematical functions, such as linear algebraic functions, only on information stored in code and / or data memory 701 or code and / or data memory 705, respectively, the result of which is stored in activation memory 720. In at least one embodiment, each of the code and / or data storage units 701 and 705, or corresponding computing hardware 702 and 706, corresponds to different layers of a neural network, such that the resulting activation from a "memory / computing pair 701 / 702" of code and / or data storage unit 701 and computing hardware 702 is provided as an input for a "memory / computing pair 705 / 706" of code and / or data storage unit 705 and computing hardware 706, to reflect the conceptual organization of a neural network. In at least one embodiment, each of the memory / computing pairs 701 / 702 and 705 / 706 can correspond to more than one neural network layer. In at least one embodiment, additional memory / computing pairs (not shown) may be included after or in parallel to memory / computing pairs 701 / 702 and 705 / 706 in inference and / or training logic 715. DATA CENTER Fig. 8 illustrates an exemplary data center 800 in which at least one embodiment can be used. In at least one embodiment, data center 800 includes a data center infrastructure layer 810, a framework layer 820, a software layer 830, and an application layer 840. In at least one embodiment, as shown in Fig. 8, data center infrastructure layer 810 can include a resource orchestrator 812, clustered compute resources 814, and node compute resources (“Node CRs”) 816(1)-816(N), where “N” is any positive integer. In at least one embodiment, the Node CRs 816(1)-816(N) can include, but are not limited to, any number of central processing units (“CPUs”) or other processors (including accelerators, field-programmable gate arrays (FPGAs), graphics processing units, etc.), short-term memory devices (e.g., dynamic read-only memory), storage devices (e.g., solid-state or disk drives), network input / output devices (“NW I / O”), network switches, virtual machines (“VMs”), power modules, and cooling modules, etc. In at least one embodiment, one or more nodes CRs can be made up of the nodes CRs 816(1)-816(N) be a server, with one or more of the above-mentioned computing resources. In at least one embodiment, clustered compute resources 814 can include separate groupings of node CRs located in one or more racks (not shown), or many racks located in data centers at different geographic locations (also not shown). Separate groupings of node CRs within clustered compute resources 814 can include clustered compute, network, memory, or storage resources that can be configured or allocated to support one or more workloads. In at least one embodiment, multiple node CRs, including CPUs or processors, can be grouped in one or more racks to provide compute resources to support one or more workloads.In at least one embodiment, one or more racks can also include any number of power modules, cooling modules and network switches in any combination. In at least one embodiment, Resource Orchestrator 812 can configure or otherwise control one or more nodes CRs 816(1)-816(N) and / or grouped compute resources 814. In at least one embodiment, Resource Orchestrator 812 can include a software design infrastructure (“SDI”) management entity for data center 800. In at least one embodiment, Resource Orchestrator 812 can include hardware, software, or a combination thereof. In at least one embodiment, as shown in Fig. 8, framework layer 820 includes a job scheduler 822, a configuration manager 824, a resource manager 826, and a distributed file system 828. In at least one embodiment, framework layer 820 can include a framework to support software 832 of software layer 830 and / or one or more application(s) 842 of application layer 840. In at least one embodiment, software 832 or application(s) 842 can each include web-based service software or applications, such as those provided by Amazon Web Services, Google Cloud, and Microsoft Azure. In at least one embodiment, framework layer 820 can be a type of free and open-source software web application framework, such as Apache Spark™ (hereinafter “Spark”), which can use, but is not limited to, the distributed file system 828 for large-scale data processing (e.g., “Big Data”).In at least one embodiment, the job scheduler 822 can include a Spark driver to facilitate the scheduling of workloads supported by different layers of the data center 800. In at least one embodiment, the configuration manager 824 can be able to configure different layers, such as the software layer 830 and the framework layer 820, including Spark and the distributed file system 828, to support large-scale data processing. In at least one embodiment, the resource manager 826 can be able to manage clustered or grouped compute resources that are mapped to or allocated to support the distributed file system 828 and the job scheduler 822. In at least one embodiment, clustered or grouped compute resources can include grouped compute resources 814 on the data center infrastructure layer 810.In at least one embodiment, Resource Manager 826 can coordinate with Resource Orchestrator 812 to manage these mapped or allocated computing resources. In at least one embodiment, software 832, which is included in software layer 830, may include software used by at least portions of node CRs 816(1)-816(N), grouped computing resources 814, and / or distributed file system 828 of frame layer 820. The one or more types of software may include, but are not limited to, internet web page search software, email virus scanning software, database software, and streaming video content software. In at least one embodiment, application(s) 842, which is / are included in application layer 840, may include one or more types of applications used by at least proportions of node CRs 816(1)-816(N), grouped compute resources 814, and / or distributed file system 828 of framework layer 820. One or more types of applications may include any number of a genomics application, a cognitive computation, and a machine learning application, including, but not limited to, training or inference software, machine learning framework software (e.g., PyTorch, TensorFlow, Caffe, etc.), or other machine learning applications used in conjunction with one or more embodiments. In at least one embodiment, any configuration manager 824, resource manager 826, and resource orchestrator 812 can implement any number and type of self-modifying actions based on any set and type of data acquired in any technically feasible way. In at least one embodiment, self-modifying actions can relieve a data center operator of data center 800 of potentially making poor configuration decisions and potentially avoiding underutilized and / or poor-performing portions of a data center. In at least one embodiment, Data Center 800 may include tools, services, software, or other resources for training one or more machine learning models or for predicting or inferring information using one or more machine learning models according to one or more embodiments described herein. For example, in at least one embodiment, a machine learning model may be trained by calculating weight parameters according to a neural network architecture using software and computing resources described above in relation to Data Center 800.In at least one embodiment, trained machine learning models corresponding to one or more neural networks can be used to infer or predict information using resources described above in relation to Data Center 800, by using weight parameters computed by one or more training techniques described herein. In at least one embodiment, the data center can use CPUs, application-specific integrated circuits (ASICs), GPUs, FPGAs, or other hardware to perform training and / or inference using the resources described above. Furthermore, one or more of the software and / or hardware resources described above can be configured as a service to allow users to train or perform information inference, such as image recognition, speech recognition, or other artificial intelligence services. Inference and / or training logic 715 is used to perform inference and / or training operations associated with one or more embodiments. Details regarding inference and / or training logic 715 are provided below in conjunction with Figures 7A and / or 7B. In at least one embodiment, inference and / or training logic 715 can be used in system Figure 8 to infer or predict operations that are based at least partially on weight parameters computed using neural network training operations, neural network functions and / or architectures, or neural network use cases described herein. Such components can be used to efficiently perform exponential or logarithmic approximation in semi-precision, floating-point format. COMPUTER SYSTEMS Fig. 9 is a block diagram illustrating an exemplary computer system, which may be a system with interconnected devices and components, a system-on-a-chip (SOC), or a combination thereof, 900, formed with a processor that may include execution units for carrying out an instruction, according to at least one embodiment. In at least one embodiment, the computer system 900 may, without limitation, include a component, such as a processor 902, for inserting execution units that include logic for executing algorithms for processing data, according to the present disclosure, such as in the embodiment described herein.In at least one embodiment, Computer System 900 may include processors such as the PENTIUM® Processor family, Xeon™, Itanium®, XScale™ and / or StrongARM™, Intel® Core™ or Intel® Nervana™ microprocessors available from Intel Corporation of Santa Clara, California, although other systems (including PCs with other microprocessors, engineering workstations, set-top boxes, and the like) may also be used. In at least one embodiment, Computer System 900 may run a version of the WINDOWS operating system available from Microsoft Corporation of Redmond, Washington, although other operating systems (for example, UNIX and Linux), embedded software, and / or graphical user interfaces may also be used. Embodiments can be used in other devices, such as handheld devices and embedded applications. Some examples of handheld devices include mobile phones, Internet Protocol devices, digital cameras, personal digital assistants (PDAs), and handheld PCs. In at least one embodiment, embedded applications can include a microcontroller, a digital signal processor (DSP), a system-on-a-chip, network computers (NetPCs), set-top boxes, network hubs, wide area network (WAN) switches, or any other system capable of executing one or more instructions according to at least one embodiment. In at least one embodiment, computer system 900 can, without limitation, include processor 902, which can, without limitation, include one or more execution units 908 for performing machine learning model training and / or inference according to the techniques described herein. In at least one embodiment, computer system 900 is a single-processor desktop or server system, but in another embodiment, computer system 900 can be a multiprocessor system. In at least one embodiment, processor 902 can, without limitation, include a microprocessor for computing complex instruction sets (“CISC”), a microprocessor for computing reduced instruction sets (“RISC”), a microprocessor for computing very long instruction words (“VLIW”), a processor implementing a combination of instruction sets, or any other processing device, such as, for example, a digital signal processor.In at least one embodiment, processor 902 can be coupled to a processor bus 910, which can transmit data signals between processor 902 and other components in computer system 900. In at least one embodiment, processor 902 can, without limitation, include an internal Level 1 cache (“L1”) 904. In at least one embodiment, processor 902 can have a single internal cache or multiple levels of internal cache. In at least one embodiment, cache memory can reside outside of processor 902. Other embodiments can also include a combination of both internal and external caches, depending on the specific implementation and requirements. In at least one embodiment, register file 906 can store different types of data in different registers, including, without limitation, integer registers, floating-point registers, status registers, and instruction pointer registers. In at least one embodiment, the execution unit 908, including, without limitation, logic for performing integer and floating-point operations, is also located in the processor 902. In at least one embodiment, the processor 902 may also include a microcode ("ucode") read memory ("ROM") that stores microcode for specific macro instructions. In at least one embodiment, the execution unit 908 may include logic for handling a packed instruction set 909. In at least one embodiment, by including a packed instruction set 909 in an instruction set of a general-purpose processor 902, together with associated switching technology for executing instructions, operations used by many multimedia applications can be performed using packed data in a general-purpose processor 902.In one or more embodiments, many multimedia applications can be accelerated and performed more efficiently by using the full width of a processor's data bus to perform operations on packed data, which can eliminate the need to transfer smaller units of data over the processor's data bus to perform one or more operations on one data element at a time. In at least one embodiment, the implementation unit 908 can also be used in microcontrollers, embedded processors, graphics devices, DSPs, and other types of logic circuits. In at least one embodiment, the computer system 900 can, without limitation, include a memory 920. In at least one embodiment, the memory 920 can be implemented as a dynamic random access memory (“DRAM”) device, a static random access memory (“SRAM”) device, a flash memory device, or another storage device. In at least one embodiment, the memory 920 can store instruction(s) 919 and / or data 921, which are represented by data signals that can be executed by the processor 902. In at least one embodiment, the system logic chip can be coupled to the processor bus 910 and memory 920. In at least one embodiment, the system logic chip can, without limitation, include a memory controller hub (“MCH”) 916, and the processor 902 can communicate with the MCH 916 via the processor bus 910. In at least one embodiment, the MCH 916 can provide a high-bandwidth memory path 918 to memory 920 for instruction and data storage and for storing graphics instructions, data, and textures. In at least one embodiment, the MCH 916 can direct data signals between the processor 902, memory 920, and other components in the computer system 900 and bridge data signals between the processor bus 910, memory 920, and a system I / O 922. In at least one embodiment, the system logic chip can provide a graphics port for coupling to a graphics controller.In at least one embodiment, MCH 916 can be coupled to memory 920 via a high-bandwidth memory path 918, and graphics / video card 912 can be coupled to MCH 916 via an Accelerated Graphics Port (“AGP”) connection 914. In at least one embodiment, computer system 900 can use system I / O 922, which is a proprietary hub interface bus, to couple MCH 916 to I / O controller hub (“ICH”) 930. In at least one embodiment, ICH 930 can provide direct connections to some I / O devices via a local I / O bus. In at least one embodiment, the local I / O bus can, without limitation, include a high-speed I / O bus for connecting peripherals to memory 920, chipset, and processor 902. Examples may include, without limitation, an audio controller 929, a firmware hub (“flash BIOS”) 928, a wireless transceiver 926, a data storage device 924, a legacy I / O controller 923 which includes user input and keyboard interfaces 925, a serial expansion port 927 such as Universal Serial Bus (“USB”), and a network controller 934.Data storage device 924 can include a hard disk drive, a floppy disk drive, a CD-ROM device, a flash memory device, or another mass storage device. In at least one embodiment, Fig. 9 illustrates a system comprising interconnected hardware devices or “chips”, whereas in other embodiments, Fig. 9 may illustrate an exemplary system-on-a-chip (“SoC”). In at least one embodiment, devices may be connected using proprietary connections, standardized interconnects (e.g., PCIe), or a combination thereof. In at least one embodiment, one or more components of the Computer System 900 are interconnected using Compute Express Link (CXL) interconnects. Inference and / or training logic 715 is used to perform inference and / or training operations associated with one or more embodiments. Details regarding inference and / or training logic 715 are provided below in conjunction with Figures 7A and / or 7B. In at least one embodiment, inference and / or training logic 715 can be used in system Figure 9 for inference or prediction operations that are based at least partially on weight parameters computed using neural network training operations, neural network functions and / or architectures, or neural network use cases described herein. Such components can be used to efficiently perform exponential or logarithmic approximation in semi-precision, floating-point format. Fig. 10 is a block diagram illustrating an electronic device 1000 for using a processor 1010 according to at least one embodiment. In at least one embodiment, the electronic device 1000 can be, for example, and without limitation, a notebook, a tower server, a rack server, a blade server, a laptop, a desktop computer, a tablet, a mobile device, a telephone, an embedded computer, or any other suitable electronic device. In at least one embodiment, the electronic device 1000 can, without limitation, include a processor 1010, which is communicatively coupled to any suitable number or type of components, peripherals, modules, or devices. In at least one embodiment, the processor 1010 is coupled using a bus or interface, such as a 1°C bus, a system management bus (“SMBus”), a low pin count (LPC) bus, a serial peripheral interface (“SPI”), a high definition audio (“HDA”) bus, a serial advance technology attachment (“SATA”) bus, a universal serial bus (“USB”) (versions 1, 2, 3), or a universal asynchronous receiver / transmitter (“UART”) bus. In at least one embodiment, Fig. 10 illustrates a system comprising interconnected hardware devices or “chips,” whereas Fig.Figure 10 illustrates an exemplary system-on-a-chip (“SoC”) in other embodiments. In at least one embodiment, devices illustrated in Figure 10 can be connected using proprietary interconnects, standardized interconnects (e.g., PCIe), or a combination thereof. In at least one embodiment, one or more components of Figure 10 are interconnected using Compute Express Link (CXL) interconnects. In at least one embodiment, Fig. 10 can show a display 1024, a touchscreen 1025, a touchpad 1030, a Near Field Communications (“NFC”) unit 1045, a sensor hub 1040, a thermal sensor 1046, an Express Chipset (“EC”) 1035, a Trusted Platform Module (“TPM”) 1038, BIOS / Firmware / Flash memory (“BIOS, FW Flash”) 1022, a DSP 1060, a drive 1020, such as a solid state disk (“SSD”) or a hard disk drive (“HDD”), a wireless local area network (“WLAN”) unit 1050, a Bluetooth unit 1052, a wireless wide area network (“WWAN”) unit 1056, a global positioning system (GPS) 1055, a camera (“USB 3.0 camera”) 1054, such as a USB 3.0 camera, and / or include a Low Power Double Data Rate (“LPDDR”) memory unit (“LPDDR3”) 1015, which is implemented, for example, in the LPDDR3 standard. These components can all be implemented in any suitable way. In at least one embodiment, other components can be communicatively coupled to processor 1010 via the components discussed above. In at least one embodiment, an accelerometer 1041, an ambient light sensor (“ALS”) 1042, a compass 1043, and a gyroscope 1044 can be communicatively coupled to sensor hub 1040. In at least one embodiment, a thermal sensor 1039, a fan 1037, a keyboard 1036, and a touchpad 1030 can be communicatively coupled to EC 1035. In at least one embodiment, loudspeakers 1063, headphones 1064, and a microphone (“mic”) 1065 can be communicatively coupled to an audio unit (“audio codec and class D amplifier”) 1062, which in turn can be communicatively coupled to DSP 1060. In at least one embodiment, audio unit 1062 may, for example and without limitation, include an audio encoder / decoder (“codec”) and a class D amplifier.In at least one embodiment, the SIM card (“SIM”) 1057 can be communicatively coupled to the WWAN unit 1056. In at least one embodiment, components such as the WLAN unit 1050 and the Bluetooth unit 1052, as well as the WWAN unit 1056, can be implemented in a Next Generation Form Factor (“NGFF”). Inference and / or training logic 715 is used to perform inference and / or training operations associated with one or more embodiments. Details regarding inference and / or training logic 715 are provided below in conjunction with Figures 7A and / or 7B. In at least one embodiment, inference and / or training logic 715 can be used in system Figure 10 for inference or prediction operations that are based at least partially on weight parameters computed using neural network training operations, neural network functions and / or architectures, or neural network use cases described herein. Such components can be used to efficiently perform exponential or logarithmic approximation in semi-precision, floating-point format. Figure 11 is a block diagram of a processing system according to at least one embodiment. In at least one embodiment, System 1100 includes one or more processor(s) 1102 and one or more graphics processor(s) 1108 and can be a single-processor desktop system, a multi-processor workstation system, or a server system with a large number of processor(s) 1102 or processor core(s) 1107. In at least one embodiment, System 1100 is a processing platform contained in an integrated system-on-a-chip (SoC) circuit for use in mobile, handheld, or embedded devices. In at least one embodiment, System 1100 can include or be included in a server-based gaming platform, a gaming console (including a gaming and media console), a mobile gaming console, a handheld gaming console, or an online gaming console. In at least one embodiment, System 1100 is a mobile phone, smartphone, tablet computer, or mobile internet device. In at least one embodiment, Processing System 1100 can also include, be coupled to, or be integrated with a wearable device, such as a wearable smartwatch device, smart glasses device, augmented reality device, or virtual reality device. In at least one embodiment, Processing System 1100 is a television or set-top box device with one or more processor(s) 1102 and a graphical interface generated by one or more graphics processor(s) 1108. In at least one embodiment, one or more processor(s) 1102 each include one or more processor core(s) 1107 for processing instructions that, when executed, perform operations for system and user software. In at least one embodiment, each of the one or more processor core(s) 1107 is configured to process a specific instruction set 1109. In at least one embodiment, the instruction set 1109 may facilitate Complex Instruction Set Computing (CISC), Reduced Instruction Set Computing (RISC), or computation via a Very Long Instruction Word (VLIW). In at least one embodiment, the processor core(s) 1107 may each process a different instruction set 1109, which may include instructions to facilitate the emulation of other instruction sets. In at least one embodiment, the processor core(s) 1107 may also include other processing devices, such as a Digital Signal Processor (DSP).In at least one embodiment, processor(s) 1102 include cache memory 1104. In at least one embodiment, processor(s) 1102 can have a single internal cache or multiple levels of internal cache. In at least one embodiment, cache memory is shared by different components of processor(s) 1102. In at least one embodiment, processor(s) 1102 also use an external cache (e.g., a Level 3 (L3) cache or Last Level Cache (LLC)) (not shown), which can be shared by processor core(s) 1107 using known cache coherence techniques. In at least one embodiment, register file 1106 is additionally included in processor(s) 1102, which can contain different types of registers for storing different types of data (e.g., integer registers, floating-point registers, status registers, and an instruction pointer register).In at least one embodiment, register file 1106 may contain general-purpose registers or other registers. In at least one embodiment, one or more processors 1102 are coupled to one or more interface buses 1110 to transmit communication signals, such as address, data, or control signals, between the processors 1102 and other components in the system 1100. In at least one embodiment, the interface bus(s) 1110 can be a processor bus, such as a version of a Direct Media Interface (DMI) bus. In at least one embodiment, the interface bus(s) 1110 are not limited to a DMI bus and can include one or more Peripheral Component Interconnect buses (e.g., PCI, PCI Express), memory buses, or other types of interface buses. In at least one embodiment, the processor(s) 1102 include an integrated memory controller 1116 and a platform controller hub 1130.In at least one embodiment, the storage controller 1116 facilitates communication between a storage device and other components of the system 1100, while the platform controller hub (PCH) 1130 provides connections to I / O devices via a local I / O bus. In at least one embodiment, the storage device 1120 can be a dynamic random access memory (DRAM) device, a static random access memory (SRAM) device, a flash memory device, a phase-change memory device, or another storage device with suitable performance to serve as process memory. In at least one embodiment, the storage device 1120 can operate as system memory for system 1100 to store data 1122 and instructions 1121 for use when one or more processor(s) 1102 execute an application or process. In at least one embodiment, the storage controller 1116 also couples with an optional external graphics processor 1112, which can communicate with one or more graphics processor(s) 1108 in processor(s) 1102 to perform graphics and media operations. In at least one embodiment, a display device 1111 can be connected to processor(s) 1102.In at least one embodiment, the display device 1111 can include one or more internal display devices, such as in a mobile electronic device or a laptop device, or an external display device attached via a display interface (e.g., DisplayPort, etc.). In at least one embodiment, the display device 1111 can include a head-mounted display (HMD), such as a stereoscopic display device, for use in virtual reality (VR) applications or augmented reality (AR) applications. In at least one embodiment, the platform controller hub 1130 enables peripherals to connect to the storage device 1120 and processor(s) 1102 via a high-speed I / O bus. In at least one embodiment, the I / O peripherals include, but are not limited to, an audio controller 1146, a network controller 1134, a firmware interface 1128, a wireless transceiver 1126, touch sensors 1125, and a data storage device 1124 (e.g., a hard disk drive, flash memory, etc.). In at least one embodiment, the data storage device 1124 can connect via a storage interface (e.g., SATA) or via a peripheral bus, such as a peripheral component interconnect bus (e.g., PCI, PCI Express). In at least one embodiment, the touch sensors 1125 can include touchscreen sensors, pressure sensors, or fingerprint sensors.In at least one embodiment, wireless transceiver 1126 can be a Wi-Fi transceiver, a Bluetooth transceiver, or a mobile network transceiver, such as a 3G, 4G, or Long Term Evolution (LTE) transceiver. In at least one embodiment, firmware interface 1128 enables communication with system firmware and can, for example, be a Unified Extensible Firmware Interface (UEFI). In at least one embodiment, network controller 1134 can enable a network connection to a wired network. In at least one embodiment, a high-performance network controller (not shown) couples with interface bus(s) 1110. In at least one embodiment, audio controller 1146 is a multi-channel, high-resolution audio controller. In at least one embodiment, system 1100 includes an optional legacy I / O controller 1140 for coupling legacy (e.g., Personal System 2 (PS / 2)) devices to system 1100.In at least one embodiment, platform controller hub 1130 can also be connected to one or more Universal Serial Bus (USB) controller(s) 1142, which connect input devices such as keyboard and mouse 1143 combinations, a camera 1144 or other USB input devices. In at least one embodiment, an instance of memory controller 1116 and platform controller hub 1130 can be integrated into a discrete external graphics processor, such as an external graphics processor 1112. In at least one embodiment, the platform controller hub 1130 and / or memory controller 1116 can be external to one or more processor(s) 1102. For example, in at least one embodiment, system 1100 can include an external memory controller 1116 and platform controller hub 1130, which can be configured as a memory controller hub and peripheral controller hub within a system chipset that communicates with processor(s) 1102. Inference and / or training logic 715 is used to perform inference and / or training operations associated with one or more embodiments. Details regarding inference and / or training logic 715 are provided below in conjunction with Figures 7A and / or 7B. In at least one embodiment, portions or all of the inference and / or training logic 715 may be contained in a graphics processor 1500. For example, in at least one embodiment, training and / or inference techniques described herein may utilize one or more ALUs embodied in a graphics processor. Furthermore, in at least one embodiment, inference and / or training operations described herein may be performed using logic other than that illustrated in Figures 7A and / or 7B.In at least one embodiment, weight parameters can be stored in on-chip or off-chip memory and / or registers (shown or not shown) that configure the ALUs of a graphics processor to execute one or more machine learning algorithms, neural network architectures, use cases or training techniques described herein. Such components can be used to efficiently perform exponential or logarithmic approximation in semi-precision, floating-point format. Fig. 12 is a block diagram of a processor 1200 comprising one or more processor core(s) 1202A-1202N, an integrated memory controller 1214, and an integrated graphics processor 1208 according to at least one embodiment. In at least one embodiment, the processor 1200 may include additional cores up to and including additional core 1202N, which are represented by boxes with dashed lines. In at least one embodiment, each of the processor core(s) 1202A-1202N includes one or more internal cache units 1204A-1204N. In at least one embodiment, each processor core also has access to one or more shared cache units 1206. In at least one embodiment, internal cache unit(s) 1204A-1204N and shared cache unit(s) 1206 constitute a cache memory hierarchy within processor 1200. In at least one embodiment, cache unit(s) 1204A-1204N can include at least one level of instruction and data cache within each processor core and one or more levels of shared cache at the middle level, such as a Level 2 (L2), Level 3 (L3), Level 4 (L4), or other levels of cache, wherein a highest level of cache prior to external memory is classified as an LLC. In at least one embodiment, cache coherence logic maintains coherence between different cache unit(s) 1206 and 1204A-1204N. In at least one embodiment, the processor 1200 can also include a set of one or more bus controller units 1216 and a system agent core 1210. In at least one embodiment, one or more bus controller units 1216 manage a set of peripheral buses, such as one or more PCI or PCI Express buses. In at least one embodiment, the system agent core 1210 provides management functionality for various processor components. In at least one embodiment, the system agent core 1210 includes one or more integrated memory controllers 1214 to manage access to various external storage devices (not shown). In at least one embodiment, one or more of the processor core(s) 1202A-1202N include support for simultaneous multi-threading. In at least one embodiment, the system agent core 1210 includes components for coordinating the processor core(s) 1202A-1202N during multi-threaded processing. In at least one embodiment, the system agent core 1210 may additionally include a power control unit (PCU) that includes logic and components for controlling one or more power states of the processor core(s) 1202A-1202N and the graphics processor 1208. In at least one embodiment, processor 1200 additionally includes graphics processor 1208 for performing graphics processing operations. In at least one embodiment, graphics processor 1208 is coupled with shared cache unit(s) 1206 and system agent core 1210, including one or more integrated memory controllers 1214. In at least one embodiment, system agent core 1210 also includes a display controller 1211 for driving graphics processor output to one or more coupled displays. In at least one embodiment, display controller 1211 can also be a separate module coupled to graphics processor 1208 via at least one interconnect, or it can be integrated into graphics processor 1208. In at least one embodiment, a ring-based interconnect unit 1212 is used to couple internal components of processor 1200. In at least one embodiment, an alternative interconnect unit can be used, such as a point-to-point interconnect, a switched interconnect, or other techniques. In at least one embodiment, graphics processor 1208 couples to a ring-based interconnect unit 1212 via an I / O link 1213. In at least one embodiment, I / O link 1213 represents at least one of several variants of I / O interconnects, including an on-package I / O interconnect that facilitates communication between different processor components and a high-performance embedded memory module 1218, such as an eDRAM module. In at least one embodiment, each of the processor core(s) 1202A-1202N and graphics processor 1208 uses embedded memory modules 1218 as a shared last-level cache. In at least one embodiment, processor core(s) 1202A-1202N are homogeneous cores implementing a common instruction set architecture. In at least one embodiment, processor core(s) 1202A-1202N are heterogeneous with respect to the instruction set architecture (ISA), wherein one or more of processor core(s) 1202A-1202N execute a common instruction set, while one or more other cores of processor core(s) 1202A-1202N execute a subset of a common instruction set or another instruction set. In at least one embodiment, processor core(s) 1202A-1202N are heterogeneous with respect to the microarchitecture, wherein one or more cores with a relatively higher power consumption are coupled with one or more power cores with a lower power consumption. In at least one embodiment, processor 1200 can be implemented on one or more chips or as an integrated SoC circuit. Inference and / or training logic 715 is used to perform inference and / or training operations associated with one or more embodiments. Details regarding inference and / or training logic 715 are provided below in conjunction with Figures 7A and / or 7B. In at least one embodiment, portions or all of the inference and / or training logic 715 may be contained in processor 1200. For example, in at least one embodiment, training and / or inference techniques described herein may utilize one or more ALUs embodied in graphics processor 1208, graphics core(s) 1202A-1202N, or other components shown in Figure 12. Furthermore, in at least one embodiment, inference and / or training operations described herein may be performed using logic other than that illustrated in Figures 7A and / or 7B.In at least one embodiment, weight parameters can be stored in on-chip or off-chip memory and / or registers (shown or not shown) that configure the ALUs of graphics processor 1200 to execute one or more machine learning algorithms, neural network architectures, use cases or training techniques described herein. Such components can be used to efficiently perform exponential or logarithmic approximation in semi-precision, floating-point format. VIRTUALIZED COMPUTING PLATFORM Figure 13 is an exemplary data flow diagram for a process 1300 for generating and deploying an image processing and inference pipeline according to at least one embodiment. In at least one embodiment, process 1300 can be used with imaging devices, processing devices, and / or other types of devices in one or more facilities 1302. Process 1300 can be performed within a training system 1304 and / or a deployment system 1306. In at least one embodiment, training system 1304 can be used to perform the training, deployment, and implementation of machine learning models (e.g., neural networks, object recognition algorithms, computer vision algorithms, etc.) for use in the deployment system 1306.In at least one embodiment, deployment system 1306 can be configured to offload processing and computing resources within a distributed computing environment to reduce infrastructure requirements in facility 1302. In at least one embodiment, one or more applications in a pipeline can use or call services (e.g., inference, visualization, computation, AI, etc.) of deployment system 1306 during application execution. In at least one embodiment, some of the applications used in advanced processing and inference pipelines can use machine learning models or other AI to perform one or more processing steps. In at least one embodiment, machine learning models can be trained in facility 1302 using data 1308 (such as imaging data) generated in facility 1302 (and stored on one or more Picture Archiving and Communication System (PACS) servers in facility 1302), or they can be trained using imaging or sequencing data 1308 from another facility (other facilities), or a combination thereof. In at least one embodiment, training system 1304 can be used to provide applications, services, and / or other resources for generating functional, deployable machine learning models for deployment system 1306. In at least one embodiment, Model Registry 1324 can be supported by object storage that can support versioning and object metadata. In at least one embodiment, object storage can be accessed, for example, via a cloud storage-compatible application programming interface (API) from within a cloud platform. In at least one embodiment, machine learning models within Model Registry 1324 can be uploaded, listed, modified, or deleted by developers or partners of a system that interacts with an API. In at least one embodiment, an API can provide access to procedures that allow users with appropriate credentials to associate models with applications, enabling models to be executed as part of the execution of containerized application instantiations. In at least one embodiment, training system 1304 (Fig. 13) can include a scenario in which facility 1302 trains its own machine learning model or has an existing machine learning model that needs to be optimized or updated. In at least one embodiment, imaging data 1308 generated by imaging device(s), sequencing devices, and / or other types of equipment can be received. In at least one embodiment, once imaging data 1308 is received, AI-assisted annotation 1310 can be used to assist in generating annotations corresponding to the imaging data 1308, which are to be used as ground-truth data for a machine learning model. In at least one embodiment, AI-assisted annotation 1310 can be used to annotate one or more machine learning models (e.g.,This includes convolutional neural networks (CNNs) that can be trained to generate annotations corresponding to certain types of imaging data 1308 (e.g., from certain devices). In at least one embodiment, AI-assisted annotation 1310 can then be used directly or can be adapted or fine-tuned using an annotation tool to generate ground-truth data. In at least one embodiment, AI-assisted annotation 1310, labeled data 1312, or a combination thereof can be used as ground-truth data to train a machine learning model. In at least one embodiment, a trained machine learning model can be designated as output model(s) 1316 and can be used by deployment system 1306 as described herein. In at least one embodiment, a training pipeline may include a scenario in which facility 1302 requires a machine learning model for use in performing one or more processing tasks for one or more applications in the deployment system 1306, but facility 1302 does not currently need (or cannot have) such a machine learning model that is optimized, efficient, or effective for such purposes. In at least one embodiment, an existing machine learning model may be selected from a model registry 1324. In at least one embodiment, model registry 1324 may contain machine learning models trained to perform a variety of different inference tasks on imaging data. In at least one embodiment, machine learning models in model registry 1324 may have been trained on imaging data from facilities other than facility 1302 (e.g., remote facilities).In at least one embodiment, machine learning models can be trained on imaging data from one location, two locations, or any number of locations. In at least one embodiment, when training on imaging data from a specific location, training can take place at that location or at least in a manner that protects the confidentiality of imaging data or prevents the transmission of imaging data off-premises. In at least one embodiment, once a model is trained—or partially trained—at a location, a machine learning model can be added to Model Registry 1324. In at least one embodiment, a machine learning model can then be retrained or updated at any number of other locations, and a retrained or updated model can be made available in Model Registry 1324.In at least one embodiment, a machine learning model can then be selected from model registry 1324 - and designated as output model(s) 1316 - and can be used in the deployment system 1306 to perform one or more processing tasks for one or more applications of a deployment system. In at least one embodiment, a scenario may involve that facility 1302 requires a machine learning model for use in performing one or more processing tasks for one or more applications in the deployment system 1306, but facility 1302 does not currently need to have such a machine learning model (or cannot have a model that is optimized, efficient, or effective for such purposes). In at least one embodiment, a machine learning model selected from model registry 1324 cannot be fine-tuned or optimized for imaging data 1308 generated at facility 1302 due to differences in the population, robustness of training data used to train a machine learning model, diversity in anomalies of training data, and / or other problems with training data.In at least one embodiment, AI-assisted annotation 1310 can be used to assist in generating annotations corresponding to imaging data 1308, which are to be used as ground-truth data for retraining or updating a machine learning model. In at least one embodiment, labeled data 1312 can be used as ground-truth data for training a machine learning model. In at least one embodiment, retraining or updating a machine learning model can be referred to as model training 1314. In at least one embodiment, model training 1314—e.g., AI-assisted annotation 1310, labeled data 1312, or a combination thereof—can be used as ground-truth data for retraining or updating a machine learning model.In at least one embodiment, a trained machine learning model can be designated as output model(s) 1316 and can be used by deployment system 1306 as described herein. In at least one embodiment, deployment system 1306 can include software 1318, services 1320, hardware 1322, and / or other components, features, and functionality. In at least one embodiment, deployment system 1306 can include a software "stack" such that software 1318 can be built on top of services 1320 and use services 1320 to perform some or all of its processing tasks, and services 1320 and software 1318 can be built on top of hardware 1322 and use hardware 1322 to perform processing, storage, and / or other computational tasks of deployment system 1306. In at least one embodiment, software 1318 can include any number of different containers, each container being capable of instantiating an application. In at least one embodiment, each application can perform one or more processing tasks in an advanced processing and inference pipeline (e.g.,Inference, object recognition, feature recognition, segmentation, image enhancement, calibration, etc.). In at least one embodiment, an advanced processing and inference pipeline can be defined based on selections of different containers desired or required for processing imaging data 1308, in addition to containers that receive and configure imaging data for use by each container and / or for use by facility 1302 after processing by a pipeline (e.g., to convert outputs back into a usable data type). In at least one embodiment, a combination of containers within software 1318 (e.g.,a pipeline) can be referred to as a virtual instrument (as described in more detail herein), and a virtual instrument can use services 1320 and hardware 1322 to perform some or all of the processing tasks of applications instantiated in containers. In at least one embodiment, a data processing pipeline can receive input data (e.g., imaging data 1308) in a specific format in response to an inference request (e.g., a request from a user of deployment system 1306). In at least one embodiment, input data can be representative of one or more images, video, and / or other data representations generated by one or more imaging devices. In at least one embodiment, data can undergo preprocessing as part of the data processing pipeline to prepare data for processing by one or more applications.In at least one embodiment, post-processing can be performed on an output from one or more inference tasks or other processing tasks of a pipeline to prepare output data for a subsequent application and / or to prepare output data for transmission and / or use by a user (e.g., in response to an inference request). In at least one embodiment, inference tasks can be performed by one or more machine learning models, such as trained or deployed neural networks, which may include output model(s) 1316 from training system 1304. In at least one embodiment, tasks of a data processing pipeline can be grouped into a container(s), each representing a discrete, fully functional instantiation of an application and a virtualized computing environment capable of referencing machine learning models. In at least one embodiment, containers or applications can be published in a private (e.g., restricted-access) area of ​​a container registry (described in more detail here), and trained or deployed models can be stored in the model registry 1324 and associated with one or more applications. In at least one embodiment, images of applications (e.g.,Container images) are available in a container registry, and once a user has selected an image from a container registry for use in a pipeline, it can be used to create a container for instantiating an application for use by a user's system. In at least one embodiment, developers (e.g., software developers, clinicians, physicians, etc.) can develop, publish, and store applications (e.g., as containers) for performing image processing and / or inference on supplied data. In at least one embodiment, development, publication, and / or storage can be performed using a software development kit (SDK) associated with a system (e.g., to ensure that an application and / or a developed container is compliant or compatible with a system). In at least one embodiment, an application under development can be tested locally (e.g., at a first facility, on data from a first facility) using an SDK that can support at least some of Services 1320 as a system (e.g., System 1200 of Fig. 12).In at least one embodiment, because DICOM objects can contain anywhere from one to hundreds of images or other data types, and due to the variation in data, a developer may be responsible for managing (e.g., setting constructs, building preprocessing in an application, etc.) the extraction and preparation of incoming data. In at least one embodiment, once validated by System 1300 (e.g., for accuracy), an application in a container registry may be available for selection and / or implementation by a user to perform one or more data processing tasks at a user facility (e.g., a second facility). In at least one embodiment, developers can then share applications or containers over a network for access and use by users of a system (e.g., System 1300 of Fig. 13). In at least one embodiment, completed and validated applications or containers can be stored in a container registry, and associated machine learning models can be stored in the model registry 1324. In at least one embodiment, a requesting entity—providing an inference or image processing request—can search a container registry and / or model registry 1324 for an application, container, dataset, machine learning model, etc., select a desired combination of elements for inclusion in a data processing pipeline, and submit an image processing request.In at least one embodiment, a query may include input data (and in some examples, associated patient data) necessary to execute a query, and / or may include a selection of application(s) and / or machine learning models to be executed when processing a query. In at least one embodiment, a query may then be passed to one or more components of Deployment System 1306 (e.g., a cloud) to perform data processing in a pipeline. In at least one embodiment, processing by Deployment System 1306 may involve referencing selected elements (e.g., applications, containers, models, etc.) from a container registry and / or model registry 1324. In at least one embodiment, once results are generated by a pipeline, results may be sent to a user for reference (e.g.,(for viewing in a viewing application suite performed on a local, on-site workstation or terminal). In at least one embodiment, services 1320 can be used to assist in processing or executing applications or containers in pipelines. In at least one embodiment, services 1320 can include compute services, artificial intelligence (AI) services, visualization services, and / or other types of services. In at least one embodiment, services 1320 can provide functionality common to one or more applications in software 1318, allowing functionality to be abstracted into a service that can be called or used by applications. In at least one embodiment, functionality provided by services 1320 can run dynamically and more efficiently while also scaling well by enabling applications to process data in parallel (e.g., using a parallel computing platform 1230 (Fig. 12)).In at least one embodiment, instead of each application sharing the same functionality offered by Services 1320 having its own instance of Services 1320, Services 1320 can be shared between and among different applications. In at least one embodiment, Services can include an inference server or engine that can be used as non-restrictive examples to perform detection or segmentation tasks. In at least one embodiment, a model training service can be included that can provide machine learning model training and / or retraining capabilities. In at least one embodiment, a data augmentation service can also be included that can provide GPU-accelerated data (e.g., DICOM, RIS, CIS, REST-compliant, RPC, raw, etc.) extraction, resizing, scaling, and / or other augmentation.In at least one embodiment, a visualization service can be used that can add image rendering effects—such as ray tracing, rasterization, denoising, sharpening, etc.—to add realism to two-dimensional (2D) and / or three-dimensional (3D) models. In at least one embodiment, virtual instrument services can be included that provide beam shaping, segmentation, inference, imaging, and / or support for other applications within virtual instrument pipelines. In at least one embodiment, where services 1320 include an AI service (e.g., an inference service), one or more machine learning models can be executed by calling (e.g., as an API call) an inference service (e.g., an inference server) to perform machine learning model(s) or processing them as part of application execution. In at least one embodiment, where another application includes one or more machine learning models for segmentation tasks, an application can call an inference service to execute machine learning models to perform one or more processing operations associated with segmentation tasks.In at least one embodiment, software 1318, which implements an advanced processing and inference pipeline that includes a segmentation application and an anomaly detection application, can be streamlined because each application can call the same inference service to perform one or more inference tasks. In at least one embodiment, hardware 1322 can include GPUs, CPUs, graphics cards, an AI / deep learning system (e.g., an AI supercomputer such as NVIDIA's DGX), a cloud platform, or a combination thereof. In at least one embodiment, different types of hardware 1322 can be used to provide efficient, custom-built support for software 1318 and services 1320 in deployment system 1306. In at least one embodiment, the use of GPU processing can be implemented for processing locally (e.g., in facility 1302), within an AI / deep learning system, in a cloud system, and / or in other processing components of deployment system 1306 to improve the efficiency, accuracy, and effectiveness of image processing and generation.In at least one embodiment, software 1318 and / or services 1320 can be optimized for GPU processing with respect to deep learning, machine learning, and / or high-performance computing, as non-limiting examples. In at least one embodiment, at least part of the computing environment of deployment system 1306 and / or training system 1304 can be located in a data center, one or more supercomputers, or high-performance computing systems with GPU-optimized software (e.g., a hardware and software combination of NVIDIA's DGX system). In at least one embodiment, hardware 1322 can include any number of GPUs that can be called upon to perform parallel data processing as described herein. In at least one embodiment, the cloud platform can further include GPU processing for GPU-optimized execution of deep learning tasks, machine learning tasks, or other computing tasks.In at least one embodiment, the cloud platform (e.g., NVIDIA's NGC) can be implemented using one or more AI / deep learning supercomputers and / or GPU-optimized software (e.g., as deployed on NVIDIA's DGX systems) as a hardware abstraction and scaling platform. In at least one embodiment, the cloud platform can integrate an application container clustering or orchestration system (e.g., Kubernetes) across multiple GPUs to enable seamless scaling and load balancing. Figure 14 is a system diagram for an exemplary System 1400 for generating and deploying an imaging deployment pipeline according to at least one embodiment. In at least one embodiment, System 1400 can be used to implement Process 1300 of Figure 13 and / or other processes, including advanced processing and inference pipelines. In at least one embodiment, System 1400 can include Training System 1304 and Deployment System 1306. In at least one embodiment, Training System 1304 and Deployment System 1306 can be implemented using Software 1318, Services 1320, and / or Hardware 1322, as described herein. In at least one embodiment, System 1400 (e.g., Training System 1304 and / or Deployment System 1306) can be implemented in a cloud computing environment (e.g., using Cloud 1426). In at least one embodiment, System 1400 can be implemented locally with respect to a healthcare facility or as a combination of both cloud and local computing resources. In at least one embodiment, access to APIs in Cloud 1426 can be restricted to authorized users by means of security measures or protocols. In at least one embodiment, a security protocol can include web tokens that can be signed by an authentication service (e.g., AuthN, AuthZ, Gluecon, etc.) and carry appropriate authorization.In at least one embodiment, APIs of virtual instruments (described herein) or other instantiations of System 1400 may be restricted to a set of public IPs that have been audited or authorized for interaction. In at least one embodiment, various components of System 1400 can communicate with each other using any of a variety of different network types, including, but not limited to, local area networks (LANs) and / or wide area networks (WANs) via wired and / or wireless communication protocols. In at least one embodiment, communication between devices and components of System 1400 (e.g., for transmitting inference requests, receiving results of inference requests, etc.) can be achieved via data bus(s), wireless data protocols (Wi-Fi), wired data protocols (e.g., Ethernet), etc. In at least one embodiment, training system 1304 can execute training pipelines 1404, similar to those described herein with reference to Fig. 13. In at least one embodiment, where one or more machine learning models are to be used in the deployment pipeline(s) 1410 by deployment system 1306, training pipelines 1404 can be used to train or retrain one or more (e.g., pre-trained) models and / or to implement one or more of the pre-trained models 1406 (e.g., without the need for retraining or updating). In at least one embodiment, output model(s) 1316 can be generated as a result of training pipelines 1404. In at least one embodiment, training pipelines 1404 can include any number of processing steps, such as, but not limited to, the conversion or adaptation of imaging data (or other input data).In at least one embodiment, different training pipelines 1404 can be used for different machine learning models used by the deployment system 1306. In at least one embodiment, training pipeline 1404, similar to a first example described with reference to Fig. 13, can be used for a first machine learning model; training pipeline 1404, similar to a second example described with reference to Fig. 13, can be used for a second machine learning model; and training pipeline 1404, similar to a third example described with reference to Fig. 13, can be used for a third machine learning model. In at least one embodiment, any combination of tasks within training system 1304 can be used, depending on the requirements of each respective machine learning model.In at least one embodiment, one or more of the machine learning models can already be trained and ready for use, so that the machine learning models do not need to be processed by training system 1304 and can be implemented by deployment system 1306. In at least one embodiment, output model(s) 1316 and / or pretrained models 1406 may include any type of machine learning model, depending on the implementation or embodiment. In at least one embodiment and without limitation, machine learning models used by System 1400 may include machine learning model(s) employing linear regression, logistic regression, decision trees, support vector machines (SVMs), Naive Bayes, k-nearest neighbor (Knn), K-means clustering, random forest, dimensionality reduction algorithms, gradient enhancement algorithms, neural networks (e.g., autocoders, convolutional, recurrent, perceptrons, long / short term memory (LSTM), Hopfield, Boltzmann, deep belief, deconvolutional, generative adversarial, liquid state machines, etc.), and / or other types of machine learning models. In at least one embodiment, training pipelines 1404 can include AI-assisted annotation, as described in more detail herein with reference to at least Fig. 14B. In at least one embodiment, labeled data 1312 (e.g., traditional annotation) can be generated by any number of techniques. In at least one embodiment, labels or other annotations can be generated within a drawing program (e.g., an annotation program), a computer-aided design (CAD) program, a labeling program, another type of program suitable for generating annotations or labels for ground truth, and / or, in some examples, can be hand-drawn. In at least one embodiment, ground truth data can be synthetically produced (e.g., generated from computer models or renderings), actually produced (e.g., designed and produced from real data), or machine-automated (e.g.,using feature analysis and learning to extract features from data and then generate labels), human annotation (e.g., by a labeler or annotation expert who defines the location of labels), and / or a combination thereof. In at least one embodiment, for each instance of imaging data 1308 (or other data type used by machine learning models), corresponding ground-truth data generated by training system 1304 may exist. In at least one embodiment, AI-assisted annotation may be performed as part of deployment pipeline(s) 1410, either in addition to or instead of AI-assisted annotation included in training pipelines 1404. In at least one embodiment, system 1400 may include a multi-layered platform comprising a software layer (e.g.,Software 1318) of diagnostic applications (or other application types) that can perform one or more medical imaging and diagnostic functions. In at least one embodiment, System 1400 can be communicatively connected to (e.g., via encrypted links) PACS server networks of one or more facilities. In at least one embodiment, System 1400 can be configured to access and reference data from PACS servers to perform operations such as training machine learning models, deploying machine learning models, image processing, inference, and / or other operations. In at least one embodiment, a software layer can be implemented as a secure, encrypted, and / or authenticated API through which applications or containers can be invoked (e.g., called) by one or more external environments (e.g., facility 1302). In at least one embodiment, applications can then invoke or perform one or more services 1320 to execute computational, AI, or visualization tasks associated with the respective applications, and software 1318 and / or services 1320 can utilize hardware 1322 to perform processing tasks effectively and efficiently. In at least one embodiment, communications sent to or received from a training system 1304 and a deployment system 1306 can be made using a pair of DICOM adapters 1402A, 1402B. In at least one embodiment, deployment system 1306 can execute deployment pipeline(s) 1410. In at least one embodiment, deployment pipeline(s) 1410 can include any number of applications that can be applied sequentially, non-sequentially, or otherwise to imaging data (and / or other data types) generated by imaging devices, sequencing devices, genomics devices, etc. – including AI-assisted annotation, as described above. In at least one embodiment, as described herein, deployment pipeline(s) 1410 for a single device can be designated as a virtual instrument for a device (e.g., a virtual ultrasound instrument, a virtual CT scan instrument, a virtual sequencing instrument, etc.).In at least one embodiment, there can be more than one input pipeline(s) 1410 for a single device, depending on the information desired from data generated by that device. In at least one embodiment, where anomaly detection from an MRI machine is desired, there can be a first input pipeline(s) 1410, and where image enhancement from the output of an MRI machine is desired, there can be a second input pipeline(s) 1410. In at least one embodiment, an image generation application may include a processing task that involves the use of a machine learning model. In at least one embodiment, a user may choose to use their own machine learning model or select a machine learning model from the model registry 1324. In at least one embodiment, a user may implement their own machine learning model or select a machine learning model for inclusion in an application to perform a processing task. In at least one embodiment, applications may be selectable and customizable, and by defining constructs of applications, the use and implementation of applications for an individual user are presented as a more seamless user experience.In at least one embodiment, by exploiting other features of System 1400 - such as Services 1320 and Hardware 1322 - deployment pipeline(s) 1410 can be even more user-friendly, provide simpler integration and produce more accurate, efficient and timely results. In at least one embodiment, deployment system 1306 may include a user interface (“UI”) 1414 (e.g., a graphical user interface, a web interface, etc.) that can be used to select applications for inclusion in deployment pipeline(s) 1410, to order applications, to modify or change applications or parameters or constructs thereof, to use and interact with deployment pipeline(s) 1410 during setup and / or deployment, and / or to otherwise interact with deployment system 1306. In at least one embodiment, although not illustrated with respect to training system 1304, UI 1414 (or another user interface) may be used to select models for use in deployment system 1306, to select models for training or retraining in training system 1304, and / or to otherwise interact with training system 1304. In at least one embodiment, Pipelinemanager 1412 can be used in addition to an application orchestration system 1428 to manage interaction between applications or containers of deployment pipeline(s) 1410 and services 1320 and / or hardware 1322. In at least one embodiment, Pipelinemanager 1412 can be configured to facilitate application-to-application, application-to-services 1320, and / or application-or-service-to-hardware 1322 interactions. In at least one embodiment, although illustrated as being contained in software 1318, this is not intended to be limiting, and in some examples, Pipelinemanager 1412 can be contained in services 1320. In at least one embodiment, the application orchestration system 1428 (e.g., Kubernetes, Docker, etc.) can include a container orchestration system that can group applications into containers as logical units for coordination, management, scaling, and deployment.In at least one embodiment, by associating applications of deployment pipeline(s) 1410 (e.g., a reconstruction application, a segmentation application, etc.) with individual containers, each application can be run in a self-contained environment (e.g., at a kernel level) to increase speed and efficiency. In at least one embodiment, each application and / or container (or each image thereof) can be developed, modified, and deployed individually (e.g., a first user or developer can develop, modify, and deploy a first application, and a second user or developer can develop, modify, and deploy a second application separate from the first user or developer). This allows users to focus on and devote attention to a task of a single application and / or container without being hindered by tasks of another application (or applications) or container (or containers). In at least one embodiment, communication and cooperation between different containers or applications can be facilitated by Pipeline Manager 1412 and Application Orchestration System 1428.In at least one embodiment, as long as an expected input and / or output from each container or application is known to a system (e.g., based on constructs of applications or containers), application orchestration system 1428 and / or pipeline manager 1412 can facilitate communication among and between applications or containers and the sharing of resources among and between each of them. In at least one embodiment, since one or more of applications or containers in deployment pipeline(s) 1410 can share the same services and resources, application orchestration system 1428 can determine orchestration, load balancing, and the sharing of services or resources between and among different applications or containers.In at least one embodiment, a scheduler can be used to track resource requests from applications or containers, the current or planned use of these resources, and resource availability. In at least one embodiment, a scheduler can thus allocate resources to different applications and distribute resources between and among applications with respect to system requirements and availability. In some examples, a scheduler (and / or another component of application orchestration system 1428) can determine resource availability and distribution based on constraints imposed on a system (e.g., user constraints), such as quality of service (QoS), the urgency of data output (e.g., to determine whether real-time or delayed processing should be performed), and so on. In at least one embodiment, services 1320, which are utilized and shared by applications or containers in the deployment system 1306, may include compute service(s) 1416, AI service(s) 1418, visualization service(s) 1420, and / or other service types. In at least one embodiment, applications may call (e.g., execute) one or more of the services 1320 to perform processing operations for an application. In at least one embodiment, compute service(s) 1416 may be utilized by applications to perform supercomputing or other high-performance computing (HPC) tasks. In at least one embodiment, compute service(s) 1416 may be utilized to perform parallel processing (e.g., using a parallel computing platform 1430) for processing data by one or more applications and / or performing one or more tasks of a single application substantially simultaneously.In at least one embodiment, the Parallel Computing Platform 1430 (e.g., NVIDIA's CUDA) can enable general-purpose computing on GPUs (GPGPU) (e.g., GPUs / Graphics 1422). In at least one embodiment, a software layer of the Parallel Computing Platform 1430 can provide access to virtual instruction sets and parallel computational elements of GPUs for execution by computation cores. In at least one embodiment, the Parallel Computing Platform 1430 can include memory, and in some embodiments, memory can be shared between and among multiple containers and / or between and among different processing tasks within a single container. In at least one embodiment, inter-process communication (IPC) calls can be generated for multiple containers and / or for multiple processes within a container to use the same data from a shared segment of memory of the Parallel Computing Platform 1430.B. where several different stages of an application or multiple applications process the same information). In at least one embodiment, instead of making a copy of data and moving data to different locations in memory (e.g., a read / write operation), the same data can be used in the same location of memory for any number of processing tasks (e.g., at the same time, at different times, etc.). In at least one embodiment, when data is used to generate new data as a result of processing, this information can be stored at a new location of data and shared between different applications. In at least one embodiment, the location of data and a location of updated or modified data can be part of a definition of how a payload is understood within containers. In at least one embodiment, AI service(s) 1418 can be used to perform inference services for running machine learning model(s) associated with applications (e.g., tasked with performing one or more processing tasks of an application). In at least one embodiment, AI service(s) 1418 can exploit AI system 1424 to run machine learning model(s) (e.g., neural networks, such as CNNs) for segmentation, reconstruction, object detection, feature recognition, classification, and / or other inference tasks. In at least one embodiment, applications of deployment pipeline(s) 1410 can use one or more output model(s) 1316 of training system 1304 and / or other application models to perform inference on imaging data. In at least one embodiment, two or more examples of inference can be performed using application orchestration system 1428 (e.g.,a scheduler) may be available. In at least one embodiment, a first category may include a high-priority / low-latency path that can achieve higher service-level agreements, such as for performing inference on urgent requests during an emergency or for a radiologist during diagnosis. In at least one embodiment, a second category may include a standard priority path that can be used for requests that may not be urgent or where analysis can be performed at a later time. In at least one embodiment, application orchestration system 1428 can distribute resources (e.g., services 1320 and / or hardware 1322) based on priority paths for different inference tasks of AI service(s) 1418. In at least one embodiment, shared memory can be attached to AI service(s) 1418 within system 1400. In at least one embodiment, shared memory can function as a cache (or other type of storage device) and can be used to process inference requests from applications. In at least one embodiment, when an inference request is submitted, a request can be received by a set of API instances of deployment system 1306, and one or more instances can be selected (e.g., for best fit, for load balancing, etc.) to process a request. In at least one embodiment, to process a request, a request can be entered into a database; a machine learning model can be located from model registry 1324 if it is not already in a cache; a validation step can ensure that an appropriate machine learning model is placed in a cache (e.g.,In at least one embodiment, a model can be loaded from shared memory, and / or a copy of a model can be stored in a cache. In at least one embodiment, a scheduler (e.g., from Pipelinemanager 1412) can be used to start an application referenced in a request if an application is not already running or if there are not enough instances of an application. In at least one embodiment, if an inference server is not already started to execute a model, an inference server can be started. Any number of inference servers can be started per model. In at least one embodiment, in a pull model where inference servers are clustered, models can be cached whenever load balancing is advantageous. In at least one embodiment, inference servers can be statically loaded onto corresponding distributed servers. In at least one embodiment, inference can be performed using an inference server running in a container. In at least one embodiment, an instance of an inference server can be associated with a model (and optionally a plurality of versions of a model). In at least one embodiment, if an instance of an inference server is not present when a request to perform inference on a model is received, a new instance can be loaded. In at least one embodiment, when an inference server is started, a model can be passed to an inference server, so that the same container can be used to serve different models, as long as the inference server is running as a separate instance. In at least one embodiment, during application execution, an inference request for a given application can be received, and a container (e.g., hosting an instance of an inference server) can be loaded (if not already done), and a start procedure can be invoked. In at least one embodiment, preprocessing logic within a container can load, decode, and / or perform any additional preprocessing on incoming data (e.g., using a CPU(s) and / or GPU(s)). In at least one embodiment, once data is prepared for inference, a container can perform inference on data as needed. In at least one embodiment, this can involve a single inference call on a single image (e.g., a hand X-ray) or it can require inference on hundreds of images (e.g., a breast CT scan).In at least one embodiment, an application can summarize results prior to completion, which may include, without limitation, a single confidence score, pixel-level segmentation, voxel-level segmentation, generating a visualization, or generating text to summarize findings. In at least one embodiment, different models or applications may be assigned different priorities. For example, some models may have a real-time priority (TAT < 1 min), while others may have a lower priority (e.g., TAT < 10 min). In at least one embodiment, model execution times can be measured by the requesting institution or entity and may include partner network traversal time as well as execution on an inference service. In at least one embodiment, the transfer of requests between Services 1320 and inference applications can be hidden behind a software development kit (SDK), and robust transport can be provided through a queue. In at least one embodiment, a request is placed in a queue via an API for a unique application / tenant ID combination, and an SDK pulls a request from the queue and sends it to an application. In at least one embodiment, a queue name can be provided in an environment from which an SDK will retrieve it. In at least one embodiment, asynchronous communication through a queue can be beneficial because it allows each instance of an application to retrieve work as it becomes available. Results can be transferred back through a queue to ensure that no data is lost.In at least one embodiment, queues can also provide a capability to segment work, since highest-priority work can go to a queue with the most instances of an application associated with it, while lowest-priority work can go to a queue with a single instance associated with it, processing tasks in a received order. In at least one embodiment, an application can run on a GPU-accelerated instance created in Cloud 1426, and an inference service can perform inference on a GPU. In at least one embodiment, visualization service(s) 1420 can be used to generate visualizations for viewing outputs from applications and / or deployment pipeline(s) 1410. In at least one embodiment, GPUs / graphics 1422 can be used by visualization service(s) 1420 to generate visualizations. In at least one embodiment, rendering effects, such as ray tracing, can be implemented by visualization service(s) 1420 to generate higher-quality visualizations. In at least one embodiment, visualizations can include, without limitation, 2D image renderings, 3D volume renderings, 3D volume reconstruction, 2D tomography slices, virtual reality displays, augmented reality displays, etc. In at least one embodiment, virtualized environments can be used to provide a virtual interactive display or environment (e.g.,to create a virtual environment for interaction by users of a system (e.g., doctors, nurses, radiologists, etc.). In at least one embodiment, visualization service(s) 1420 may include an internal visualizer, cinematography, and / or other rendering or image processing capabilities or functionality (e.g., ray tracing, rasterization, internal optics, etc.). In at least one embodiment, Hardware 1322 can include GPUs / Graphics 1422, AI System 1424, Cloud 1426 and / or any other hardware used to run Training System 1304 and / or Deployment System 1306. In at least one embodiment, GPUs / Graphics 1422 (e.g., NVIDIA TESLA and / or QUADRO GPUs) can include any number of GPUs that can be used to perform processing tasks of Computing Service(s) 1416, AI Service(s) 1418, Visualization Service(s) 1420, other services and / or any features or functionality of Software 1318. For example, with regard to AI service(s), 1418 GPUs / Graphics 1422 can be used to perform preprocessing on imaging data (or other data types used by machine learning models), postprocessing on outputs of machine learning models, and / or to perform inference (e.g., to run machine learning models).In at least one embodiment, Cloud 1426, AI System 1424, and / or other components of System 1400 can utilize GPUs / Graphics 1422. In at least one embodiment, Cloud 1426 can include a GPU-optimized platform for deep learning tasks. In at least one embodiment, AI System 1424 can utilize GPUs, and Cloud 1426—or at least a portion tasked with deep learning or inference—can be performed using one or more AI Systems 1424. Although Hardware 1322 is illustrated as discrete components, this is not intended to be restrictive, and any components of Hardware 1322 can be combined with or utilized by any other components of Hardware 1322. In at least one embodiment, AI System 1424 may include a purpose-built computing system (e.g., a supercomputer or an HPC) configured for inference, deep learning, machine learning, and / or other artificial intelligence tasks. In at least one embodiment, AI System 1424 (e.g., NVIDIA's DGX) may include GPU-optimized software (e.g., a software stack) that can be executed using a variety of GPUs / Graphics 1422 in addition to CPUs, RAM, memory, and / or other components, features, or functionality. In at least one embodiment, one or more AI Systems 1424 may be deployed in Cloud 1426 (e.g., in a data center) to perform some or all of the AI-based processing tasks of System 1400. In at least one embodiment, Cloud 1426 can include a GPU-accelerated infrastructure (e.g., NVIDIA's NGC) that can provide a GPU-optimized platform for performing processing tasks from System 1400. In at least one embodiment, Cloud 1426 can include an AI system 1424 for performing one or more AI-based tasks from System 1400 (e.g., as a hardware abstraction and scaling platform). In at least one embodiment, Cloud 1426 can be integrated with an application orchestration system 1428 that utilizes multiple GPUs to enable seamless scaling and load balancing between and among applications and services 1320. In at least one embodiment, Cloud 1426 can be tasked with performing at least some of the services 1320 of System 1400, including compute service(s) 1416, AI service(s) 1418 and / or visualization service(s) 1420, as described herein.In at least one embodiment, Cloud 1426 can perform small and large batch inference (e.g., running NVIDIA's TENSOR RT), provide an accelerated parallel computing API and platform 1430 (e.g., NVIDIA's CUDA), run an application orchestration system 1428 (e.g., KUBERNETES), provide a graphics rendering API and platform (e.g., for ray tracing, 2D graphics, 3D graphics, and / or other rendering techniques to produce higher-quality cinematography), and / or provide other functionality for System 1400. Fig. 15A illustrates a data flow diagram for a Process 1500 for training, retraining, or updating a machine learning model according to at least one embodiment. In at least one embodiment, Process 1500 can be performed using System 1400 from Fig. 14 as a non-limiting example. In at least one embodiment, Process 1500 can utilize services and / or hardware as described herein. In at least one embodiment, refined models 1512 generated by Process 1500 can be deployed by a deployment system to one or more containerized applications in deployment pipelines. In at least one embodiment, model training 1514 can involve retraining or updating an initial model 1504 (e.g., a pre-trained model) using new training data (e.g., new input data, such as a customer record 1506, and / or new ground-truth data associated with the input data). In at least one embodiment, retraining or updating the initial model 1504 can involve resetting, deleting, and / or replacing output or loss layer(s) of the initial model 1504 with updated or new output or loss layer(s). In at least one embodiment, the initial model 1504 can have previously fine-tuned parameters (e.g., weights and / or biases) remaining from previous training, so that training or retraining 1514 may not take as long or require as much processing as training a model from scratch.In at least one embodiment, during model training 1514, by resetting or replacing output or loss layer(s) of the initial model 1504, parameters for a new data set can be updated and retuned based on loss calculations associated with the accuracy of output or loss layer(s) when generating predictions about a new customer data set 1506. In at least one embodiment, pre-trained models 1506 can be stored in a data store or registry. In at least one embodiment, pre-trained models 1506 can have been trained, at least partially, in one or more facilities other than the facility performing process 1500. In at least one embodiment, to protect the privacy and rights of patients, subjects, or clients of different facilities, pre-trained models 1506 can have been trained on-site using client or patient data generated on-site. In at least one embodiment, pre-trained models 1506 can be trained using a cloud and / or other hardware, but confidential, privacy-protected patient data may not be transferred to, used by, or accessible to components of a cloud (or other off-site hardware).In at least one embodiment, where pre-trained models 1506 are trained using patient data from more than one institution, the pre-trained models 1506 may have been individually trained for each institution before being trained on patient or customer data from another institution. In at least one embodiment, such as when customer or patient data has been released due to privacy concerns (e.g., by waiver, for experimental use, etc.), or when customer or patient data is included in a public dataset, customer or patient data from any number of institutions may be used to train pre-trained models 1506 on-premises and / or off-premises, such as in a data center or other cloud computing infrastructure. In at least one embodiment, when applications are selected for use in deployment pipelines, a user can also select machine learning models to be used for specific applications. In at least one embodiment, a user may not have a model available for use, allowing a user to select a pre-trained model for use with an application. In at least one embodiment, the pre-trained model may be optimized to produce accurate results on a user's facility's customer data set (e.g., based on patient diversity, demographics, types of medical imaging devices used, etc.). In at least one embodiment, before inserting a pre-trained model into a deployment pipeline for use with an application, the pre-trained model may be updated, retrained, and / or fine-tuned for use at a particular facility. In at least one embodiment, a user can select a pre-trained model to be updated, retrained, and / or fine-tuned, and this pre-trained model can be designated as the initial model 1504 for a training system within process 1500. In at least one embodiment, a customer dataset 1506 (e.g., imaging data, genomic data, sequencing data, or other data types generated by devices at a facility) can be used to perform model training (which, without limitation, may include transfer learning) on ​​the initial model 1504 to produce a refined model 1512. In at least one embodiment, ground-truth data corresponding to the customer dataset 1506 can be generated by training system 1304. In at least one embodiment, ground-truth data can be generated, at least partially, by clinicians, scientists, physicians, or practitioners at a facility. In at least one embodiment, AI-assisted annotation can be used in some examples to generate ground-truth data. In at least one embodiment, AI-assisted annotation (e.g., implemented using an AI-assisted annotation SDK) can leverage machine learning models (e.g., neural networks) to generate suggested or predicted ground-truth data for a customer dataset. In at least one embodiment, a user can use annotation tools within a user interface (a graphical user interface (GUI)) on a computing device. In at least one embodiment, user 1510 can interact with a GUI via computing device 1508 to edit or fine-tune (auto-)annotations. In at least one embodiment, a polygon editing feature can be used to move vertices of a polygon to more accurate or fine-tuned locations. In at least one embodiment, once customer dataset 1506 has associated ground-truth data, ground-truth data (e.g., from AI-assisted annotation, manual labeling, etc.) can be used during model training to generate refined model 1512. In at least one embodiment, customer dataset 1506 can be applied to initial model 1504 any number of times, and ground-truth data can be used to update parameters of initial model 1504 until an acceptable level of accuracy is achieved for refined model 1512. In at least one embodiment, once refined model 1512 is generated, refined model 1512 can be deployed within one or more deployment pipelines at a facility to perform one or more processing tasks related to medical imaging data. In at least one embodiment, refined model 1512 can be uploaded to pretrained models in a model registry for selection by another facility. In at least one embodiment, this process can be completed at any number of facilities, allowing refined model 1512 to be further refined any number of times on new datasets to generate a more universal model. Figure 15B is an exemplary illustration of a client-server architecture 1532 for improving annotation tools with pre-trained annotation models according to at least one embodiment. In at least one embodiment, an AI-assisted annotation tool 1536 can be instantiated based on a client-server architecture 1532. In at least one embodiment, the AI-assisted annotation tool 1536 can assist radiologists in imaging applications, for example, to identify organs and anomalies. In at least one embodiment, imaging applications can include software tools that assist users 1510 in identifying some extreme points on a single organ of interest in raw images 1534 (e.g., in a 3D MRI or CT scan) as a non-restrictive example and receiving auto-annotated results for all 2D sections of a single organ.In at least one embodiment, results can be stored in a data store as training data 1538 and used as (for example, and without limitation) ground-truth data for training. In at least one embodiment, when a computing device 1508 sends extreme points for AI-assisted annotation, a deep learning model can, for example, receive this data as input and return inference results of a segmented organ or anomaly. In at least one embodiment, pre-instantiated annotation tools, such as the AI-assisted annotation tool 1536 in Fig. 15B, can be enhanced by making API calls (e.g., API call 1544) to a server, such as an Annotation Assistant Server 1540, which may contain a set of pre-trained models 1542 stored, for example, in an annotation model registry.In at least one embodiment, an annotation model registry can store pre-trained models (e.g., machine learning models, such as deep learning models) that are pre-trained to perform AI-assisted annotation on a single organ or anomaly. These models can be further updated using training pipelines. In at least one embodiment, pre-installed annotation tools can be improved over time as new labeled data are added. Various embodiments can be described by the following paragraphs: 1. At least one processor, comprising: one or more logical units for: determining, using a machine learning model, an inference operation to be performed, wherein the inference operation involves a floating-point value to be exponentially scaled; generating a fixed-point representation of the value, wherein the fixed-point representation includes a bias factor; generating, using the fixed-point representation, an intermediate representation of the value with a specified number of bits; incrementing the intermediate representation to cause a mantissa of the incremented intermediate representation to correspond to the fixed-point representation; shifting a decimal point of the incremented intermediate representation to produce an exponential approximation of the value; and executing, using the machine learning model,1. The inference operation using the exponential approximation. 2. The at least one processor according to paragraph 1, wherein the one or more logical units further serve to: provide the exponential approximation of the received value in order to compute a normalized probability for the value as output by a neural network. 3. The at least one processor according to paragraph 1, wherein the one or more logical units further serve to: increment the intermediate representation by adding a value of 1 to the intermediate representation. 4. The at least one processor according to paragraph 1, wherein a number of bits by which the decimal point is to be shifted depends partially on a number of bits of the exponential approximation. 5. The at least one processor according to paragraph 1, wherein the intermediate representation comprises at most a number of bits determined for a hardware register.which is to be used to store the intermediate representation. 6. The at least one processor according to paragraph 1, wherein the one or more logical units further serve to: clear a sign bit of the incremented intermediate representation after shifting the decimal point. 7. The at least one processor according to paragraph 1, wherein the one or more logical units further serve to: provide the exponential approximation for use with a SoftMax activation layer of the machine learning model. 8. The at least one processor according to paragraph 1, wherein the one or more logical units further serve to: produce the exponential approximation of the received value without generating an integer representation of the received value. 9. The at least one processor according to paragraph 1,wherein the at least one processor is present in at least one of: a system for performing simulation operations; a system for performing simulation operations for testing or validating autonomous machine applications; a system for performing digital twin operations; a system for performing light transport simulation; a system for rendering graphical output; a system for performing deep learning operations; a system implemented using an edge device; a system for generating or displaying virtual reality (VR) content; a system for generating or displaying augmented reality (AR) content; a system for generating or displaying mixed reality (MR) content; a system containing one or more virtual machines (VMs); a system,that is at least partially implemented in a data center; a system for performing hardware tests using simulation; a system for generating synthetic data; a system for performing generative operations using a large language model (LLM); a system for performing generative operations using a vision language model (VLM); a system for performing generative operations using a multimodal language model; a system that uses or employs one or more inference microservices; a system that includes one or more machine learning models deployed in a service or microservice along with an OS-level virtualization package (e.g., a container); a collaborative content creation platform for 3D assets; or a system that is at least partially implemented using cloud computing resources. 10. A system,comprising: one or more processing units for generating at least one exponential or logarithmic approximation using a floating-point representation, partly by generating an intermediate representation using a fixed-point representation of the floating-point representation and a bias factor, adjusting a value of the intermediate representation, and shifting the intermediate representation by a specified number of bits. 11. The system according to paragraph 10, wherein the at least one exponential or logarithmic approximation is to be used to perform an inference operation using a machine learning model. 12. The system according to paragraph 11, wherein the one or more processing units further serve to provide the exponential approximation for calculating a normalized probability for at least one value output by the machine learning model. 13. The system according to paragraph 10,wherein the one or more processing units further serve to increment the intermediate representation such that a mantissa of the intermediate representation represents the fixed-point representation. 14. The system according to paragraph 10, wherein the intermediate representation comprises at most a number of bits designated for a hardware register to be used for storing the intermediate representation. 15. The system according to paragraph 10, wherein the one or more processing units further serve to provide the exponential approximation for use with a SoftMax activation layer of a machine learning model. 16. The system according to paragraph 10,wherein the system comprises at least one of: a system for performing simulation operations; a system for performing simulation operations for testing or validating autonomous machine applications; a system for performing digital twin operations; a system for performing light transport simulation; a system for rendering graphical output; a system for performing deep learning operations; a system for performing generative operations using a large language model (LLM); a system for performing generative operations using a vision language model (VLM); a system for performing generative operations using a multimodal language model; a system,that is implemented using an edge device; a system for generating or displaying virtual reality (VR) content; a system for generating or displaying augmented reality (AR) content; a system for generating or displaying mixed reality (MR) content; a system that contains one or more virtual machines (VMs); a system that is at least partially implemented in a data center; a system for running hardware tests using simulation; a system for generating synthetic data; a system that uses or employs one or more inference microservices; a system that contains one or more machine learning models deployed in a service or microservice along with an OS-level virtualization package (e.g., a container); a collaborative content creation platform for 3D assets; or a systemwhich is implemented at least partially using cloud computing resources.17. An inference system comprising: a machine learning model including an activation layer; and one or more processors for: generating a fixed-point representation of a value received at the activation layer in a floating-point format, the fixed-point representation including a bias factor; generating, using the fixed-point representation, an intermediate representation of the value with a specified number of bits; incrementing the intermediate representation to cause a mantissa of the incremented intermediate representation to be equal to the fixed-point representation; shifting a decimal point of the incremented intermediate representation to produce an exponential approximation of the received value; and calculating a probability of an inference outcome generated by the machine learning model.18. The inference system of paragraph 17, wherein the one or more probability is calculated from the received value without conversion to a single precision format or an integer value. 19. The inference system of paragraph 17, wherein the probability is a normalized probability calculated using exponential approximations of a multitude of values ​​received at the activation layer. 20. The inference system of paragraph 17,wherein the inference system comprises at least one of: a system for performing simulation operations; a system for performing simulation operations for testing or validating autonomous machine applications; a system for performing digital twin operations; a system for performing light transport simulation; a system for rendering graphical output; a system for performing deep learning operations; a system for performing generative operations using a large language model (LLM); a system for performing generative operations using a vision language model (VLM); a system for performing generative operations using a multimodal language model; a system,that is implemented using an edge device; a system for generating or displaying virtual reality (VR) content; a system for generating or displaying augmented reality (AR) content; a system for generating or displaying mixed reality (MR) content; a system that contains one or more virtual machines (VMs); a system that is at least partially implemented in a data center; a system for running hardware tests using simulation; a system for generating synthetic data; a system that uses or employs one or more inference microservices; a system that contains one or more machine learning models deployed in a service or microservice along with an OS-level virtualization package (e.g., a container); a collaborative content creation platform for 3D assets; or a systemwhich is implemented at least partially using cloud computing resources. Other variations are within the scope of this disclosure. While the disclosed techniques are thus receptive to various modifications and alternative constructions, certain illustrated embodiments thereof are shown in the drawings and have been described in detail above. It should be understood, however, that the disclosure is not intended to be limited to any particular disclosed form or forms, but rather, on the contrary, to cover all modifications, alternative constructions, and equivalents that fall within the scope and meaning of the disclosure as defined in the attached claims. The use of the terms "a," "an," "the," and similar references in connection with the description of disclosed embodiments (particularly in connection with the following claims) is to be interpreted as covering both the singular and the plural unless otherwise specified herein or the context clearly contradicts this, and not as a definition of a term. The terms "having," "incorporating," "including," and "containing" are to be interpreted as open terms (meaning "including but not limited to") unless otherwise specified. The term "connected," when unmodified and referring to physical connections, is to be interpreted as including, in whole or in part, within, attached to, or connected to one another, even if something is in between.The recitation of ranges of values ​​herein is intended merely as a shorthand procedure for individually referring to each value falling within the range, unless otherwise specified herein, and each value is included in the specification as if it were individually recited herein. The use of the term "sentence" (e.g., "a set of elements") or "substance," unless otherwise specified or the context contradicts, is to be interpreted as a non-empty collection containing one or more elements. Furthermore, unless otherwise specified or the context contradicts, the term "substance" of a corresponding sentence does not necessarily denote a true substance of a corresponding sentence, but substance and corresponding sentence may be synonymous. Connective language, such as phrases of the form "at least one of A, B, and C" or "at least one of A, B, and C," unless expressly stated otherwise or the context clearly contradicts, is otherwise understood with context as it is generally used to indicate that an element, term, etc., can be either A, B, C, or any non-empty subclause of the sentence of A, B, and C. For example, in an illustrative example of a sentence with three elements, connective phrases "at least one of A, B, and C" and "at least one of A, B, and C" refer to any one of the following: {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}. Thus, such connective language is generally not intended to imply that certain embodiments require the presence of at least one of A, at least one of B, and at least one of C, respectively.Additionally, unless otherwise stated or the context contradicts it, the term "multitude" indicates a plural state (e.g., "a multitude of elements" indicates multiple elements). A multitude is at least two elements, but may be more if this is either explicitly stated or indicated by context. Furthermore, unless otherwise stated or the context is otherwise clear, the phrase means "based on," "at least partly based on," and not "exclusively based on." Operations of the processes described herein may be performed in any suitable order unless otherwise specified herein or the context clearly indicates otherwise. In at least one embodiment, a process such as the processes described herein (or variations and / or combinations thereof) is executed under the control of one or more computer systems configured with executable instructions and is implemented as code (e.g., executable instructions, one or more computer programs, or one or more applications) that is executed collectively on one or more processors by hardware or combinations thereof. In at least one embodiment, code is stored on a computer-readable storage medium, for example, in the form of a computer program comprising a plurality of instructions that are executable by one or more processors.In at least one embodiment, a computer-readable storage medium is a non-volatile computer-readable storage medium that excludes volatile signals (e.g., a propagating transient electrical or electromagnetic transmission) but includes non-volatile data storage circuitry (e.g., buffers, caches, and queues) within transceivers of volatile signals. In at least one embodiment, code (e.g., executable code or source code) is stored on a set of one or more non-volatile computer-readable storage media on which executable instructions (or other memory for storing executable instructions) are stored. When executed (i.e., as a result of execution) by one or more processors of a computer system, these instructions cause the computer system to perform the operations described herein.In at least one embodiment, a set of non-volatile, computer-readable storage media comprises multiple non-volatile storage media, and one or more individual non-volatile storage media within this set lack all code, while multiple non-volatile storage media collectively store all code. In at least one embodiment, executable instructions are executed such that different instructions are executed by different processors—for example, a non-volatile storage medium stores instructions, and a central processing unit (CPU) executes some of the instructions, while a graphics processing unit (GPU) executes other instructions.In at least one embodiment, different components of a computer system have separate processors, and different processors execute different subsets of instructions. Accordingly, in at least one embodiment, computer systems are configured to implement one or more services that individually or jointly perform operations of the processes described herein, and such computer systems are configured with applicable hardware and / or software that enables the execution of operations. Furthermore, a computer system implementing at least one embodiment of the present disclosure is a single device, and in another embodiment, it is a distributed computer system comprising multiple devices that operate differently, such that the distributed computer system performs the operations described herein and a single device does not perform all operations. The use of any and all examples or exemplary language (e.g., "like") provided herein is intended only to better illuminate embodiments of the disclosure and does not constitute a limitation of the scope of the disclosure unless otherwise claimed. No language in the specification should be interpreted as indicating that an unclaimed element is essential for the practical implementation of the disclosure. All references, including publications, patent applications and patents cited herein, are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference, and as if they were set forth herein in their entirety. In the description and claims, the terms "coupled" and "connected," along with their derivatives, may be used. It is understood that these terms are not necessarily intended as synonyms. Rather, in certain examples, "connected" or "coupled" may be used to indicate that two or more elements are in direct or indirect physical or electrical contact with each other. "Coupled" may also mean that two or more elements are not in direct contact with each other but nevertheless cooperate or interact. Unless expressly stated otherwise, terms such as "processing", "calculating", "calculating", "determining" or the like are understood to refer throughout this specification to actions and / or processes of a computer or computing system or similar electronic computing device that manipulate and / or convert data represented as physical, such as electronic, quantities within the registers and / or memory of the computing system into other data represented similarly as physical quantities within the memory, registers or other such information storage, transmission or display devices of the computing system. Similarly, the term "processor" can refer to any device or any part of a device that processes electronic data from registers and / or memory and converts that electronic data into other electronic data that can be stored in registers and / or memory. As non-restrictive examples, "processor" can be a CPU or a GPU. A "computing platform" can have one or more processors. As used herein, "software" processes can include, for example, software and / or hardware entities that perform work over time, such as tasks, threads, and intelligent agents. Furthermore, each process can refer to multiple processes for executing instructions sequentially or in parallel, continuously or intermittently.The terms “system” and “procedure” are used interchangeably herein, provided that the system can embody one or more procedures and procedures can be considered as a system. This document may refer to obtaining, acquiring, receiving, or inputting analog or digital data into a subsystem, computer system, or computer-implemented machine. Obtaining, acquiring, receiving, or inputting analog and digital data can be accomplished in a variety of ways, such as receiving data as a parameter of a function call or an application programming interface (API) call. In some implementations, the process of obtaining, acquiring, receiving, or inputting analog or digital data can be accomplished by transmitting data over a serial or parallel interface. In another implementation, the process of obtaining, acquiring, receiving, or inputting analog or digital data can be accomplished by transmitting data over a computer network from a providing entity to a receiving entity.It can also refer to providing, outputting, transmitting, sending, or presenting analog or digital data. In various examples, the process of providing, outputting, transmitting, sending, or presenting analog or digital data can be achieved by transferring data as an input or output parameter of a function call, a parameter of an application programming interface, or an interprocess communication mechanism. Although the above discussion presents exemplary implementations of the described techniques, other architectures may be used to implement the described functionality and are intended to be within the scope of this disclosure. While specific distributions of responsibilities are defined above for the purpose of discussion, various functions and responsibilities may be distributed and subdivided in different ways depending on the circumstances. Although the subject matter was described in a language specific to structural features and / or methodological actions, it is further understood that the subject matter claimed in the attached claims is not necessarily limited to specific features or actions. Rather, specific features and actions are disclosed as exemplary forms of implementing the claims.

Claims

At least one processor comprising: one or more logical units for: determining, using a machine learning model, an inference operation to be performed, wherein the inference operation involves a floating-point value to be exponentially approximated; generating a fixed-point representation of the value, wherein the fixed-point representation includes a bias factor; generating, using the fixed-point representation, an intermediate representation of the value with a specified number of bits; incrementing the intermediate representation to cause a mantissa of the incremented intermediate representation to be equal to the fixed-point representation; shifting a decimal point of the incremented intermediate representation to produce an exponential approximation of the value; and executing, using the machine learning model, the inference operation using the exponential approximation. The at least one processor according to claim 1, wherein the one or more logical units further serve to: provide the exponential approximation of the received value in order to calculate a normalized probability for the value as output by a neural network. The at least one processor according to claim 1, wherein the one or more logical units further serve to: increment the intermediate representation by adding a value of 1 to the intermediate representation. The at least one processor according to claim 1, wherein a number of bits by which the decimal point is to be shifted depends partially on a number of bits of the exponential approximation. The at least one processor according to claim 1, wherein the intermediate representation comprises at most a number of bits which is designated for a hardware register which is to be used to store the intermediate representation. The at least one processor according to claim 1, wherein the one or more logical units further serve to: clear a sign bit of the incremented intermediate representation after shifting the decimal point. The at least one processor according to claim 1, wherein the one or more logical units further serve to: provide the exponential approximation for use with a SoftMax activation layer of the machine learning model. The at least one processor according to claim 1, wherein the one or more logical units further serve to: produce the exponential approximation of the received value without generating an integer representation of the received value. The at least one processor according to claim 1, wherein the at least one processor is incorporated in at least one of: a system for performing simulation operations; a system for performing simulation operations for testing or validating autonomous machine applications; a system for performing digital twin operations; a system for performing light transport simulation; a system for rendering graphical output; a system for performing deep learning operations; a system implemented using an edge device; a system for generating or displaying virtual reality (VR) content; a system for generating or displaying augmented reality (AR) content; a system for generating or displaying mixed reality (MR) content; a system containing one or more virtual machines (VMs); a system that is at least partially implemented in a data center;a system for performing hardware tests using simulation; a system for generating synthetic data; a system for performing generative operations using a large language model (LLM); a system for performing generative operations using a vision language model (VLM); a system for performing generative operations using a multimodal language model; a system that uses or employs one or more inference microservices; a system that includes one or more machine learning models deployed in a service or microservice along with an OS-level virtualization package (e.g., a container); a collaborative content creation platform for 3D assets; or a system that is implemented, at least in part, using cloud computing resources. A system comprising: one or more processing units for generating at least one of an exponential or logarithmic approximation using a floating-point representation, partly by generating an intermediate representation using a fixed-point representation of the floating-point representation and a bias factor, adjusting a value of the intermediate representation and shifting the intermediate representation by a specified number of bits. The system according to claim 10, wherein at least one of the exponential approximation or the logarithmic approximation is to be used to perform an inference operation using a machine learning model. The system according to claim 11, wherein the one or more processing units further provide the exponential approximation to calculate a normalized probability for at least one value output by the machine learning model. The system according to claim 10, wherein the one or more processing units are further said to increment the intermediate representation, insofar as a mantissa of the intermediate representation represents the fixed-point representation. The system according to claim 10, wherein the intermediate representation comprises at most a number of bits which is designated for a hardware register to be used for storing the intermediate representation. The system according to claim 10, wherein the one or more processing units are further said to provide the exponential approximation for use with a SoftMax activation layer of a machine learning model. The system according to claim 10, wherein the system comprises at least one of: a system for performing simulation operations; a system for performing simulation operations for testing or validating autonomous machine applications; a system for performing digital twin operations; a system for performing light transport simulation; a system for rendering graphical output; a system for performing deep learning operations; a system for performing generative operations using a large language model (LLM); a system for performing generative operations using a vision language model (VLM); a system for performing generative operations using a multimodal language model; a system implemented using an edge device; a system for generating or displaying virtual reality (VR) content;a system for generating or displaying augmented reality (AR) content; a system for generating or displaying mixed reality (MR) content; a system containing one or more virtual machines (VMs); a system that is at least partially implemented in a data center; a system for running hardware tests using simulation; a system for generating synthetic data; a system that uses or employs one or more inference microservices; a system that contains one or more machine learning models deployed in a service or microservice along with an OS-level virtualization package (e.g., a container); a collaborative content creation platform for 3D assets; or a system that is at least partially implemented using cloud computing resources. An inference system comprising: a machine learning model including an activation layer; and one or more processors for: generating a fixed-point representation of a value received at the activation layer in a floating-point format, the fixed-point representation including a bias factor; generating, using the fixed-point representation, an intermediate representation of the value with a specified number of bits; incrementing the intermediate representation to cause a mantissa of the incremented intermediate representation to be equal to the fixed-point representation; shifting a decimal point of the incremented intermediate representation to produce an exponential approximation of the received value; and calculating a probability of an inference result produced by the machine learning model using the exponential approximation. The inference system according to claim 17, wherein one or more of the probabilities are calculated from the received value without conversion into a single precision format or an integer value. The inference system according to claim 17, wherein the probability is a normalized probability calculated using exponential approximations of a plurality of values ​​received at the activation layer. The inference system according to claim 17, wherein the inference system comprises at least one of: a system for performing simulation operations; a system for performing simulation operations for testing or validating autonomous machine applications; a system for performing digital twin operations; a system for performing light transport simulation; a system for rendering graphical output; a system for performing deep learning operations; a system for performing generative operations using a large language model (LLM); a system for performing generative operations using a vision language model (VLM); a system for performing generative operations using a multimodal language model; a system implemented using an edge device; a system for generating or displaying virtual reality (VR) content;a system for generating or displaying augmented reality (AR) content; a system for generating or displaying mixed reality (MR) content; a system containing one or more virtual machines (VMs); a system that is at least partially implemented in a data center; a system for running hardware tests using simulation; a system for generating synthetic data; a system that uses or employs one or more inference microservices; a system that contains one or more machine learning models deployed in a service or microservice along with an OS-level virtualization package (e.g., a container); a collaborative content creation platform for 3D assets; or a system that is at least partially implemented using cloud computing resources.

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