Non-exchangeable conformal prediction with optimal transport

Abstract

A processor-implemented method of non-exchangeable conformal prediction for an artificial neural network (ANN) model includes receiving the ANN model with a calibration dataset and a set of test samples. Calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples. The calibration samples of the calibration set are reweighted using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples. A conformal prediction process is performed on the reweighted calibration samples to produce a set of confidence intervals.

Description

Qualcomm Ref. No.2407827WO NON-EXCHANGEABLE CONFORMAL PREDICTION WITH OPTIMAL TRANSPORT CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the benefit of Greece Patent Application No.20240100667, filed on September 30, 2024, and titled “NON-EXCHANGEABLE CONFORMAL PREDICTION WITH OPTIMAL TRANSPORT,” and Greece Patent Application No.20240100661, filed on September 27, 2024, and titled “NON- EXCHANGEABLE CONFORMAL PREDICTION WITH OPTIMAL TRANSPORT,” the disclosures of which are expressly incorporated by reference in their entireties. FIELD OF THE DISCLOSURE

[0002] Aspects of the present disclosure generally relate to uncertainty estimation inmachine learning models and more particularly to non-exchangeable conformal prediction with optimal transport. BACKGROUND

[0003] Artificial neural networks may comprise interconnected groups of artificialneurons (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 increasingdemand 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,Seyfarth Ref. No. 72178-006717 1315930806v.1Qualcomm Ref. No.2407827WO uncertainty with respect to classification results may hinder confidence in the neural network model. Thus, it may be desirable to estimate the uncertainty of the neural network model. SUMMARY

[0005] In various aspects of the present disclosure, a processor-implementedmethod performed by at least one processor includes receiving an artificial neural network (ANN) model with a calibration dataset and a set of test samples. Calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples. The processor-implemented method also includes reweighting the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples. The processor-implemented method further includes performing a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

[0006] Some aspects of the present disclosure are directed to an apparatus. Theapparatus includes means for receiving an artificial neural network (ANN) model with a calibration dataset and a set of test samples. Calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples. The apparatus also includes means for reweighting the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples. The apparatus further includes means for performing a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

[0007] Various aspects of the present disclosure are directed to an apparatus. Theapparatus has 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 with a calibration dataset and a set of test samples. Calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples. The processor(s) is also configured to reweight the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples. TheSeyfarth Ref. No. 72178-006717 2315930806v.1Qualcomm Ref. No.2407827WO processor(s) is further configured to perform a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

[0008] 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

[0009] The features, nature, and advantages of the present disclosure will becomemore apparent from the detailed description set forth below when taken in conjunction with the drawings in which like reference characters identify correspondingly throughout.

[0010] FIGURE 1 illustrates an example implementation of a neural network usinga system-on-a-chip (SOC), including a general-purpose processor in accordance with certain aspects of the present disclosure.

[0011] FIGURES 2A, 2B, and 2C are diagrams illustrating a neural network inaccordance with aspects of the present disclosure.

[0012] FIGURE 2D is a diagram illustrating an exemplary deep convolutionalnetwork (DCN) in accordance with aspects of the present disclosure.

[0013] FIGURE 3 is a block diagram illustrating an exemplary deep convolutionalnetwork (DCN) in accordance with aspects of the present disclosure.Seyfarth Ref. No. 72178-006717 3315930806v.1Qualcomm Ref. No.2407827WO

[0014] FIGURE 4 is a block diagram illustrating an exemplary software architecturethat may modularize artificial intelligence (AI) functions, in accordance with aspects of the present disclosure.

[0015] FIGURE 5 illustrates a processor-implemented method for non-exchangeable conformal prediction, in accordance with aspects of the present disclosure. DETAILED DESCRIPTION

[0016] The detailed description set forth below, in connection with the appendeddrawings, 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.

[0017] Based on the teachings, one skilled in the art should appreciate that the scopeof 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.

[0018] The word “exemplary” is used to mean “serving as an example, instance, orillustration.” Any aspect described as “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects.

[0019] Although particular aspects are described, many variations and permutationsof 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 notSeyfarth Ref. No. 72178-006717 4315930806v.1Qualcomm Ref. No.2407827WO intended to be limited to particular benefits, uses or objectives. Rather, aspects of the 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.

[0020] Uncertainty estimation for machine learning (ML) models may involvespecific 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.

[0021] Recently, conformal prediction has become an area of exploration for adistribution-free approach to uncertainty quantification. Conformal prediction is an 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.

[0022] Conformal prediction is a distribution-free uncertainty quantification methodthat has gained popularity in the machine learning community due to its finite-sample guarantees and ease of use.

[0023] Given the many useful applications of artificial neural networks includinggenerative artificial intelligence and other large language models, for instance, there is increasing demand for use thereof on edge devices such as smartphones or in sensitive environments such as medical diagnostics. Because the training datasets for such models may be very large and / or may include sensitive data, the artificial neural network models may be deployed without access to a training dataset used to train the deployed model. As a result, independently determining the accuracy of outputs of the deployed model may not be possible. In some cases, such as the medical diagnostic setting, inaccurate results may have significant consequences, and thus, may impact the usability of such models.

[0024] Many of the artificial neural network models may produce outputs that aresingle point predictions (e.g., a classification). Conformal prediction techniques may adapt the artificial neural network model to generate a range of predictions referred to asSeyfarth Ref. No. 72178-006717 5315930806v.1Qualcomm Ref. No.2407827WO a prediction region. Conformal prediction employs a calibration dataset including data samples not seen by the pre-trained model to generate the predicted region (may also be referred to as a “prediction set”). The predicted region may be guaranteed to include the correct prediction according to a user-defined confidence level (e.g., 95%) set in view of a trade-off with the size of the calibration dataset. The higher the confidence level in turn uses a larger calibration dataset (and thus more memory consumption).

[0025] A common variant of conformal prediction is split conformal prediction.Split conformal prediction is computationally efficient as it involves collecting statistics of the model predictions on some calibration data not yet seen by the model. However, the computational efficiency may only hold if the calibration and test data are exchangeable. That is, conformal prediction operates under the assumption that the calibration and test data (e.g., real world data) are exchangeable.

[0026] Exchangeability refers to the property of a probability distribution to remainunchanged under permutations of the elements in a sequence. Exchangeability is a weaker requirement than the more common independent and identically distributed (i.i.d.) assumption, but still implies that data samples are identically distributed. However, invariance of a probability distribution is a condition that is difficult to verify and may often be violated in practice due to distribution shifts, for example.

[0027] Distribution drift (may also be referred to as “distribution shift”) may refer toa change in statistical properties of a data distribution over time. The statistical properties of the data encountered during model training differ for the data observed during testing or deployment. Types of distribution shifts may include covariate shift, label shift, and concept shift. In covariate shift (data drift), the distribution of in the input data feature changes, but the relationship between the input and outputs remains the same. In label shift, the distribution of the output labels changes, but the input distribution remains the same. In concept shift, the relationship between the inputs and outputs changes. In any case, the distribution shift may result in reduced performance of a machine learning model because the models were trained on data that may no longer represent the environment.

[0028] To address these and other issues, aspects of the present disclosure aredirected to adapting conformal prediction for potential distribution shifts using optimalSeyfarth Ref. No. 72178-006717 6315930806v.1Qualcomm Ref. No.2407827WO transport techniques. In some aspects, a gap in coverage caused by a distribution shift may be quantified.

[0029] Particular aspects of the subject matter described in this disclosure can beimplemented to realize one or more of the following potential advantages. In some examples, the described techniques (e.g., reweighting calibration samples of the calibration dataset using an optimal transport and calibrating the artificial neural network (ANN) model based on the reweighted calibration samples to produce a calibrated ANN model) may improve model accuracy.

[0030] Moreover, the described techniques may be broadly applicable to artificialneural network models such as deep convolutional networks (DCNs), as well as large language models, vision transformer models, generative models, and other models. Further, the described techniques may be applicable to a wide range of tasks such as uncertainty quantification for guard models, autonomous driving, and uncertainty quantification for object detection. Moreover, the described techniques may be employed in safety critical domains and healthcare settings.

[0031] 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 non-exchangeable conformal prediction. 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.

[0032] The SOC 100 may also include additional processing blocks tailored tospecific 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, andSeyfarth Ref. No. 72178-006717 7315930806v.1Qualcomm Ref. No.2407827WO 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 signal processors (ISPs) 116, and / or navigation module 120, which may include a global positioning system.

[0033] The SOC 100 may be based on an ARM, RISC-V (RISC-five), or anyreduced instruction set computing (RISC) architecture. 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 with a calibration dataset and a set of test samples. Calibration samples of the calibration dataset are non- exchangeable with selected test samples in the set of test samples. The general-purpose processor 102 may also include code to reweight the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates the set of test samples. The instructions loaded into the general-purpose processor 102 may further include code to perform a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

[0034] Deep learning architectures may perform an object recognition task bylearning 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 addresses a major 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.Seyfarth Ref. No. 72178-006717 8315930806v.1Qualcomm Ref. No.2407827WO

[0035] A deep learning architecture may learn a hierarchy of features. If presentedwith 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 represent complex shapes in visual data or words in auditory data. Still higher layers may learn to recognize common visual objects or spoken phrases.

[0036] Deep learning architectures may perform especially well when applied toproblems 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.

[0037] Neural networks may be designed with a variety of connectivity patterns. Infeed-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.

[0038] The connections between layers of a neural network may be fully connectedor 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 2BSeyfarth Ref. No. 72178-006717 9315930806v.1Qualcomm Ref. No.2407827WO 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 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.

[0039] One example of a locally connected neural network is a convolutional neuralnetwork. 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.

[0040] 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.

[0041] The DCN 200 may be trained with supervised learning. During training, theDCN 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.Seyfarth Ref. No. 72178-006717 10315930806v.1Qualcomm Ref. No.2407827WO

[0042] 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 further convolved via one or more subsequent convolutional layers (not shown) to generate one or more subsequent sets of feature maps (not shown).

[0043] In the example of FIGURE 2D, the second set of feature maps 220 isconvolved 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.

[0044] 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.

[0045] To adjust the weights, a learning algorithm may compute a gradient vectorfor 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.Seyfarth Ref. No. 72178-006717 11315930806v.1Qualcomm Ref. No.2407827WO

[0046] In practice, the error gradient of weights may be calculated over a smallnumber 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 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.

[0047] Deep belief networks (DBNs) are probabilistic models comprising multiplelayers of hidden nodes. DBNs may be used to extract a hierarchical representation of training data sets. 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.

[0048] DCNs are networks of convolutional networks, configured with additionalpooling 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.

[0049] DCNs may be feed-forward networks. In addition, as described above, theconnections 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.Seyfarth Ref. No. 72178-006717 12315930806v.1Qualcomm Ref. No.2407827WO

[0050] The processing of each layer of a convolutional network may be considereda 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 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.

[0051] FIGURE 3 is a block diagram illustrating a DCN 350. The DCN 350 mayinclude 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.

[0052] Although only two of the convolution blocks 354A, 354B are shown, thepresent 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.

[0053] 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.

[0054] The parallel filter banks, for example, of a deep convolutional network maybe loaded on a CPU 102 or GPU 104 of an SOC 100 (e.g., FIGURE 1) to achieve highSeyfarth Ref. No. 72178-006717 13315930806v.1Qualcomm Ref. No.2407827WO 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.

[0055] The DCN 350 may also include one or more fully connected layers 362 (FC1and 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.

[0056] FIGURE 4 is a block diagram illustrating an exemplary software architecture400 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 non-exchangeable conformal prediction 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.

[0057] The AI application 402 may be configured to call functions defined in a userspace 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 requestSeyfarth Ref. No. 72178-006717 14315930806v.1Qualcomm Ref. No.2407827WO 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.

[0058] The run-time engine 408, which may be compiled code of a runtimeframework, 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 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.

[0059] As described, aspects of the present disclosure are directed to adaptingconformal prediction for potential distribution shifts using optimal transport techniques. In some aspects, a gap in coverage caused by a distribution shift may be quantified.

[0060] A pre-trained model ^^: ^^ → ^^, maps input ^^ to an output ^^. The modelmay observe a new test point of the test distribution ^^^^+1 ∼ ^^, where ^^ represents thetest distribution.

[0061] A prediction set ^^(^^^^+1) is constructed such that the prediction set containsthe true label ^^^^+1 with at least a user-defined probability 1 − ^^, where ^^ is a user-defined threshold referred to as a significance level and (1 − ^^) represents the user-defined probability, which may be referred to as a target confidence level.

[0062] Conformal prediction may provide uncertainty estimates in scenarios such aswhen a pre-trained model is provided but the data distribution is inaccessible. Inconformal prediction, for a given (^^^^^^^^^^, ^^^^^^^^^^)~^^ ^^^^^^ ^^~^^, a prediction set ^^(^^^^^^^^^^)may be constructed that includes the correct prediction (^^^^^^^^^^) as follows:Seyfarth Ref. No. 72178-006717 15315930806v.1Qualcomm Ref. No.2407827WO 1− ^^ ≤ ℙ(^^^^^^^ ∈ ^^(^^ )) ≤ 1 − ^^ +1 ^^^ ^^^^^^^^^^+1.(1) For example, inconformal may a a diseases (e.g., three diseases) that the patient may have contracted with an estimate of uncertainty (e.g., 90% likelihood that the patient has one of the diseases in the prediction set). The user-defined threshold ^^ may enable control of a limit on acceptable model accuracy, which may provide some assurance of a level of model ( ) performance. The size of the prediction set ^^ ^^ may present a trade-off with the^^^^^^^^( ) degree of uncertainty, for example, the larger the prediction set ^^ ^^ , the greater the^^^^^^^^uncertainty in identifying the true label (^^ ).^^^^^^^^( )

[0063] However, if the calibration data ^^ and the test data (e.g., ^^ , ^^ ) are^^^^^^^^ ^^^^^^^^not identically distributed, for example due to distribution shift, then the guarantee (confidence level) may no longer hold for the test distribution. Accordingly, in various aspects, a coverage gap away from the target confidence level may be estimated.

[0064] In various aspects of the present disclosure, the conformal prediction (e.g.,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.

[0065] Given a complete and separable metric space ( ^^, c), where ^^ ∶ ^^ x ^^ → ℝ( ) is a metric. Let ^^ ^^ be the set of all probability measures P on ( ^^, c) with finite^^^^ for some ^^ ∈ ^^. A Wasserstein distancemoments of order p ≥ 1, e.g., ∫^^ ( )^^ ^^ <∞ 0^^(^^ ,^^)0^^ is a distance distributions on a given metric space.( ) The p-Wasserstein distance is a metric on ^^ ^^ that is defined for any measures P and^^( ) Q in ^^ ^^ as:^^inf^^ 1 / ^^ ^^ ^^ ^^^^ (2)^^( where Γ ^^, Q.∗( ) A probability measure in Γ ^^, ^^ may be referred to as a coupling of P and Q and π (P,Q) may denote p-Wasserstein optimal couplings (e.g., any coupling that attains theSeyfarth Ref. No. 72178-006717 16315930806v.1Qualcomm Ref. No.2407827WOinfimum in Equation 2). In some aspects, the metric ^^ may be an absolute distancewhere ^^(^^, ^^) = |^^ − ^^|. The moment order p is an integer (e.g., p=1),

[0066] Wasserstein distances may also be defined for discrete measures, andempirical measures in particular. Given ^^ and ^^ denote the empirical distributions of^^ ^^samples{^^^^}^^ , ^^~^^ and {^^} ^^^^=1 ^^ ^^ ^^=1 , ^^^^~^^, which induce empirical measures ^^ ^^ =∑^^^^ and ^^ = ∑^^ ^^=1 ^^^^ ^^ ^^=1 ^^^^^^, a coupling may be identified with a matrix Γ, where Γ^^,^^is the mass to be from ^^^^to ^^^^. Similarly, the metric or cost function c reducesto a matrix with ^^=− ^^‖^^such that the transportation problem may be given^^ ^^^^ ^^ 1 1 ^^ ^ ^ ^^ubject to ^^ = ∀^^ ∈ ^^ , ^^ = ∀^^ ∈ ^^ ∑ ∑^^^^^^ ^^ ^^ , ∑ (3)^^,^^ ^^,^^ ^^,^^ ^^,^^^^ ^^ ^^ ^^,^^ where ^^ represents the set

[0067] Nonconformity scores may be defined by a scoring function ^^: ^^ × ^^ → ℝ.Focusing on the distribution over nonconformity scores ^^ = ^^(^^, ^^), which is one-dimensional, the p-Wasserstein may be simplified to: 1 / ^^ 1 −1−1 ^^(4)( ) ( ) ^^ ^^, ^^ = ^^ ^^ − ^^ , (^^^^^^ ^^ ^^ ^^^^ ^^where ^^ is thescoring function ^^) and ^^ (·) represents the cumulative distribution function (CDF)^^^^−1 −1() () under measure ^^ and ^^ ∙ is the inverse of ^^ (·). ^^ ∙ may be referred to as the^^ ^^^^ ^^^^^^ ^^quantile function. When dealing with empirical the distance simplifiesfurther and when the same number of samples are included in P and Q, the p- Wasserstein distance may be given by the sum of the differences between the sorted samples: ^^ ^^1 / ^^ ^^ ^^ ^^ ^^ ^^ (5)

[0068] Given ^^[ ] ^^: ^^ × ^^ → 0,1 is a (nonconformity) score function, which may be bounded to theunit interval without loss of generality. Regardless of how the distribution shift presents itself (e.g., covariate or label shifts) the effect on the conformal prediction guaranteesSeyfarth Ref. No.72178-006717 17315930806v.1Qualcomm Ref. No.2407827WO may manifest in the distribution over calibration and test scores. Accordingly, invarious aspects, the distribution of scores ^^ = ^^(^^, ^^) may be directly manipulated.^^^^and ^^^^may respectively denote the calibration distribution and test distribution over [0, 1]. Scores observed during calibration may be represented using ^^^^and scores observed at test time may be represented using ^^^^(note: uppercase letters may be used for random variables and lowercase letters may be used for the realizations (e.g., ^^^^= ^^^^). The coverage under each distribution may be expressed as: ^^(^^^^ ∈ ^^(^^^^)) = ^^(^^^^ ≤ ℚ1−^^(^^^^)) = ^^^^^^~^^^^ [^^^^^^~^^^^[^^(^^^^ ≤ ℚ1−^^(^^^^))]] (6)(7)of random variable S.

[0069] In general, guaranteeing valid coverage under arbitrary test distributions Qmay not be possible and thus it may not be possible to ensure ^^(^^^^^^^^^^ ∈ ^^(^^^^^^^^^^)) ≥1 − ^^. Therefore, quantifying the gap in coverage induced by the change in distributionfrom P to Q may be beneficial. To that end, let ∆(^^)denote the coverage gap for a specific α value: ∆^^,^^(^^) = |(1 − ^^) − ^^(^^^^ ≤ ℚ1−^^(^^^^))| (8a)unique). The coverage gap may be upper bounded by the total variation distance. The total variation between two distributions ^^ and ^^ may be given by: ^^^^^^(^^, ^^) ≥ |^^^^[^^] − ^^^^[^^]|, (9)for f, an arbitrary 1-)],which is clearly bounded with |^^(^^)| ≤ 1 for all≤^^^^^^(^^^^, ^^^^) ≤ ^^^^^^(^^, ^^), with the last inequality due to the data processing inequality.Seyfarth Ref. No. 72178-006717 18315930806v.1Qualcomm Ref. No.2407827WO

[0070] However, estimating the total variation distance between ^^ and ^^ withoutaccess to the respective densities is challenging.

[0071] In accordance with aspects of the present disclosure, the (1 − ^^) quantilemay be computed over an empirical measure over scores ^^^^^^^^ = {(^^^^)}^^^=^1. ^^ ^^ =1 ^^^^∑^^^^^^(10) ^^=1

[0072] The calibration samples may be reweighted such that the weights may begreater than zero and sum to one and the empirical measure over the scores resembles the test distribution ^^^^as follows: ^^ ^^ ^^ =1 →^^^^ 1 ^^∑^^ ^^^^^^ ^^= ∑^^ ^^^^ ^^^^^^ ≈ ^^^^ (11)

[0073] Large^^, e.g., ^^ =^^^^ ^^^^.

[0074] Instead, optimal transport may be employed to compute an estimate of thecoverage gap ∆(^^) as well as the set of weights {^^^^}^^^=^1 that minimize the coverage gap. In both cases, given access to labeled samples from both ^^ and ^^: ^^ ^^ ^^1 ^^ =∑^^^^ , ^^ ^ =1 ∑^^ ^^^^ ^(12) ^^ 1 ^^^^^^= ^^=1 where m represents the number of samples of distribution ^^. In some aspects, the distribution Q may include a small number of samples (e.g., ^^ = 5 ).

[0075] The ^^-Wasserstein distances are valid and computable for empiricalmeasures such as ^^^^and ^^^^. An optimization for the weights{^^^^}^^^^=1may be performed as follows: {^^ ^^ ^^^}^^=1 = ^^^^^^^^^^^^ {^^^^}^^^^=1 ^^1(^^ ^^^ , ^^ ^^), (13)where ^^1(^^^^^^ , ^^ ^^) is the 1-Wasserstein distance between the weighted empirical^^^^and the empirical measure ^^^^defined by samples from ^^. The weights (^^^^) have to be greater than zero and sum to one. Seyfarth Ref. No. 72178-006717 19315930806v.1Qualcomm Ref. No.2407827WO

[0076] The optimization problem of Equation 13 may be solved in various ways.For example, the weights may be optimized directly wherein the weights may be considered{^^^^}^^^=^1 as learnable parameters.

[0077] network may be defined such that the neural network outputs{^^^^}^^^=^1 given, for example, scores{^^^^}^^^=^1 as input. However, the weights learned with the neural network do not depend on the order in which the input is presented (e.g., the neural network may be permutation equivariant).

[0078] Once the weights are computed, a split conformal prediction technique maybe employed. However, the quantile statistics may be computed over the weighted empirical measure ^^^^^^.

[0079] The coverage gap across all α values simultaneously, which may be referredto as the total coverage gap may be denoted as ∆1 ^^,^^= ∫0∆^^,^^(^^)^^^^ = ^^^^(^^)[∆(^^)].The total coverage gap between ^^ and ^^ may precisely be the 1-Wasserstein distance^^1(^^, ^^).

[0080] Given that ^^ and ^^ are two probability measures over the space ^^ × ^^ and^^^^ and ^^^^ be the cumulative distribution functions (CDFs) over the scores S induced by^^ and ^^, respectively, the total coverage gap is upper-bounded by the 1-Wassersteindistance ∆^^,^^≤ ^^1(^^^^ , ^^^^).1 ∫[^^^^^^~^^^^[^^(^^^^ ≤ ℚ1−^^(^^^^))]]Seyfarth Ref. No. 72178-006717 20315930806v.1Qualcomm Ref. No.2407827WO 1 =^^ −1 −^^ ~^^ [∫ |^^ (^^ (1 − ^^)) − ^^ (^^ 1^^ ^^ ^^^^^^^^ ^^^^^^^^ (1 − ^^))| ^^^^] 0 where the ofEquation 14 follows given a range of ^^ to be ℝ.

[0081] With access to few samples from Q, the total coverage gap may be reducedby including these samples in the calibration data as well. As such, the calibration data ′( ) [ ] may follow a mixture distribution given by ^^ = ^^^^ + 1 − ^^ ^^ with ^^ ∈ 0,1, and′ ′ ( ) the coverage gap between ^^ and ^^ satisfies ∆ ≤ ^^^^ ^^, ^^ .1 ^^ ^^^^,^^( )

[0082] In practice, quantifying the coverage gap ∆ ^^ , for a specific value of α^^,^^( ) may be beneficial. In some aspects, the coverage gap ∆ ^^ may be quantified by^^,^^applying Markov’s inequality as follows: (15) ^^(∆(^^) ≥ ^^) ≤ (^^_^^(^^) [∆(^^)]) / ^^ ≤ ^^(^^_^^, ^^_^^ ) / ^^ ^^^^^^ ^^ > 0,( ) ( ) ( ] which can be rewritten as ℙ ∆ ^^ ≥ ^^ ^^, ^^ ≤ ^^ for some ^^ ∈ 0, 1, so that with( )^^ ^^( ) ^^^^,^^^^ ^^( ) probability 1 − δ the value ∆ ^^ ≤. ^^

[0083] However, the by Markov’s inequality is loose (e.g., less( ) precise). As such, a tighter (e.g., more precise) upper-bound to ∆ ^^ can be derived^^,^^directly.

[0084] ^^ and ^^ are probability measures over scores ^^ and ^^ and ^^ are their^^ ^^ ^^ ^^^^ ^^respective cumulative distribution functions. ^^ and ^^ are the empirical measures ^^ ^^defined by ^^ samples from ^^ and ^^ samples from ^^, respectively, with corresponding^^ ^^empirical CDFs ^^ and ^^ . Then, if ^^ is the 1 ^^ quantile for the calibration scores^^^^ ^^ ^^ ^^( ) ^^, e.g., ^^ = ℚ ^^ with probability 1 − 2^^ such that:^^ ^^ 1−^^ ^^^^^^^^ ^^^^^^Seyfarth Ref. No.72178-006717 21315930806v.1Qualcomm Ref. No.2407827WO ∆^^,^^(^^) = |^^^^^^~^^^^ [^^^^^^~^^^^[^^(^^^^ ≤ ^^^^)]] − ^^^^^^~^^^^ [^^^^^^~^^^^[^^(^^^^ ≤ ^^^^)]]|However, a confidence interval 1 − ^^ may be constructed for the true quantile (e.g.,confidence level given the coverage gap), using a binomial function. For example, if{^^^^ t^^}^^=1 is a set of scores under ^^^^ and ^^(^^) denotes the jh order statistic among the set ofscores, ^^ and ^^ are both integers such that ℙ(^^^^ ≥ ^^) − ℙ(^^^^ ≥ ^^) ≥ 1 − ^^ for ^^^^~Binom (^^, ^^), where Binom represents the binomial distribution (may also be referred toas the “discrete probability distribution”). Accordingly, the true quantile may bedetermined to be one of the endpoints of the set of scores (e.g., ^^(^^), ^^(^^)) according tothe following: ^^−1^^^^ (^^) ∈ [^^(^^),^^(^^)] ^^^^^^ℎ ^^^^^^^^^^^^^^^^^^^^^^ 1 − ^^. (18)

[0087] Because the CDF is monotonic (e.g., a function that is either increasing ordecreasing), an upper-bound may be determined by only checking the endpoints of the interval. Thus, the upper-bound of the coverage gap may be reduced and given by: (2

[0088] testdata. In various aspects, the coverage gap may be determined test distribution ^^ without labels (e.g., unlabeled data).

[0089] A random variable capturing the calibration scores may be defined as ^^^^(e.g., ^^^^ ∼ ^^^^) and a random variable capturing the test scores may be defined as ^^^^(e.g., ^^^^ ∼ ^^^^). A joint distribution ^^ may be defined to couple ^^^^ and ^^^^ (e.g.,^^(^^^^, ^^^^)) and a score function ^^^^(^^) = ^^ may assign ^^ to all samples ^^.

[0090] Previous results may indicate that Δ^^,^^ ≤ ^^1(^^^^, ^^^^). In cases where onlyunlabeled test data is available, ^^^^is two suitable auxiliary distributions ^^^′ ^Seyfarth Ref. No. 72178-006717 22315930806v.1Qualcomm Ref. No.2407827WO and ^^^′^′may be defined, such that ^^^′^′stochastically dominates ^^^^, and ^^^^stochastically dominates ^^′^^ . That is, the cumulative distributions of ^^^^, ^^^′^ , and ^^^′^′satisfy: ^^^^^′^(^^) ≥ ^^^^^^(^^) for all ^^ in ℝ(20) ^^^^^′^′(^^) ≤ ^^^^^^(^^) for all ^^ in ℝ.

[0091] may be learned using an optimizationprocess such as (but not limited to) Stochastic gradient descent (SGD), as expressed. That is, the weights {^^^^}^^^=^1 may be learned, as given by: {^^^^}^^^^=1 = ^^^^^^^^^^^^ {^^^^}^^^^=1 [^^1(^^ ^^, ^^ ′ + ^^ (^^ ^^ ′′^^ ^^) 1 ^^ , ^^ ^^ )], (21)where ^^1the ^^^^and the empirical measures ^^^′^and ^^ ^′^′defined byunlabeled samples from ^^ such that ^^^′^′stochastically dominates the empirical measure ^^^^, and ^^^^stochastically dominates ^^^′^, with the unknown ^^^^also defined by the same unlabeled samples.

[0092] Accordingly, aspects of the present disclosure may reduce, and in someaspects mitigate, the impacts of distribution shift on conformal prediction. The weights ^^^^may be learned to minimize the coverage gap, thereby increasing reliability of prediction under distribution shift. In addition, the described techniques may enable computation of an upper-bound of the coverage gap which may improve the uncertainty estimate and in turn improve safety. For instance, where the upper-bound is determined to be above a threshold, decision (e.g., in medical applications, medical diagnosis, or treatment) may be deferred to human experts.

[0093] In some aspects, the weights ^^^^ may be computed at test time, withoutlabeled data. Additionally, the disclosed techniques may be applicable to any existing conformal prediction approach, including regression problems, using a conversion to a classification problem by binning the output space of the regression problem.

[0094] FIGURE 5 is a flow diagram illustrating a processor-implemented method500 for non-exchangeable conformal prediction, in accordance with various aspects of the present disclosure. The processor-implemented method 500 may be performed by Seyfarth Ref. No. 72178-006717 23315930806v.1Qualcomm Ref. No.2407827WO one or more processors such as the CPU (e.g., 102, 422), GPU (e.g., 104, 426), and / or other processing unit (e.g., DSP 424, NPU 428), for example.

[0095] Referring to FIGURE 5, at block 502, the one or more processors receive anartificial neural network (ANN) model with a calibration dataset and a set of test samples. Calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples. As described, the statistical properties of the data encountered during model training may differ for the data observed during testing or deployment.

[0096] At block 504, the one or more processors reweight the calibration samples ofthe calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples. For example, as described, the calibration samples may be reweighted such that the weights may be greater than zero and sum to one and the empirical measure over the scores resembles the test distribution ^^^^. Optimal transport may be employed to compute an estimate ofthe coverage gap |1 − ∆^^| as well as the set of weights {^^^^}^^^=^1 that minimize the coverage gap.

[0097] At block 506, the one or more processors perform a conformal predictionprocess on the reweighted calibration samples to produce a set of confidence intervals. For example, once the weights are computed, a split conformal prediction technique may be employed. Example Aspects

[0098] Aspect 1: An apparatus, comprising: at least one memory; and at least oneprocessor coupled to the at least one memory, the at least one processor configured to: receive an artificial neural network (ANN) model with a calibration dataset and a set of test samples, wherein calibration samples of the calibration dataset are non- exchangeable with selected test samples in the set of test samples; reweight the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples; and perform a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.Seyfarth Ref. No. 72178-006717 24315930806v.1Qualcomm Ref. No.2407827WO

[0099] Aspect 2: The apparatus of Aspect 1, wherein the at least one processor isfurther configured to quantify a coverage gap between the calibration dataset and the set of test samples.

[0100] Aspect 3: The apparatus of Aspect 1 or 2, wherein the at least one processoris further configured to compute the coverage gap using a 1-Wasserstein distance.

[0101] Aspect 4: The apparatus of any preceding Aspect, wherein the upper-boundof the coverage gap is an endpoint of a confidence interval corresponding to a set of scores under the calibration dataset and the distribution of the set of test samples.

[0102] Aspect 5: The apparatus of any preceding Aspect, wherein the at least oneprocessor is further configured to estimate a total variation distance between the calibration dataset and the distribution of the set of test samples without respective probability densities.

[0103] Aspect 6: The apparatus of any preceding Aspect, in which the reweightedcalibration samples are learned by minimizing the coverage gap based on the 1- Wasserstein distance.

[0104] Aspect 7: The apparatus of any preceding Aspect, in which the set of testsamples comprises unlabeled test samples.

[0105] Aspect 8: A processor-implemented method performed by at least oneprocessor, the processor-implemented method comprising: receiving an artificial neural network (ANN) model with a calibration dataset and a set of test samples, wherein calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples; reweighting the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples; and performing a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

[0106] Aspect 9: The processor-implemented method of Aspect 8, furthercomprising quantifying a coverage gap between the calibration dataset and the set of test samples.Seyfarth Ref. No. 72178-006717 25315930806v.1Qualcomm Ref. No.2407827WO

[0107] Aspect 10: The processor-implemented method of Aspect 8 or 9, furthercomprising computing the coverage gap using a 1-Wasserstein distance.

[0108] Aspect 11: The processor-implemented method of any of Aspects 8-10,wherein the upper-bound of the coverage gap is an endpoint of a confidence interval corresponding to a set of scores under the calibration dataset and the distribution of the set of test samples.

[0109] Aspect 12: The processor-implemented method of any of Aspects 8-11,further comprising estimating the total variation distance between the calibration dataset and the distribution of the set of test samples without respective probability densities.

[0110] Aspect 13: The processor-implemented method of any of Aspects 8-12, inwhich the reweighted calibration samples are learned by minimizing the coverage gap based on the 1-Wasserstein distance.

[0111] Aspect 14: The processor-implemented method of any of Aspects 8-13, inwhich the set of test samples comprises unlabeled test samples.

[0112] Aspect 15: An apparatus, comprising: means for receiving an artificialneural network (ANN) model with a calibration dataset and a set of test samples, wherein calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples; means for reweighting the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples; and means for performing a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

[0113] Aspect 16: The apparatus of Aspect 15, further comprising means forquantifying a coverage gap between the calibration dataset and the set of test samples.

[0114] Aspect 17: The apparatus of Aspect 15 or 16, further comprising means forcomputing the coverage gap using a 1-Wasserstein distance.

[0115] Aspect 18: The apparatus of any of Aspects 15-17, wherein the upper-boundof the coverage gap is an endpoint of a confidence interval corresponding to a set of scores under the calibration dataset and the distribution of the set of test samples.Seyfarth Ref. No. 72178-006717 26315930806v.1Qualcomm Ref. No.2407827WO

[0116] Aspect 19: The apparatus of any of Aspects 15-18, further comprising meansfor estimating the total variation distance between the calibration dataset and the distribution of the set of test samples without respective probability densities.

[0117] Aspect 20: The apparatus of any of Aspects 15-19, in which the reweightedcalibration samples are learned by minimizing the coverage gap based on the 1- Wasserstein distance.

[0118] In one aspect, the receiving means, reweighting means, performing means,computing means and / or estimating means may be the CPU 102 / 422, GPU 104 / 426, program memory associated with the CPU 102 / 422 or GPU 104 / 426, fully connected layers 362, NPU 108 / 428, and / or the routing connection processing unit 216 configured to perform the functions recited. In another configuration, the aforementioned means may be any module or any apparatus configured to perform the functions recited by the aforementioned means.

[0119] The various operations of methods described above may be performed byany 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.

[0120] As used, the term “determining” encompasses a wide variety of actions. Forexample, “determining” may include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database, or another data 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.

[0121] As used, a phrase referring to “at least one of” a list of items refers to anycombination 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.Seyfarth Ref. No. 72178-006717 27315930806v.1Qualcomm Ref. No.2407827WO

[0122] The various illustrative logical blocks, modules and circuits described inconnection 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.

[0123] The steps of a method or algorithm described in connection with the presentdisclosure 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.

[0124] The methods disclosed comprise one or more steps or actions for achievingthe 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.

[0125] The functions described may be implemented in hardware, software,firmware, or any combination thereof. If implemented in hardware, an exampleSeyfarth Ref. No. 72178-006717 28315930806v.1Qualcomm Ref. No.2407827WO 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.

[0126] The processor may be responsible for managing the bus and generalprocessing, 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 thereof. The machine-readable media may be embodied in a computer-program product. The computer-program product may comprise packaging materials.

[0127] In a hardware implementation, the machine-readable media may be part ofthe 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 throughSeyfarth Ref. No. 72178-006717 29315930806v.1Qualcomm Ref. No.2407827WO 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.

[0128] The processing system may be configured as a general-purpose processingsystem 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.

[0129] The machine-readable media may comprise a number of software modules.The software modules include instructions that, when executed by the processor, cause 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 understoodSeyfarth Ref. No. 72178-006717 30315930806v.1Qualcomm Ref. No.2407827WO 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.

[0130] If implemented in software, the functions may be stored or transmitted overas 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 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.

[0131] Thus, certain aspects may comprise a computer program product forperforming 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.Seyfarth Ref. No. 72178-006717 31315930806v.1Qualcomm Ref. No.2407827WO

[0132] Further, it should be appreciated that modules and / or other appropriatemeans 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.

[0133] It is to be understood that the claims are not limited to the preciseconfiguration 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. 72178-006717 32315930806v.1

Claims

Qualcomm Ref. No.2407827WO CLAIMS 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 with a calibration dataset and a set of test samples, wherein calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples; reweight the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples; and perform a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

2. The apparatus of claim 1, wherein the at least one processor is further configured to quantify a coverage gap between the calibration dataset and the set of test samples.

3. The apparatus of claim 2, wherein the at least one processor is further configured to compute the coverage gap using a 1-Wasserstein distance.

4. The apparatus of claim 3, wherein the upper-bound of the coverage gap is an endpoint of a confidence interval corresponding to a set of scores under the calibration dataset and the distribution of the set of test samples.

5. The apparatus of claim 3, wherein the at least one processor is further configured to estimate a total variation distance between the calibration dataset and the distribution of the set of test samples without respective probability densities.

6. The apparatus of claim 3, in which the reweighted calibration samples are learned by minimizing the coverage gap based on the 1-Wasserstein distance.

7. The apparatus of claim 1, in which the set of test samples comprises unlabeled test samples.Seyfarth Ref. No. 72178-006717 33315930806v.1Qualcomm Ref. No.2407827WO 8. A processor-implemented method performed by at least one processor, the processor-implemented method comprising: receiving an artificial neural network (ANN) model with a calibration dataset and a set of test samples, wherein calibration samples of the calibration dataset are non- exchangeable with selected test samples in the set of test samples; reweighting the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples; and performing a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

9. The processor-implemented method of claim 8, further comprising quantifying a coverage gap between the calibration dataset and the set of test samples.

10. The processor-implemented method of claim 9, further comprising computing the coverage gap using a 1-Wasserstein distance.

11. The processor-implemented method of claim 10, wherein the upper-bound of the coverage gap is an endpoint of a confidence interval corresponding to a set of scores under the calibration dataset and the distribution of the set of test samples.

12. The processor-implemented method of claim 10, further comprising estimating the total variation distance between the calibration dataset and the distribution of the set of test samples without respective probability densities.

13. The processor-implemented method of claim 10, in which the reweighted calibration samples are learned by minimizing the coverage gap based on the 1- Wasserstein distance.

14. The processor-implemented method of claim 10, in which the set of test samples comprises unlabeled test samples.Seyfarth Ref. No. 72178-006717 34315930806v.1Qualcomm Ref. No.2407827WO 15. An apparatus, comprising: means for receiving an artificial neural network (ANN) model with a calibration dataset and a set of test samples, wherein calibration samples of the calibration dataset are non-exchangeable with selected test samples in the set of test samples; means for reweighting the calibration samples of the calibration dataset using an optimal transport such that a weighted empirical measure over scores approximates a distribution of the set of test samples; and means for performing a conformal prediction process on the reweighted calibration samples to produce a set of confidence intervals.

16. The apparatus of claim 15, further comprising means for quantifying a coverage gap between the calibration dataset and the set of test samples.

17. The apparatus of claim 16, further comprising means for computing the coverage gap using a 1-Wasserstein distance.

18. The apparatus of claim 17, wherein the upper-bound of the coverage gap is an endpoint of a confidence interval corresponding to a set of scores under the calibration dataset and the distribution of the set of test samples.

19. The apparatus of claim 17, further comprising means for estimating the total variation distance between the calibration dataset and the distribution of the set of test samples without respective probability densities.

20. The apparatus of claim 15, in which the reweighted calibration samples are learned by minimizing the coverage gap based on the 1-Wasserstein distance.Seyfarth Ref. No. 72178-006717 35315930806v.1

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