Conformal predictions to upper-bound intrinsic aleatoric uncertainty

Abstract

A processor-implemented method for estimating uncertainty includes receiving an artificial neural network (ANN) model and a calibration dataset. An upper-bound on a conditional entropy of a data distribution of the ANN model is computed using conformal prediction. The conditional entropy of the model is estimated based on the upper-bound. In turn, the uncertainty of the data distribution of the ANN model may be estimated based on the conditional entropy and a prediction set size.

Description

Qualcomm Ref. No.2309552WO CONFORMAL PREDICTIONS TO UPPER-BOUND INTRINSIC ALEATORIC UNCERTAINTY CROSS-REFERENCE TO RELATED APPLICATION

[0001] The present application claims priority to Greece Patent Application No. 20230100902, filed on October 31, 2023, and titled “CONFORMAL PREDICTIONS TO UPPER-BOUND INTRINSIC ALEATORIC UNCERTAINTY,” the disclosure of which is expressly incorporated by reference in its entirety. FIELD OF THE DISCLOSURE

[0002] Aspects of the present disclosure generally relate to neural networks, and more particularly to conformal predictions to upper-bound intrinsic aleatoric uncertainty. BACKGROUND

[0003] Artificial neural networks may comprise interconnected groups of artificial neurons (e.g., neuron models). The artificial neural network (ANN) may be a computational device or be represented as a method to be performed by a computational device. Convolutional neural networks (CNNs) are a type of feed-forward ANN. Convolutional neural networks may include collections of neurons that each have a receptive field and that collectively tile an input space. Convolutional neural networks, such as deep convolutional neural networks (DCNs), have numerous applications. In particular, these neural network architectures are used in various technologies, such as image recognition, speech recognition, acoustic scene classification, keyword spotting, autonomous driving, and other classification tasks.

[0004] Given the many useful applications of neural networks, there is increasing demand for use thereof on edge devices such as smartphones or in sensitive environments such as medical diagnostics. In such instances, the neural network model may be provided without access to a training dataset. As such it may not be possible to independently determine the accuracy of results of the neural network model. That is, uncertainty with respect to classification results may hinder confidence in the neural Seyfarth Ref. No.72178-006653 1 313495666v.1Qualcomm Ref. No.2309552WO network model. Thus, it may be desirable to estimate the uncertainty of the neural network model. SUMMARY

[0005] The present disclosure is set forth in the independent claims, respectively. Some aspects of the disclosure are described in the dependent claims.

[0006] Various aspects of the present disclosure are directed to an apparatus having at least one memory and one or more processors coupled to the at least one memory. The processor(s) is configured to receive an artificial neural network (ANN) model and a calibration dataset. The processor(s) is also configured to compute, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction. The processor(s) is further configured to estimate the conditional entropy of the ANN model based on the upper-bound.

[0007] In some aspects of the present disclosure, a processor-implemented method performed by one or more processors includes receiving an artificial neural network (ANN) model and a calibration dataset. The processor-implemented method also includes computing, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction. The processor- implemented method further includes estimating the conditional entropy of the ANN model based on the upper-bound.

[0008] Various aspects of the present disclosure are directed to an apparatus including means for receiving an artificial neural network (ANN) model and a calibration dataset. The apparatus further includes means for computing, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction. The apparatus also includes means for estimating the conditional entropy of the ANN model based on the upper-bound.

[0009] In some aspects of the present disclosure, a non-transitory computer-readable medium with non-transitory program code recorded thereon is disclosed. The program code is executed by at least one processor and includes program code to receive an artificial neural network (ANN) model and a calibration dataset. The program code also includes program code to compute, by the ANN model, an upper-bound on a Seyfarth Ref. No.72178-006653 2 313495666v.1Qualcomm Ref. No.2309552WO conditional entropy of a data distribution of the ANN model using conformal prediction. The program code further includes program code to estimate the conditional entropy of the ANN model based on the upper-bound.

[0010] Additional features and advantages of the disclosure will be described below. It should be appreciated by those skilled in the art that this disclosure may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes of the present disclosure. It should also be realized by those skilled in the art that such equivalent constructions do not depart from the teachings of the disclosure as set forth in the appended claims. The novel features, which are believed to be characteristic of the disclosure, both as to its organization and method of operation, together with further objects and advantages, will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The features, nature, and advantages of the present disclosure will become more apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout.

[0012] FIGURE 1 illustrates an example implementation of a neural network using a system-on-a-chip (SOC), including a general-purpose processor, in accordance with certain aspects of the present disclosure.

[0013] FIGURES 2A, 2B, and 2C are diagrams illustrating a neural network, in accordance with various aspects of the present disclosure.

[0014] FIGURE 2D is a diagram illustrating an exemplary deep convolutional network (DCN), in accordance with various aspects of the present disclosure.

[0015] FIGURE 3 is a block diagram illustrating an exemplary deep convolutional network (DCN), in accordance with various aspects of the present disclosure. Seyfarth Ref. No.72178-006653 3 313495666v.1Qualcomm Ref. No.2309552WO

[0016] FIGURE 4 is a block diagram illustrating an exemplary software architecture that may modularize artificial intelligence (AI) functions, in accordance with various aspects of the present disclosure.

[0017] FIGURE 5 is a flow diagram illustrating a processor-implemented method for uncertainty estimation, in accordance with various aspects of the present disclosure. DETAILED DESCRIPTION

[0018] The detailed description set forth below, in connection with the appended drawings, is intended as a description of various configurations and is not intended to represent the only configurations in which the concepts described may be practiced. The detailed description includes specific details for the purpose of providing a thorough understanding of the various concepts. However, it will be apparent to those skilled in the art that these concepts may be practiced without these specific details. In some instances, well-known structures and components are shown in block diagram form in order to avoid obscuring such concepts.

[0019] Based on the teachings, one skilled in the art should appreciate that the scope of the disclosure is intended to cover any aspect of the disclosure, whether implemented independently of or combined with any other aspect of the disclosure. For example, an apparatus may be implemented or a method may be practiced using any number of the aspects set forth. In addition, the scope of the disclosure is intended to cover such an apparatus or method practiced using other structure, functionality, or structure and functionality in addition to or other than the various aspects of the disclosure set forth. It should be understood that any aspect of the disclosure disclosed may be embodied by one or more elements of a claim.

[0020] The word “exemplary” is used to mean “serving as an example, instance, or illustration.” Any aspect described as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects.

[0021] Although particular aspects are described, many variations and permutations of these aspects fall within the scope of the disclosure. Although some benefits and advantages of the preferred aspects are mentioned, the scope of the disclosure is not intended to be limited to particular benefits, uses or objectives. Rather, aspects of the Seyfarth Ref. No.72178-006653 4 313495666v.1Qualcomm Ref. No.2309552WO disclosure are intended to be broadly applicable to different technologies, system configurations, networks and protocols, some of which are illustrated by way of example in the figures and in the following description of the preferred aspects. The detailed description and drawings are merely illustrative of the disclosure rather than limiting, the scope of the disclosure being defined by the appended claims and equivalents thereof.

[0022] Uncertainty estimation for machine learning (ML) models may involve specific assumptions for the task at hand such as in a distribution over model parameters, for example, to formulate and train the model to learn well-calibrated uncertainties.

[0023] Recently, conformal prediction has become an area of exploration for a distribution-free approach to uncertainty quantification. Conformal prediction is a ML framework that may provide a mechanism for assigning confidence levels to point predictions (which may also be referred to as estimates) of the ML model.

[0024] However, sensitive applications, such as those related to medical diagnostics, may demand further insight into the ML model output, for example. In some scenarios, the data distribution may not be accessible and the ML model may essentially be supplied in the form of a black box. By using distribution-free uncertainty, such as conformal predictions, it may be challenging to discern between epistemic and aleatoric uncertainties. Epistemic uncertainty refers to uncertainty arising from a lack of knowledge or statistical evidence.

[0025] On the other hand, aleatoric uncertainty refers to an inherent randomness of data. In aleatoric uncertainty, the uncertainty may be considered intrinsic to the data generation process, and thus may be irreducible. Furthermore, in aleatoric uncertainty, a label may not depend on the input in a deterministic manner. Accordingly, even if the process that generates labels Y from inputs X is known, complete certainty over Y may not be achieved, but rather a probability distribution over the possible labels. For instance, a label may not indicate a specific point estimate for a single class but rather may indicate a probability over the space of possible classes for each input. This may, for example, occur when a group of different people label a particular instance. The Seyfarth Ref. No.72178-006653 5 313495666v.1Qualcomm Ref. No.2309552WO different people may label the particular instance differently, resulting in a probability distribution corresponding to labels of the different people.

[0026] To address these and other challenges, aspects of the present disclosure are directed to uncertainty estimation based on a bounded conditional entropy. An expected size of a prediction set in conformal prediction may be determined. In various aspects, a distribution-free upper-bound may be determined based on conformal prediction and Fano’s inequality. In some aspects, the upper-bound may be determined based on conformal prediction and data processing inequality (DPI).

[0027] Particular aspects of the subject matter described in this disclosure can be implemented to realize one or more of the following potential advantages. In some examples, the described techniques for estimating a prediction set in conformal prediction may increase model accuracy and user confidence in the ML model output.

[0028] FIGURE 1 illustrates an example implementation of a system-on-a-chip (SOC) 100, which may include a central processing unit (CPU) 102 or a multi-core CPU configured for determining an upper-bound of uncertainty estimation. Variables (e.g., neural signals and synaptic weights), system parameters associated with a computational device (e.g., neural network with weights), delays, frequency bin information, and task information may be stored in a memory block associated with a neural processing unit (NPU) 108, in a memory block associated with a CPU 102, in a memory block associated with a graphics processing unit (GPU) 104, in a memory block associated with a digital signal processor (DSP) 106, in a memory block 118, or may be distributed across multiple blocks. Instructions executed at the CPU 102 may be loaded from a program memory associated with the CPU 102 or may be loaded from a memory block 118.

[0029] The SOC 100 may also include additional processing blocks tailored to specific functions, such as a GPU 104, a DSP 106, a connectivity block 110, which may include fifth generation (5G) connectivity, fourth generation long term evolution (4G LTE) connectivity, Wi-Fi connectivity, USB connectivity, Bluetooth connectivity, and the like, and a multimedia processor 112 that may, for example, detect and recognize gestures. In one implementation, the NPU 108 is implemented in the CPU 102, DSP 106, and / or GPU 104. The SOC 100 may also include a sensor processor 114, image Seyfarth Ref. No.72178-006653 6 313495666v.1Qualcomm Ref. No.2309552WO signal processors (ISPs) 116, and / or navigation module 120, which may include a global positioning system.

[0030] The SOC 100 may be based on an ARM instruction set. In aspects of the present disclosure, the instructions loaded into the general-purpose processor 102 may include code to receive, an artificial neural network (ANN) model and a calibration dataset. The instructions loaded into the general-purpose processor 102 may also include code to compute an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction. The instructions loaded into the general-purpose processor 102 may also include code to estimate the conditional entropy of the ANN model based on the upper-bound.

[0031] Deep learning architectures may perform an object recognition task by learning to represent inputs at successively higher levels of abstraction in each layer, thereby building up a useful feature representation of the input data. In this way, deep learning may address a significant bottleneck of traditional machine learning. Prior to the advent of deep learning, a machine learning approach to an object recognition problem may have relied heavily on human engineered features, perhaps in combination with a shallow classifier. A shallow classifier may be a two-class linear classifier, for example, in which a weighted sum of the feature vector components may be compared with a threshold to predict to which class the input belongs. Human engineered features may be templates or kernels tailored to a specific problem domain by engineers with domain expertise. Deep learning architectures, in contrast, may learn to represent features that are similar to what a human engineer might design, but through training. Furthermore, a deep network may learn to represent and recognize new types of features that a human might not have considered.

[0032] A deep learning architecture may learn a hierarchy of features. If presented with visual data, for example, the first layer may learn to recognize relatively simple features, such as edges, in the input stream. In another example, if presented with auditory data, the first layer may learn to recognize spectral power in specific frequencies. The second layer, taking the output of the first layer as input, may learn to recognize combinations of features, such as simple shapes for visual data or combinations of sounds for auditory data. For instance, higher layers may learn to Seyfarth Ref. No.72178-006653 7 313495666v.1Qualcomm Ref. No.2309552WO represent complex shapes in visual data or words in auditory data. Still higher layers may learn to recognize common visual objects or spoken phrases.

[0033] Deep learning architectures may perform especially well when applied to problems that have a natural hierarchical structure. For example, the classification of motorized vehicles may benefit from first learning to recognize wheels, windshields, and other features. These features may be combined at higher layers in different ways to recognize cars, trucks, and airplanes.

[0034] Neural networks may be designed with a variety of connectivity patterns. In feed-forward networks, information is passed from lower to higher layers, with each neuron in a given layer communicating to neurons in higher layers. A hierarchical representation may be built up in successive layers of a feed-forward network, as described above. Neural networks may also have recurrent or feedback (also called top- down) connections. In a recurrent connection, the output from a neuron in a given layer may be communicated to another neuron in the same layer. A recurrent architecture may be helpful in recognizing patterns that span more than one of the input data chunks that are delivered to the neural network in a sequence. A connection from a neuron in a given layer to a neuron in a lower layer is called a feedback (or top-down) connection. A network with many feedback connections may be helpful when the recognition of a high-level concept may aid in discriminating the particular low-level features of an input.

[0035] The connections between layers of a neural network may be fully connected or locally connected. FIGURE 2A illustrates an example of a fully connected neural network 202. In a fully connected neural network 202, a neuron in a first layer may communicate its output to every neuron in a second layer, so that each neuron in the second layer will receive input from every neuron in the first layer. FIGURE 2B illustrates an example of a locally connected neural network 204. In a locally connected neural network 204, a neuron in a first layer may be connected to a limited number of neurons in the second layer. More generally, a locally connected layer of the locally connected neural network 204 may be configured so that each neuron in a layer will have the same or a similar connectivity pattern, but with connections strengths that may have different values (e.g., 210, 212, 214, and 216). The locally connected connectivity pattern may give rise to spatially distinct receptive fields in a higher layer because the Seyfarth Ref. No.72178-006653 8 313495666v.1Qualcomm Ref. No.2309552WO higher layer neurons in a given region may receive inputs that are tuned through training to the properties of a restricted portion of the total input to the network.

[0036] One example of a locally connected neural network is a convolutional neural network. FIGURE 2C illustrates an example of a convolutional neural network 206. The convolutional neural network 206 may be configured such that the connection strengths associated with the inputs for each neuron in the second layer are shared (e.g., 208). Convolutional neural networks may be well suited to problems in which the spatial location of inputs is meaningful.

[0037] One type of convolutional neural network is a deep convolutional network (DCN). FIGURE 2D illustrates a detailed example of a DCN 200 designed to recognize visual features from an image 226 input from an image capturing device 230, such as a car-mounted camera. The DCN 200 of the current example may be trained to identify traffic signs and a number provided on the traffic sign. Of course, the DCN 200 may be trained for other tasks, such as identifying lane markings or identifying traffic lights.

[0038] The DCN 200 may be trained with supervised learning. During training, the DCN 200 may be presented with an image, such as the image 226 of a speed limit sign, and a forward pass may then be computed to produce an output 222. The DCN 200 may include a feature extraction section and a classification section. Upon receiving the image 226, a convolutional layer 232 may apply convolutional kernels (not shown) to the image 226 to generate a first set of feature maps 218. As an example, the convolutional kernel for the convolutional layer 232 may be a 5x5 kernel that generates 28x28 feature maps. In the present example, because four different feature maps are generated in the first set of feature maps 218, four different convolutional kernels were applied to the image 226 at the convolutional layer 232. The convolutional kernels may also be referred to as filters or convolutional filters.

[0039] The first set of feature maps 218 may be subsampled by a max pooling layer (not shown) to generate a second set of feature maps 220. The max pooling layer reduces the size of the first set of feature maps 218. That is, a size of the second set of feature maps 220, such as 14x14, is less than the size of the first set of feature maps 218, such as 28x28. The reduced size provides similar information to a subsequent layer while reducing memory consumption. The second set of feature maps 220 may be Seyfarth Ref. No.72178-006653 9 313495666v.1Qualcomm Ref. No.2309552WO further convolved via one or more subsequent convolutional layers (not shown) to generate one or more subsequent sets of feature maps (not shown).

[0040] In the example of FIGURE 2D, the second set of feature maps 220 is convolved to generate a first feature vector 224. Furthermore, the first feature vector 224 is further convolved to generate a second feature vector 228. Each feature of the second feature vector 228 may include a number that corresponds to a possible feature of the image 226, such as “sign,” “60,” and “100.” A softmax function (not shown) may convert the numbers in the second feature vector 228 to a probability. As such, an output 222 of the DCN 200 may be a probability of the image 226 including one or more features.

[0041] In the present example, the probabilities in the output 222 for “sign” and “60” are higher than the probabilities of the others of the output 222, such as “30,” “40,” “50,” “70,” “80,” “90,” and “100”. Before training, the output 222 produced by the DCN 200 may likely be incorrect. Thus, an error may be calculated between the output 222 and a target output. The target output is the ground truth of the image 226 (e.g., “sign” and “60”). The weights of the DCN 200 may then be adjusted so the output 222 of the DCN 200 is more closely aligned with the target output.

[0042] To adjust the weights, a learning algorithm may compute a gradient vector for the weights. The gradient may indicate an amount that an error would increase or decrease if the weight were adjusted. At the top layer, the gradient may correspond directly to the value of a weight connecting an activated neuron in the penultimate layer and a neuron in the output layer. In lower layers, the gradient may depend on the value of the weights and on the computed error gradients of the higher layers. The weights may then be adjusted to reduce the error. This manner of adjusting the weights may be referred to as “back propagation” as it involves a “backward pass” through the neural network.

[0043] In practice, the error gradient of weights may be calculated over a small number of examples, so that the calculated gradient approximates the true error gradient. This approximation method may be referred to as stochastic gradient descent. Stochastic gradient descent may be repeated until the achievable error rate of the entire system has stopped decreasing or until the error rate has reached a target level. After Seyfarth Ref. No.72178-006653 10 313495666v.1Qualcomm Ref. No.2309552WO learning, the DCN 200 may be presented with new images (e.g., the speed limit sign of the image 226) and a forward pass through the DCN 200 may yield an output 222 that may be considered an inference or a prediction of the DCN 200.

[0044] Deep belief networks (DBNs) are probabilistic models comprising multiple layers of hidden nodes. DBNs may be used to extract a hierarchical representation of training datasets. A DBN may be obtained by stacking up layers of Restricted Boltzmann Machines (RBMs). An RBM is a type of artificial neural network that can learn a probability distribution over a set of inputs. Because RBMs can learn a probability distribution in the absence of information about the class to which each input should be categorized, RBMs are often used in unsupervised learning. Using a hybrid unsupervised and supervised paradigm, the bottom RBMs of a DBN may be trained in an unsupervised manner and may serve as feature extractors, and the top RBM may be trained in a supervised manner (on a joint distribution of inputs from the previous layer and target classes) and may serve as a classifier.

[0045] DCNs are networks of convolutional networks, configured with additional pooling and normalization layers. DCNs have achieved state-of-the-art performance on many tasks. DCNs can be trained using supervised learning in which both the input and output targets are known for many exemplars and are used to modify the weights of the network by use of gradient descent methods.

[0046] DCNs may be feed-forward networks. In addition, as described above, the connections from a neuron in a first layer of a DCN to a group of neurons in the next higher layer are shared across the neurons in the first layer. The feed-forward and shared connections of DCNs may be exploited for fast processing. The computational burden of a DCN may be much less, for example, than that of a similarly sized neural network that comprises recurrent or feedback connections.

[0047] The processing of each layer of a convolutional network may be considered a spatially invariant template or basis projection. If the input is first decomposed into multiple channels, such as the red, green, and blue channels of a color image, then the convolutional network trained on that input may be considered three-dimensional, with two spatial dimensions along the axes of the image and a third dimension capturing color information. The outputs of the convolutional connections may be considered to Seyfarth Ref. No.72178-006653 11 313495666v.1Qualcomm Ref. No.2309552WO form a feature map in the subsequent layer, with each element of the feature map (e.g., 220) receiving input from a range of neurons in the previous layer (e.g., feature maps 218) and from each of the multiple channels. The values in the feature map may be further processed with a non-linearity, such as a rectification, max(0, x). Values from adjacent neurons may be further pooled, which corresponds to down sampling, and may provide additional local invariance and dimensionality reduction. Normalization, which corresponds to whitening, may also be applied through lateral inhibition between neurons in the feature map.

[0048] FIGURE 3 is a block diagram illustrating a DCN 350. The DCN 350 may include multiple different types of layers based on connectivity and weight sharing. As shown in FIGURE 3, the DCN 350 includes the convolution blocks 354A, 354B. Each of the convolution blocks 354A, 354B may be configured with a convolution layer (CONV) 356, a normalization layer (LNorm) 358, and a max pooling layer (MAX POOL) 360.

[0049] Although only two of the convolution blocks 354A, 354B are shown, the present disclosure is not so limiting, and instead, any number of the convolution blocks 354A, 354B may be included in the DCN 350 according to design preference.

[0050] The convolution layers 356 may include one or more convolutional filters, which may be applied to the input data to generate a feature map. The normalization layer 358 may normalize the output of the convolution filters. For example, the normalization layer 358 may provide whitening or lateral inhibition. The max pooling layer 360 may provide down sampling aggregation over space for local invariance and dimensionality reduction.

[0051] The parallel filter banks, for example, of a deep convolutional network may be loaded on a CPU 102 or GPU 104 of an SOC 100 (e.g., FIGURE 1) to achieve high performance and low power consumption. In alternative embodiments, the parallel filter banks may be loaded on the DSP 106 or an ISP 116 of an SOC 100. In addition, the DCN 350 may access other processing blocks that may be present on the SOC 100, such as sensor processor 114 and navigation module 120, dedicated, respectively, to sensors and navigation. Seyfarth Ref. No.72178-006653 12 313495666v.1Qualcomm Ref. No.2309552WO

[0052] The DCN 350 may also include one or more fully connected layers 362 (FC1 and FC2). The DCN 350 may further include a logistic regression (LR) layer 364. Between each layer 356, 358, 360, 362, 364 of the DCN 350 are weights (not shown) that are to be updated. The output of each of the layers (e.g., 356, 358, 360, 362, 364) may serve as an input of a succeeding one of the layers (e.g., 356, 358, 360, 362, 364) in the DCN 350 to learn hierarchical feature representations from input data 352 (e.g., images, audio, video, sensor data and / or other input data) supplied at the first of the convolution blocks 354A. The output of the DCN 350 is a classification score 366 for the input data 352. The classification score 366 may be a set of probabilities, where each probability is the probability of the input data including a feature from a set of features.

[0053] FIGURE 4 is a block diagram illustrating an exemplary software architecture 400 that may modularize artificial intelligence (AI) functions. Using the architecture 400, applications may be designed that may cause various processing blocks of an SOC 420 (for example a CPU 422, a DSP 424, a GPU 426 and / or an NPU 428) (which may be similar to SOC 100 of FIGURE 1) to support uncertainty estimation for an AI application 402, according to aspects of the present disclosure. The architecture 400 may, for example, be included in a computational device, such as a smartphone.

[0054] The AI application 402 may be configured to call functions defined in a user space 404 that may, for example, provide for the detection and recognition of a scene indicative of the location at which the computational device including the architecture 400 currently operates. The AI application 402 may, for example, configure a microphone and a camera differently depending on whether the recognized scene is an office, a lecture hall, a restaurant, or an outdoor setting such as a lake. The AI application 402 may make a request to compiled program code associated with a library defined in an AI function application programming interface (API) 406. This request may ultimately rely on the output of a deep neural network configured to provide an inference response based on video and positioning data, for example.

[0055] The run-time engine 408, which may be compiled code of a runtime framework, may be further accessible to the AI application 402. The AI application 402 may cause the run-time engine 408, for example, to request an inference at a particular time interval or triggered by an event detected by the user interface of the AI application Seyfarth Ref. No.72178-006653 13 313495666v.1Qualcomm Ref. No.2309552WO 402. When caused to provide an inference response, the run-time engine 408 may in turn send a signal to an operating system in an operating system (OS) space 410, such as a Kernel 412, running on the SOC 420. In some examples, the Kernel 412 may be a LINUX Kernel. The operating system, in turn, may cause a continuous relaxation of quantization to be performed on the CPU 422, the DSP 424, the GPU 426, the NPU 428, or some combination thereof. The CPU 422 may be accessed directly by the operating system, and other processing blocks may be accessed through a driver, such as a driver 414, 416, or 418 for, respectively, the DSP 424, the GPU 426, or the NPU 428. In the exemplary example, the deep neural network may be configured to run on a combination of processing blocks, such as the CPU 422, the DSP 424, and the GPU 426, or may be run on the NPU 428.

[0056] As described, aspects of the present disclosure are directed to uncertainty estimation using conformal prediction.

[0057] Conformal prediction may provide uncertainty estimates in scenarios such as when a pre-trained model is provided but the data distribution is inaccessible. In conformal prediction, for a given input output pair(^^^^ ^^ ^^ ^^, ^^^^ ^^ ^^ ^^)at test time, using a calibration dataset ^^ of size ^^, a prediction set ^^( ^^^^ ^^ ^^ ^^) may be constructed that includes the correct prediction ( ^^^^ ^^ ^^ ^^) as follows: (1)where ^^ represents a user-defined threshold. The user-defined threshold may indicate a limit on acceptable model accuracy, which may provide some assurance of a level of model performance. Accordingly, a machine learning (ML) model may be calibrated such that the ML model provides a set of predictions rather than a point estimate that includes the correct prediction within a certain probability (e.g., based on the user- defined threshold). That is, the prediction set may include multiple estimates for a given input. However, where the prediction set ^^(^^^^ ^^ ^^ ^^)is larger, the uncertainty may likewise be larger. Conversely, where the prediction set ^^(^^^^ ^^ ^^ ^^)is smaller, the uncertainty may also be smaller (Small → Small uncertainty).

[0058] In various aspects of the present disclosure, the conformal prediction (Equation 1) may be linked with an inequality that relates the conditional entropy of the Seyfarth Ref. No.72178-006653 14 313495666v.1Qualcomm Ref. No.2309552WO data with the probability of an error. In other words, the probability that the prediction set does not include the correct prediction (e.g., the correct class) may be determined.

[0059] Given that ^^ and ^^ are random variables, and ^^ = ^^(^^), where ^^ is a point estimate given by a ML model ^^, an error rate ^^ = ^^( ^^ ≠ ^^), and a binary entropyℎ ^^( ^^), the inequality (e.g., Fano’s inequality) may be expressed as:H( ^^| ^^) ≤ ℎ ^^( ^^) + ^^ log(|Y| − 1), (2)where H represents the conditional entropy and presents the probability of a mistake in classification.

[0060] Considering an event ^^ ={^^ ∈ ^^(^^)}, where ^^ ∈{0,1}, and the conformal prediction’s user-defined threshold, an upper-bound on the conditional entropy H(^^| ^^)may be constructed using Equation 1 and may be expressed as follows: ^^(^^| ^^, ^^)≤ ℎ^^(^^)+ ^^ ^^(log (| ^^|)− | ^^( ^^)|)) + ^^(log(|^^(^^)|))(1− ^^ +1^^+1). (3)

[0061] Equation 3 may be derived similar to Fano’s inequality in Equation 1, by defining an error as the probability that the prediction set ^^( ^^^^ ^^ ^^ ^^) does not include the correct class. Thus, the conformal prediction results, which bound the probability of the event(^^^^ ^^ ^^ ^^)in ^^(^^^^ ^^ ^^ ^^), may be used to construct an upper-bound on the conditional entropy (H(^^| ^^)) by using a calibration dataset ^^. Thus, the conditional entropy (H(^^| ^^)) of the data-generating distribution may be estimated using a pre-trained ML model fitted to such distribution, without access to direct information about the data distribution besides samples (dataset D) and without any assumptions on the ML model, which may comprise (but is not limited to) a black-box model, for instance.

[0062] In Equation 3, the probability of an error (e.g., mistake in classification) may replace the probability that the prediction set ^^(^^^^ ^^ ^^ ^^)includes a correct class (in Equation 1). Thus, the conformal prediction results, which bound the probability of the event may be used to construct an upper-bound on the conditional entropy given the calibration dataset ^^. Thus, the conditional entropy of the ML model may be estimated using a pre-trained ML model (e.g., black box model) without access to the data distribution or ML model distribution. Seyfarth Ref. No.72178-006653 15 313495666v.1Qualcomm Ref. No.2309552WO

[0063] Accordingly, given a pre-trained ML model and a calibration dataset, the expected size of the prediction set may be estimated using conformal prediction and the upper-bound may determine the estimated conditional entropy. The bound may provide information on how difficult the problem investigated may be or quantify the uncertainty.

[0064] FIGURE 5 is a flow diagram illustrating a processor-implemented method 500 for uncertainty estimation, in accordance with aspects of the present disclosure. The processor-implemented method 500 may be performed by at least one processor such as the CPU (e.g., 102, 422), the GPU (e.g., 104, 426), and / or other processing units (e.g., DSP 424 or NPU 428), for example.

[0065] As shown in FIGURE 5, at block 502, the processor receives an artificial neural network (ANN) model and a calibration dataset. The ANN may, for example, comprise a deep neural network such as the DCN 350 (shown in FIGURE 3). The ANN may be pre-trained using a dataset that is not accessible. In some examples, the ANN may be implemented in a federated learning framework, for instance.

[0066] At block 504, the processor computes an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction. For instance, as described, the conformal prediction (Equation 1) may be linked with an inequality that relates the conditional entropy of the data with the probability of an error. In other words, the probability that the prediction set does not include the correct prediction (e.g., the correct class) may be determined. The conformal prediction results, which bound the probability of the event ( ^^^^ ^^ ^^ ^^) in ^^( ^^^^ ^^ ^^ ^^), may be used to construct an upper-bound on the conditional entropy (H(^^| ^^)) by using the calibration dataset ^^. In some aspects, the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold. In some aspects, the upper-bound of the conditional entropy may be computed based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size.

[0067] At block 506, the processor estimates the conditional entropy of the model based on the upper-bound. For example, as, described, the conditional entropy of the ML model may be estimated using a pre-trained ML model (e.g., black box model) Seyfarth Ref. No.72178-006653 16 313495666v.1Qualcomm Ref. No.2309552WO without access to the data distribution or ML model distribution based on the upper- bound.

[0068] Implementation examples are provided in the following numbered clauses. 1. An apparatus, comprising: at least one memory; and at least one processor coupled to the at least one memory, the at least one processor configured to: receive an artificial neural network (ANN) model and a calibration dataset; compute, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and estimate the conditional entropy of the ANN model based on the upper- bound. 2. The apparatus of clause 1, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold. 3. The apparatus of clause 1 or 2, in which the at least one processor is further configured to estimate an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set. 4. The apparatus of any of clauses 1-3, in which the at least one processor is further configured to compute an estimate of a prediction set size using the conformal prediction. 5. The apparatus of any of clauses 1-4, in which the at least one processor is further configured to compute the upper-bound of the conditional entropy based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size. 6. The apparatus of any of clauses 1-5, in which the ANN model is pre-trained using a training dataset that is inaccessible. Seyfarth Ref. No.72178-006653 17 313495666v.1Qualcomm Ref. No.2309552WO 7. The apparatus of any of clauses 1-6, in which the data distribution of the ANN model has an aleatoric uncertainty. 8. A processor-implemented method performed by one or more processors, the processor-implemented method comprising: receiving an artificial neural network (ANN) model and a calibration dataset; computing, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and estimating the conditional entropy of the ANN model based on the upper-bound. 9. The processor-implemented method of clause 8, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold. 10. The processor-implemented method of clause 8 or 9, further comprising estimating an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set. 11. The processor-implemented method of any of clauses 8-10, further comprising computing an estimate of a prediction set size using the conformal prediction. 12. The processor-implemented method of any of clauses 8-11, in which the upper- bound of the conditional entropy is computed based on a binary entropy and a first quantity of potential labels and the estimate of the prediction set size. 13. The processor-implemented method of any of clauses 8-12, in which the ANN model is pre-trained using a training dataset that is inaccessible. 14. The processor-implemented method of any of clauses 8-13, in which the data distribution of the ANN model has an aleatoric uncertainty. 15. A non-transitory computer-readable medium having program code recorded thereon, the program code executed by a processor and comprising: program code to receive an artificial neural network (ANN) model and a calibration dataset; Seyfarth Ref. No.72178-006653 18 313495666v.1Qualcomm Ref. No.2309552WO program code to compute, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and program code to estimate the conditional entropy of the ANN model based on the upper-bound. 16. The non-transitory computer-readable medium of clause 15, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold. 17. The non-transitory computer-readable medium of clause 15 or 16, in which the program code comprises program code to estimate an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set. 18. The non-transitory computer-readable medium of any of clauses 15-17, in which the program code comprises program code to compute an estimate of a prediction set size using the conformal prediction. 19. The non-transitory computer-readable medium of any of clauses 15-18, in which the program code comprises program code to compute the upper-bound of the conditional entropy based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size. 20. The non-transitory computer-readable medium of any of clauses 15-19, in which the ANN model is pre-trained using a training dataset that is inaccessible. 21. The non-transitory computer-readable medium of any of clauses 15-20, in which the data distribution of the ANN model has an aleatoric uncertainty. 22. An apparatus, comprising: means for receiving an artificial neural network (ANN) model and a calibration dataset; means for computing, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and Seyfarth Ref. No.72178-006653 19 313495666v.1Qualcomm Ref. No.2309552WO means for estimating the conditional entropy of the ANN model based on the upper-bound. 23. The apparatus of clause 22, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold. 24. The apparatus of clause 22 or 23, further comprising means for estimating an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set. 25. The apparatus of any of clauses 22-24, further comprising means for computing an estimate of a prediction set size using the conformal prediction. 26. The apparatus of any of clauses 22-25, further comprising means for computing the upper-bound of the conditional entropy based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size. 27. The apparatus of any of clauses 22-26, in which the ANN model is pre-trained using a training dataset that is inaccessible. 28. The apparatus of any of clauses 22-27, in which the data distribution of the ANN model has an aleatoric uncertainty.

[0069] The various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and / or software component(s) and / or module(s), including, but not limited to, a circuit, an application specific integrated circuit (ASIC), or processor. Generally, where there are operations illustrated in the figures, those operations may have corresponding counterpart means-plus-function components with similar numbering.

[0070] As used, the term “determining” encompasses a wide variety of actions. For example, “determining” may include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database, or another data Seyfarth Ref. No.72178-006653 20 313495666v.1Qualcomm Ref. No.2309552WO structure), ascertaining and the like. Additionally, “determining” may include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Furthermore, “determining” may include resolving, selecting, choosing, establishing, and the like.

[0071] As used, a phrase referring to “at least one of” a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover: a, b, c, a-b, a-c, b-c, and a-b-c.

[0072] The various illustrative logical blocks, modules and circuits described in connection with the present disclosure may be implemented or performed with a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array signal (FPGA) or other programmable logic device (PLD), discrete gate or transistor logic, discrete hardware components or any combination thereof designed to perform the functions described. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any commercially available processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration.

[0073] The steps of a method or algorithm described in connection with the present disclosure may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in any form of storage medium that is known in the art. Some examples of storage media that may be used include random access memory (RAM), read only memory (ROM), flash memory, erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, a hard disk, a removable disk, a CD-ROM and so forth. A software module may comprise a single instruction, or many instructions, and may be distributed over several different code segments, among different programs, and across multiple storage media. A storage medium may be coupled to a processor such that the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. Seyfarth Ref. No.72178-006653 21 313495666v.1Qualcomm Ref. No.2309552WO

[0074] The methods disclosed comprise one or more steps or actions for achieving the described method. The method steps and / or actions may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of steps or actions is specified, the order and / or use of specific steps and / or actions may be modified without departing from the scope of the claims.

[0075] The functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in hardware, an example hardware configuration may comprise a processing system in a device. The processing system may be implemented with a bus architecture. The bus may include any number of interconnecting buses and bridges depending on the specific application of the processing system and the overall design constraints. The bus may link together various circuits including a processor, machine-readable media, and a bus interface. The bus interface may be used to connect a network adapter, among other things, to the processing system via the bus. The network adapter may be used to implement signal processing functions. For certain aspects, a user interface (e.g., keypad, display, mouse, joystick, etc.) may also be connected to the bus. The bus may also link various other circuits such as timing sources, peripherals, voltage regulators, power management circuits, and the like, which are well known in the art, and therefore, will not be described any further.

[0076] The processor may be responsible for managing the bus and general processing, including the execution of software stored on the machine-readable media. The processor may be implemented with one or more general-purpose and / or special- purpose processors. Examples include microprocessors, microcontrollers, DSP processors, and other circuitry that can execute software. Software shall be construed broadly to mean instructions, data, or any combination thereof, whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise. Machine-readable media may include, by way of example, random access memory (RAM), flash memory, read only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable Read-only memory (EEPROM), registers, magnetic disks, optical disks, hard drives, or any other suitable storage medium, or any combination Seyfarth Ref. No.72178-006653 22 313495666v.1Qualcomm Ref. No.2309552WO thereof. The machine-readable media may be embodied in a computer-program product. The computer-program product may comprise packaging materials.

[0077] In a hardware implementation, the machine-readable media may be part of the processing system separate from the processor. However, as those skilled in the art will readily appreciate, the machine-readable media, or any portion thereof, may be external to the processing system. By way of example, the machine-readable media may include a transmission line, a carrier wave modulated by data, and / or a computer product separate from the device, all which may be accessed by the processor through the bus interface. Alternatively, or in addition, the machine-readable media, or any portion thereof, may be integrated into the processor, such as the case may be with cache and / or general register files. Although the various components discussed may be described as having a specific location, such as a local component, they may also be configured in various ways, such as certain components being configured as part of a distributed computing system.

[0078] The processing system may be configured as a general-purpose processing system with one or more microprocessors providing the processor functionality and external memory providing at least a portion of the machine-readable media, all linked together with other supporting circuitry through an external bus architecture. Alternatively, the processing system may comprise one or more neuromorphic processors for implementing the neuron models and models of neural systems described. As another alternative, the processing system may be implemented with an application specific integrated circuit (ASIC) with the processor, the bus interface, the user interface, supporting circuitry, and at least a portion of the machine-readable media integrated into a single chip, or with one or more field programmable gate arrays (FPGAs), programmable logic devices (PLDs), controllers, state machines, gated logic, discrete hardware components, or any other suitable circuitry, or any combination of circuits that can perform the various functionality described throughout this disclosure. Those skilled in the art will recognize how best to implement the described functionality for the processing system depending on the particular application and the overall design constraints imposed on the overall system.

[0079] The machine-readable media may comprise a number of software modules. The software modules include instructions that, when executed by the processor, cause Seyfarth Ref. No.72178-006653 23 313495666v.1Qualcomm Ref. No.2309552WO the processing system to perform various functions. The software modules may include a transmission module and a receiving module. Each software module may reside in a single storage device or be distributed across multiple storage devices. By way of example, a software module may be loaded into RAM from a hard drive when a triggering event occurs. During execution of the software module, the processor may load some of the instructions into cache to increase access speed. One or more cache lines may then be loaded into a general register file for execution by the processor. When referring to the functionality of a software module below, it will be understood that such functionality is implemented by the processor when executing instructions from that software module. Furthermore, it should be appreciated that aspects of the present disclosure result in improvements to the functioning of the processor, computer, machine, or other system implementing such aspects.

[0080] If implemented in software, the functions may be stored or transmitted over as one or more instructions or code on a computer-readable medium. Computer- readable media include both computer storage media and communication media including any medium that facilitates transfer of a computer program from one place to another. A storage medium may be any available medium that can be accessed by a computer. By way of example, and not limitation, such computer-readable media can comprise RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code in the form of instructions or data structures and that can be accessed by a computer. Additionally, any connection is properly termed a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared (IR), radio, and microwave, then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included in the definition of medium. Disk and disc, as used, include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray® disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Thus, in some aspects, computer-readable media may comprise non-transitory computer- readable media (e.g., tangible media). In addition, for other aspects computer-readable Seyfarth Ref. No.72178-006653 24 313495666v.1Qualcomm Ref. No.2309552WO media may comprise transitory computer- readable media (e.g., a signal). Combinations of the above should also be included within the scope of computer-readable media.

[0081] Thus, certain aspects may comprise a computer program product for performing the operations presented. For example, such a computer program product may comprise a computer-readable medium having instructions stored (and / or encoded) thereon, the instructions being executable by one or more processors to perform the operations described. For certain aspects, the computer program product may include packaging material.

[0082] Further, it should be appreciated that modules and / or other appropriate means for performing the methods and techniques described can be downloaded and / or otherwise obtained by a user terminal and / or base station as applicable. For example, such a device can be coupled to a server to facilitate the transfer of means for performing the methods described. Alternatively, various methods described can be provided via storage means (e.g., RAM, ROM, a physical storage medium such as a compact disc (CD) or floppy disk, etc.), such that a user terminal and / or base station can obtain the various methods upon coupling or providing the storage means to the device. Moreover, any other suitable technique for providing the methods and techniques described to a device can be utilized.

[0083] It is to be understood that the claims are not limited to the precise configuration and components illustrated above. Various modifications, changes, and variations may be made in the arrangement, operation, and details of the methods and apparatus described above without departing from the scope of the claims. Seyfarth Ref. No.72178-006653 25 313495666v.1

Claims

Qualcomm Ref. No.2309552WO CLAIMS WHAT IS CLAIMED IS:

1. An apparatus, comprising: at least one memory; and at least one processor coupled to the at least one memory, the at least one processor configured to: receive an artificial neural network (ANN) model and a calibration dataset; compute, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and estimate the conditional entropy of the ANN model based on the upper- bound.

2. The apparatus of claim 1, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold.

3. The apparatus of claim 2, in which the at least one processor is further configured to estimate an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set.

4. The apparatus of claim 2, in which the at least one processor is further configured to compute an estimate of a prediction set size using the conformal prediction.

5. The apparatus of claim 4, in which the at least one processor is further configured to compute the upper-bound of the conditional entropy based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size.

6. The apparatus of claim 1, in which the ANN model is pre-trained using a training dataset that is inaccessible. Seyfarth Ref. No.72178-006653 26 313495666v.1Qualcomm Ref. No.2309552WO 7. The apparatus of claim 1, in which the data distribution of the ANN model has an aleatoric uncertainty.

8. A processor-implemented method performed by one or more processors, the processor-implemented method comprising: receiving an artificial neural network (ANN) model and a calibration dataset; computing, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and estimating the conditional entropy of the ANN model based on the upper-bound.

9. The processor-implemented method of claim 8, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold.

10. The processor-implemented method of claim 9, further comprising estimating an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set.

11. The processor-implemented method of claim 9, further comprising computing an estimate of a prediction set size using the conformal prediction.

12. The processor-implemented method of claim 11, in which the upper-bound of the conditional entropy is computed based on a binary entropy and a first quantity of potential labels and the estimate of the prediction set size.

13. The processor-implemented method of claim 8, in which the ANN model is pre- trained using a training dataset that is inaccessible.

14. The processor-implemented method of claim 8, in which the data distribution of the ANN model has an aleatoric uncertainty.

15. A non-transitory computer-readable medium having program code recorded thereon, the program code executed by a processor and comprising: program code to receive an artificial neural network (ANN) model and a calibration dataset; Seyfarth Ref. No.72178-006653 27 313495666v.1Qualcomm Ref. No.2309552WO program code to compute, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and program code to estimate the conditional entropy of the ANN model based on the upper-bound.

16. The non-transitory computer-readable medium of claim 15, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold.

17. The non-transitory computer-readable medium of claim 16, in which the program code comprises program code to estimate an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set.

18. The non-transitory computer-readable medium of claim 16, in which the program code comprises program code to compute an estimate of a prediction set size using the conformal prediction.

19. The non-transitory computer-readable medium of claim 18, in which the program code comprises program code to compute the upper-bound of the conditional entropy based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size.

20. The non-transitory computer-readable medium of claim 15, in which the ANN model is pre-trained using a training dataset that is inaccessible.

21. The non-transitory computer-readable medium of claim 15, in which the data distribution of the ANN model has an aleatoric uncertainty.

22. An apparatus, comprising: means for receiving an artificial neural network (ANN) model and a calibration dataset; means for computing, by the ANN model, an upper-bound on a conditional entropy of a data distribution of the ANN model using conformal prediction; and Seyfarth Ref. No.72178-006653 28 313495666v.1Qualcomm Ref. No.2309552WO means for estimating the conditional entropy of the ANN model based on the upper-bound.

23. The apparatus of claim 22, in which the conformal prediction generates a prediction set having a probability of including a correct classification based on a predefined threshold.

24. The apparatus of claim 23, further comprising means for estimating an uncertainty of the data distribution of the ANN model based on the conditional entropy and a size of the prediction set.

25. The apparatus of claim 23, further comprising means for computing an estimate of a prediction set size using the conformal prediction.

26. The apparatus of claim 25, further comprising means for computing the upper- bound of the conditional entropy based on a binary entropy, a first quantity of potential labels, and the estimate of the prediction set size.

27. The apparatus of claim 22, in which the ANN model is pre-trained using a training dataset that is inaccessible.

28. The apparatus of claim 22, in which the data distribution of the ANN model has an aleatoric uncertainty. Seyfarth Ref. No.72178-006653 29 313495666v.1

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