Systems and methods for implementing deep learning models using environment discovery

Abstract

A method for training a deep learning model includes training a first sorting deep learning model (DLM) using a training dataset to predict a presence of a target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, training a second sorting DLM using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute in the second datapoint, comparing a first difficulty score with a second difficulty score of the second sorting DLM, assigning the datapoints to a first environment in response to the first difficulty score being less than the second difficulty score, and assigning the datapoints to a second environment in response to the first difficulty score being greater than the second difficulty score.

Description

2483-14301 SYSTEMS AND METHODS FOR IMPLEMENTING DEEP LEARNING MODELS USING ENVIRONMENT DISCOVERY CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims benefit of U.S. provisional patent application Serial No. 63 / 528,159 filed July 21, 2023, and entitled "Systems and Methods for Implementing Deep Learning Models Using Environment Discovery," which is hereby incorporated herein by reference in its entirety for all purposes. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not applicable. BACKGROUND

[0003] Deep learning models (DLMs) constitute a class of the broader genus of machine learning models which utilize deep learning architectures inspired by biological systems (e.g., the human brain) and having multiple separate and distinct layers (making the respective learning architecture “deep”) for extracting desired features from a raw input or dataset. For example, deep learning methods may employ one or more neural networks (NNs) (also referred to as artificial neural networks (ANNs)) having multiple distinct layers and comprising a plurality of interconnected units or nodes sometimes referred to as “artificial neurons” modeled after biological neurons. Deep learning methods may be applied to manifold applications including, as a non-limiting example, machine translation, speech recognition, image analysis, and computer vision applications. BRIEF SUMMARY OF THE DISCLOSURE

[0004] An embodiment of a computer-implemented method for training a deep learning model to predict a presence of a target attribute in a domain set comprises (a) training a first sorting deep learning model (DLM) using a training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, (b) training a second sorting DLM using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute in the second datapoint, (c) comparing a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more2483-14301 datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset, (d) assigning the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints, and (e) assigning the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints. In some embodiments, at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN). In some embodiments, the second sorting DLM corresponds to the inverse of the first sorting DLM. In certain embodiments, the method comprises (f) applying the first environment and the second environment to predictive DLM to form a prediction regarding a presence of the target attribute in one or more datapoints of a dataset of which the training dataset comprises a sample. In certain embodiments, the predictive DLM comprises an invariant learning predictor. In some embodiments, (f) comprises satisfying an environment invariance constraint (EIC) in forming the prediction regarding the presence of the target attribute in the one or more datapoints. In some embodiments, (c) comprises comparing a relative cross-entropy loss of the first sorting DLM and the second sorting DLM for the one or more datapoints. In certain embodiments, (c) comprises comparing a first generalized cross-entropy (GCE) loss of the first sorting DLM with a second GCE loss of the second sorting DLM across the one or more datapoints. In certain embodiments, (d) comprises assigning the one or more datapoints to the first environment in response to a first generalized cross-entropy (GCE) loss of the first sorting DLM being less than a second GCE loss of the second sorting DLM across the one or more datapoints, and (e) comprises assigning the one or more datapoints to the second environment in response to the second GCE loss of the first sorting DLM being less than a first GCE loss of the second sorting DLM across the one or more datapoints. In some embodiments, the method comprises (f) updating an earlier iteration of the first environment to define a later iteration of the first environment in response to (d), and (g) updating an earlier iteration of the second environment to define a later iteration of the second environment in response to (e).

[0005] An embodiment of a system for training a deep learning model to predict a presence of a target attribute in a domain set comprises a processor, a non-transitory memory, and one or more applications stored in the non-transitory memory that, when executed by the processor: train a first sorting deep learning model (DLM) using a2483-14301 training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, train a second sorting DLM using the training dataset to predict an absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute from the second datapoint, compare a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset, assign the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints, and assign the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints. In some embodiments, at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN). In certain embodiments, the one or more applications stored in the non-transitory memory that, when executed by the processor apply the first environment and the second environment to a predictive DLM to form a prediction regarding a presence of the target attribute in one or more datapoints of the domain set. In certain embodiments, the predictive DLM comprises an invariant learning predictor. In some embodiments, the second sorting DLM corresponds to the inverse of the first sorting DLM.

[0006] Embodiments described herein comprise a combination of features and characteristics intended to address various shortcomings associated with certain prior devices, systems, and methods. The foregoing has outlined rather broadly the features and technical characteristics of the disclosed embodiments in order that the detailed description that follows may be better understood. The various characteristics and features described above, as well as others, will be readily apparent to those skilled in the art upon reading the following detailed description, and by referring to the accompanying drawings. It should be appreciated that the conception and the specific embodiments disclosed may be readily utilized as a basis for modifying or designing other structures for carrying out the same purposes as the disclosed embodiments. It should also be realized that such equivalent constructions do not depart from the spirit and scope of the principles disclosed herein.2483-14301 BRIEF DESCRIPTION OF THE DRAWINGS

[0007] For a detailed description of exemplary embodiments of the disclosure, reference will now be made to the accompanying drawings in which:

[0008] Figure 1 is a schematic view of an embodiment of a system for implementing a deep learning model using environment discovery in accordance with principles described herein;

[0009] Figure 2 is a flowchart of an embodiment of a method for training a deep learning model to predict a presence of a target attribute in a domain set in accordance with principles described herein;

[0010] Figure 3 is a flowchart of another embodiment of a method for training a deep learning model to predict a presence of a target attribute in a domain set in accordance with principles described herein;

[0011] Figure 4 is a flowchart of another embodiment of a method for training a deep learning model to predict a presence of a target attribute in a domain set in accordance with principles described herein;

[0012] Figure 5 is a block diagram of an embodiment of a computer system in accordance with principles disclosed herein;

[0013] Figure 6 is a graph illustrating average accuracy (%) as a function of label noise for a plurality of deep learning techniques; and

[0014] Figure 7 is a graph illustrating worst-group accuracy (%) as a function of label noise for a plurality of deep learning techniques;

[0015] FIG.8 and 9 are graphs illustrating training losses as a function of the number of training epochs for a predictive model trained with both aligned and conflicting training datasets. DETAILED DESCRIPTION OF THE DISCLOSED EMBODIMENTS

[0016] The following discussion is directed to various exemplary embodiments. However, one skilled in the art will understand that the examples disclosed herein have broad application, and that the discussion of any embodiment is meant only to be exemplary of that embodiment, and not intended to suggest that the scope of the disclosure, including the claims, is limited to that embodiment.

[0017] Certain terms are used throughout the following description and claims to refer to particular features or components. As one skilled in the art will appreciate, different persons may refer to the same feature or component by different names. This document2483-14301 does not intend to distinguish between components or features that differ in name but not function. The drawing figures are not necessarily to scale. Certain features and components herein may be shown exaggerated in scale or in somewhat schematic form and some details of conventional elements may not be shown in interest of clarity and conciseness.

[0018] Unless the context dictates the contrary, all ranges set forth herein should be interpreted as being inclusive of their endpoints, and open-ended ranges should be interpreted to include only commercially practical values. Similarly, all lists of values should be considered as inclusive of intermediate values unless the context indicates the contrary.

[0019] In the following discussion and in the claims, the terms "including" and "comprising" are used in an open-ended fashion, and thus should be interpreted to mean "including, but not limited to…” Also, the term "couple" or "couples" is intended to mean either an indirect or direct connection. Thus, if a first device couples to a second device, that connection may be through a direct connection, or through an indirect connection via other devices, components, and connections. In addition, as used herein, the terms "axial" and "axially" generally mean along or parallel to a central axis (e.g., central axis of a body or a port), while the terms "radial" and "radially" generally mean perpendicular to the central axis. For instance, an axial distance refers to a distance measured along or parallel to the central axis, and a radial distance means a distance measured perpendicular to the central axis.

[0020] As described above, DLMs leverage deep learning architecture including, for example, NNs for extracting desired features from an input dataset. NNs employed in DLMs may be referred to as deep neural networks (DNNs) and typically comprise an input layer, an output layer, and one or more hidden layers sandwiched between the input and output layers, where each layer is formed from a plurality of interconnected nodes of the DNN.

[0021] DNNs are generally feed-forward in nature whereby information flows from the input layer, through the one or more hidden layers, and to the output layer whereby information may be provided by the output layer of the DNN as an output of the DLM for solving a specified problem such as, for example, extracting desired features from an input dataset that is fed to the input layer of the DNN. In this configuration, information flows in one direction between each layer of the DNN such that, for example, information may not flow from the output layer to one of the hidden layers, from a downstream hidden2483-14301 layer to an upstream hidden layer, or from one of the hidden layers to the input layer of the DNN.

[0022] The connections formed between the nodes generally transmit information in a single direction (e.g., the connections are uni-directional). In addition, the nodes of the DNN forming the layers thereof each represent an artificial neuron configured to perform computations on information received from one or more connections extending to the respective node from one or more other nodes of the respective layer of the DNN. The respective node may compute the received information (e.g., input data) and generate an output (e.g., output data) based on the received input data. For example, the neuron may compute the input data (e.g., the sum of the different inputs received by the node) using one or more non-linear functions. Further, the intersection of a connection and a node which receives input data from the respective connection may be referred to as an edge, and a dynamic weight may be assigned to the different edges of a given node which may be adjusted over time.

[0023] Generally, NNs, including DNNs of DLMs, learn using a training dataset containing examples of the type of input data that the DLM will receive during operation once the DLM has been trained. As an example, a given DLM may be trained to predict the presence of a particular animal (e.g., cows) using a training dataset (corresponding to a domain set X) including a number of images some of which include cows. In this example, each image of the training dataset is labeled (corresponding to a label set Y) based on whether a cow is present in the given image (e.g., a label of “1” may be applied to an image with a cow present, and a label of “0” may be applied to an image bereft of cows).

[0024] In this example, a DLM comprising a DNN may be employed to make predictions regarding an input dataset (e.g., whether a cow is present within a respective image of the input dataset). The DLM may thus be configured for mapping the domain set space (e.g., domain set X) of the input dataset to the label set space (e.g., label set Y). The training dataset may comprise a subset of the input dataset, and the DLM may be trained (e.g., the weights applied to the edges of the nodes of the DNN of the DLM may be adjusted or tuned) on the training dataset in an effort to minimize a true error of the DLM that corresponds to the fraction of miscalculated predictions provided by the DLM across the entire input dataset (e.g., the entire domain set X).

[0025] In many applications the entire input dataset is not available for training the respective DLM in order to directly minimize the true error of the DLM. Techniques2483-14301 therefore have been developed to indirectly minimize the true error of the DLM using a training dataset that does not capture the entire input dataset. Particularly, DLMs are typically trained using a technique referred to as empirical risk minimization (ERM) which attempts to minimize the risk or empirical error of the DLM, where the empirical error refers to the fraction of miscalculated predictions provided by the DLM across the training dataset (e.g., a sample of the entire domain set X).

[0026] Given that ERM focuses on emphasizing the empirical error rather than the true error (following the assumption that in most cases a reduction in empirical error will result in a reduction in the true error), in at least some instances the empirical error of the DLM may be minimized across a given training dataset while the true error of the model is unchanged or actually increases. In some instances, the application of ERM may result in the exploitation of spurious (e.g., non-causal) correlations among the training dataset as a shortcut for forming predictions across the entire domain set (which includes the training dataset as a subsample thereof). For example, training via ERM often results in making predictions that overly rely on spurious correlations in the training dataset, which can degrade the generalization to out-of-distribution settings where these spurious correlations, often misleading and unstable, may no longer hold In other words, the exploitation of spurious correlations by a DLM may result in relatively poor performance in out-of-distribution samples (e.g., other and different samples taken from the entire domain set) that may vary in their content from that of the in-distribution sample.

[0027] To continue the cows example discussed above, the application of ERM may result in the DLM becoming biased towards particular backgrounds or environments (e.g., a farm environment, a ranch environment) associated with the presence of cows. Particularly, the application of ERM may result in the DLM becoming more adept at identifying such environments and associating the environment with the presence of cows than at actually identifying the cows themselves in the training dataset.

[0028] Several further techniques have been developed to address the shortcomings of ERM outlined above. Particularly, a technique referred to as invariant risk minimization (IRM) has been developed intended to target causally invariant correlations (correlations which persist across all environments present in the domain set) across multiple training environments to learn globally optimal (e.g., optimal across the entire domain set) predictors rather than spurious predictors (e.g., associated with the environment) that may only be effective for the training dataset but not the remainder of the input dataset. While such techniques, including IRM, can effectively mitigate biases from predictions2483-14301 provided by a DLM, these techniques typically require access to multiple training environments that differ in how labels are spuriously correlated with a particular spurious attribute or confounder (e.g., the farm or ranch environments in the cows example) present in the training dataset.

[0029] However, in at least some applications, access may only be provided to training datasets having a single environment in which the confounder is present, preventing the application of IRM from eliminating biases towards spurious correlations associated with the confounder. In other words, IRM may not be an effective technique for addressing the shortcomings of ERM in applications in which the available training dataset is limited to a single environment in which a confounder is present.

[0030] Returning to the cows example discussed above, it may be the case that the only training data which may be obtained includes cows present within farm or ranch environments instead of other environments which are not associated with the presence of cows (e.g., an underwater environment, an artic environment). In addition, in at least some applications, IRM and associated techniques may be unavailable during training due to expensive annotations, privacy constrains, and difficulties in effectively grouping the training dataset. Thus, while IRM and associated techniques (e.g., environment inference for invariant learning (EIIL)) can be effective in certain circumstances in addressing at least some of the shortcomings of ERM as outlined above, IRM and such techniques are limited in their applicability particularly with respect to applications in which the training dataset is limited in terms of the number of different environments contained therein.

[0031] Accordingly, embodiments of systems and methods for implementing DLMs using environment discovery are disclosed herein which are intended to address the shortcomings of ERM training techniques (e.g., biasing the DLM towards spurious correlations associated with spurious, non-causal attributes or confounders) while also avoiding the training dataset requirements (e.g., having multiple environments in which the confounder is present) and / or the requirement of manually partitioning the training dataset into multiple distinct environments (e.g., as is required with IRM and similar techniques). Instead, embodiments of systems and methods for implementing DLMs disclosed herein use the DLM itself to automatically infer or discover the different distinct environments present in a given training dataset inputted to the DLM.

[0032] Generally, ERM and similar approaches rely on the assumption that biased training datasets are easily identified through ERM pre-training. However, real-world2483-14301 scenarios often challenge this assumption given that an ERM model may learn a combination of biased and causal features from a given training dataset. For example, spurious predictors, which often act as shortcuts, are often learned quickly by the ERM model in early training epochs. However, with enough training, the ERM model may begin to overfit even on bias-conflicting training datasets, confirming that ERM models may have difficulty in at least some applications in identifying biased training datasets. Embodiments of systems and methods for implementing DLMs using environment discovery may intentionally leverage or promote features (e.g., spurious correlations or predictors) learned during early training epochs using a Generalized Cross-Entropy (GCE) loss function. In addition, following this initial reinforcement of features learned in early training epochs, the training dataset may be partitioned into two environments based on the model’s performance. In some embodiments, the environments thus discovered may then be used to train an invariant learning algorithm to eliminate or mitigate biases from the model.

[0033] Particularly, in an embodiment, a first sorting DLM (e.g., comprising a NN such as a DNN and / or other DLM architectures) is trained using a training dataset that is a sample of the domain set to predict the presence of a predefined target attribute in a first datapoint of the training dataset based on the presence of a first environmental attribute in the first datapoint. In addition, a second or dummy sorting DLM (e.g., comprising a NN such as a DNN and / or other DLM architectures) is trained using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on the presence of the first environmental attribute from the second datapoint. In this manner, both of the first and second sorting DLMs are trained to learn a spurious attribute (e.g., first environmental attribute), with the first sorting DLM trained using a positive correlation between the spurious attribute and the target attribute while the second sorting DLM is trained using a negative correlation between the spurious attribute and the target attribute. Further, a first difficulty score of the first sorting DLM in predicting the presence of the target attribute in one or more datapoints of the training dataset is compared with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset.

[0034] In this exemplary embodiment, the one or more datapoints are assigned to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints. Additionally, the one or more datapoints are2483-14301 assigned to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints. In some embodiments, the difficulty score corresponds to cross- entropy loss, as will be discussed further herein.

[0035] In certain embodiments, a first sorting DLM is trained using a training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, and a second sorting DLM is trained using the training dataset to predict a presence of the target attribute in a second datapoint of the training dataset based on the absence of the first environmental attribute from the second datapoint. In addition, one or more datapoints of the training dataset are assigned to either a first environment or a second environment that is different from the first environment based on which of the first sorting DLM and the second sorting DLM has a lesser cross-entropy loss for the one or more datapoints.

[0036] In an embodiment, a system for training a DLM to predict a presence of a target attribute in a domain set is disclosed which includes a processor, and a non-transitory memory. In addition, the system includes one or more applications stored in the non- transitory memory that, when executed by the processor train a first sorting DLM using a training dataset to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, and train a second sorting DLM using the training dataset to predict an absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute from the second datapoint. Additionally, the one or more applications, when executed by the processor compare a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset. Further, the one or more applications, when executed by the processor assign the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints, and assign the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints2483-14301

[0037] In this manner, the methods and system described above facilitate the creation of environments for invariant learning from a biased training dataset. Particularly, the methods and system described above amplify the spurious attribute during training and automatically (e.g., without needing to manually label or classify the training dataset) partition the dataset on the basis of this training. Without access to environment labels, the methods and system described above can, in at least some instances, outperform conventional invariant learning techniques that require environment labels or group annotations.

[0038] Referring now to FIG.1, an embodiment of a system 1 for implementing a DLM 60 using environment discovery is shown. As will be discussed further herein, system 1 is configured to implement the DLM 60 whereby the DLM 60 may avoid being biased by spurious correlations of confounders present in the training dataset 10 without needing to manually partition or classify the training dataset into multiple environments or requiring prior knowledge of the environments or metadata such as environment labels or demographic information. Additionally, in this exemplary embodiment, DLM 60 comprises an invariant learning model and thus may also be referred to herein as invariant learning model 60. However, it may be understood that in other embodiments DLM 60 may not comprise an invariant learning model. For example, in other embodiments, DLM 60 may comprise a ResNet learning model, a DenseNet learning model, and / or others.

[0039] Particularly, the system partitions a training dataset into a plurality of environments. In certain embodiments, the system partitions the training dataset into a pair of environments. The pair of environments may maximally separate spurious attributes present within the training dataset to promote effective invariant learning. In addition, in certain embodiments, the system evaluates the quality of the pair of environments by utilizing them in the invariant learning model 60

[0040] In this exemplary embodiment, system 1 generally includes a training dataset 10, an environment partitioning module 20, and an invariant learning module 60. The training dataset 10 comprises a sample of a global domain set. In addition, training dataset 10 includes a plurality of separate datapoints 12 some of which include a predefined target attribute 14, a first environmental attribute 16, and a second environmental attribute 18. In this exemplary embodiment, invariant learning model 60 is configured to detect or predict the presence of the target attributes 14 across the datapoints defining the entire domain set. Additionally, in this exemplary embodiment, datapoints 12 comprise2483-14301 individual images and the target attribute 14 is illustrated in FIG.1 are waterbirds (as contrasted with landbirds illustrated in some of the datapoints 12). Further, at least some of the datapoints 12 include the first environmental attribute 16 (illustrated in FIG.3 as a water environment such as a beach, an ocean or other body of water, a wetland) while at least some of the other datapoints 12 include the second environmental attribute 18 (illustrated in FIG.3 as a land environment such as a forest, a field).

[0041] In some embodiments, a spurious or non-causal correlation (e.g., a shortcut) is present between the target attribute 14 and the first environmental attribute 16 which is not present between target attribute 14 and second environmental attribute 18. For instance, should ERM be applied using the training dataset 10 the resulting trained DLM may be undesirably biased towards the spurious correlation between target attribute 14 and first environmental attribute 16. Through the spurious correlation between target attribute 14, the first environmental attribute 16 comprises a spurious attribute or confounder while the second environmental attribute 18 does not comprise a confounder.

[0042] It may be understood that the training dataset 10 (including, e.g., the target attribute 14 and the environmental attributes 16 and 18) may vary substantially from that shown in FIG.3 in other embodiments and depending on the given application.

[0043] In this exemplary embodiment, the environment partitioning module 20 of system 1 receives the training dataset 10 once the training dataset 10 has been randomly divided into a distinct initial pair of environments illustrated as e1 and e2, respectively, in FIG.1. Environment partitioning module 20 receives the initial environments e1 and e2 (which may not be equal in size), updates the initial environments e1 and e2, and outputs two final environments e1’ and e2’ in the form of an environmentally sorted training dataset 50, final environments e1’ and e2’ are each different from the initial environments e1 and e2 (e.g., final environment e1’ is different from initial environment e1; final environment e2’ is different from initial environment e2).

[0044] Environment partitioning module 20 generally includes a training submodule 22 and a comparison submodule 40. Training submodule 22 is generally configured to train in parallel a first sorting DLM (indicated as NN M1in FIG.3) and a second or dummy sorting DLM 26(indicated as NN M2in FIG.3). In this exemplary embodiment, sorting DLMs 24 and 26 each comprise NNs such as DNNs including a plurality of interconnected nodes and having an input layer, an output layer, and one or more hidden layers sandwiched between the input layer and the output layer. However, it may be understood that in other embodiments sorting DLMs 24 and 26 may comprise DLM2483-14301 architectures other than DNNs or even NNs. For example, in other embodiments, sorting DLMs 24 and / or 26 may comprise convolutional neural networks (CNNs), ResNet models, DenseNet models, or other types of networked models. In some embodiments, second sorting DLM 26 comprises the inverse (e.g., 1-M with M representing first sorting DLM 24 in this exemplary embodiment) of first sorting DLM 24. Alternatively, second sorting DLM 26 may comprise other DLMs having functionalities similar to that provided by second sorting DLM 26 as detailed further below.

[0045] In this exemplary embodiment, the initial first environment e1 of training dataset 10 is provided to each of the sorting DLMs 24 and 26 as an input dataset. Environment portioning module 20 is generally configured to generate the final environments e1’ and e2’ (which may not be equal in size) such that a positive correlation between the target attribute 14 and first environmental attribute 16 is maximized in the first environmental environment e1 while a reverse or negative correlation between the target attribute 14 and the first environmental attribute 16 is maximized in the second final environment e2’. As an example, in the first final environment e1’ each of the datapoints 12 in which the first environmental attribute 16 is paired with the target attribute 14 may be present to maximize the positive correlation within the first final environment e1’ between the first environmental attribute 16 and the target attribute 14. Additionally, in the second final environment e2’ may contain each of the datapoints 12 in which the first environmental attribute 16 is not paired with the target attribute 14 (e.g., datapoints 12 in which water environments are paired with landbirds instead of waterbirds) to maximize the negative correlation within the second final environment e2’ between the first environmental attribute 16 and the target attribute 14.

[0046] The training submodule 22 of environment partitioning module 20 assists in facilitating the generation of final environments e1’ and e2’ by training the first sorting DLM 24 using the training dataset 10 whereby the first sorting DLM 24 is forced to directly make predictions on the presence of the target attribute 14 in a given datapoint 12 based on the presence of the confounder (e.g., detect presence of first environmental attribute 16 in a given datapoint 12 ^ predict presence of target attribute 14 in the datapoint 12), and by converselythe second sorting DLM 26 using the training dataset 10 whereby the second sorting DLM 26 is forced to directly make predictions on the absence of the target attribute 14 in a given datapoint 12 based on the presence of the confounder (e.g., detect presence of first environmental attribute 16 in a given datapoint 12 ^ predict absence of target attribute 14 from the datapoint 12).2483-14301

[0047] In some embodiments, the pair of sorting DLMs 24 and 26 are encouraged to learn the spurious correlation (interpreted positively by the first sorting DLM 24 and negatively by the second sorting DLM 26) between the target attribute 14 and the first environmental attribute 16 by analyzing the training loss dynamics. For instance, training loss of datapoints including a spurious correlation (e.g., the spurious correlation between target attribute 14 and first environmental attribute 16 for training dataset 10) reduced rapidly whereas the loss of other datapoints 12 not including the spurious correlation typically first increases and subsequently decreases. Therefore, the pair of sorting DLMs 24 and 26 may be encouraged to learn the spurious correlation by reinforcing the predictions of sorting DLMs 24 and 26 from the early stages of training.

[0048] In certain embodiments, the predictions of sorting DLMs 24 and 26 from the early stages of training are reinforced using a generalized cross-entropy (GCE) loss function (illustrated in FIG.1 as first GCE loss function 28 and second GCE loss function 30). First CGE loss function 28 has as inputs a prediction 25 of the presence of a target attribute 14 in a given datapoint (illustrated as y’11in FIG.1) along with a target label 23 of that given datapoint 12 specifying whether the given datapoint 12 includes the target attribute 14. Additionally, second CGE loss function 30 has as inputs a prediction 27 by the second sorting DLM 26 of the presence of a target attribute 14 in a given datapoint (illustrated as y’12 in FIG. 1) along with the target label 23 of that given datapoint 12 specifying whether the given datapoint 12 includes the target attribute 14. Not intending to be bound by any particular theory, the GCE loss function may be expressed as presented below in Equation (1) where ^^ீ^ா^ ^^^ ^^^, ^^^ represents the GCE loss function, ^^^ ^^^ represents the softmax output for the j-th element of M(x) corresponding to a target attribute of y, and ^^ ∈^0,1^represents a hyperparameter to control the degree of amplification: ^^ ^ ^^^ீ^ா^ ^^^ ^^^, ^^^ ൌିெೕ ௫^ (1)

[0049] The GCE losscross-entropy (CE) when q ^0. Compared to the cross-entropy, GCE weighs the gradient of each datapoint by an additional ^^^^ ^^^^term. For example, and not intending to be bound by any particular theory, the gradient of each datapoint may be expressed in accordance with Equation (2) presented below, whereௗ^ಸ^ಶ^ெ^௫^,௬^represents the gradient of the GCE loss ௗ^ ^ ^ ^ ^function,^ಶ ெ ௫ ,௬ௗఏrepresents gradient of the CE loss function, and θ represents2483-14301 the model parameters (e.g., parameters of the respective sorting DLM 24 or sorting DLM 26): ௗ^ಸ^ಶ^ெ^௫^,௬^ൌ ^^ ^ௗ^^ಶ^ெ^௫^,௬^ ௗఏ ^^ ^^ ௗఏ(2)

[0050] As a result the additional ^^^^ ^^^^term, a given trained to place more emphasis on datapoints for which the sorting DLM has a greater confidence level (e.g., a greater softmax output) during the initial steps of training the sorting DLM. Given that spurious correlations tend to be learned from early training epochs, the sorting DLM is encouraged to focus specifically on such spurious correlations.

[0051] The comparison submodule 40 of environment partitioning module 20 compares the relative performance of sorting DLMs 24 and 26 across the training dataset 10 to update (indicated by arrows 41 in FIG. 1) the environments e1 and e2 across one or more iterations. In some embodiments, environments e1 and e2 are updated for each training epoch. In this exemplary embodiment, trained sorting DLMs 24’ and 26’, respectively, are each provided with environments e1 and e2 (e.g., initial environments e1 and e2 or environments e1 and e2 from a preceding training epoch) as input data.

[0052] In this exemplary embodiment, for each datapoint 12 of training dataset 10 a difficulty score 42 is obtained for corresponding to the degree of difficulty for each trained sorting DLM 24’ and 26’ in forming a prediction 25’ and 27’ (e.g., the degree of confidence in the respective prediction) regarding the presence of the target attribute 14 in the respective datapoint 12. Particularly, if for a given datapoint 12 of the training dataset 10 the difficulty score of first trained sorting DLM 24’ exceeds the difficulty score of second trained sorting DLM 26’ (e.g., first trained sorting DLM 24’ had greater difficulty in forming a prediction than second trained sorting DLM 26’), then the respective datapoint 12 is assigned to the first environment e1 irrespective of whether it was initially assigned to the initial first environment e1 or the initial second environment e2. Conversely, if for a given datapoint 12 of the training dataset 10 the difficulty score of second trained sorting DLM 26’ exceeds the difficulty score of first trained sorting DLM 24’ (e.g., second trained sorting DLM 26’ had greater difficulty in forming a prediction than first trained sorting DLM 24’), then the respective datapoint 12 is assigned to the second environment e2 irrespective of whether it was initially assigned to the initial first environment e1 or the initial second environment e2.2483-14301

[0053] In some embodiments, the difficulty score 42 of comparison submodule 40 is the relative cross-entropy loss per datapoint 12. For example, a respective datapoint 12 is assigned to fist environment e1 when ^^ீ^ா^ ^^^^ ^^^, ^^^ is less than ^^ீ^ா^ ^^ଶ^ ^^^, ^^^ for the datapoint 12, and is assigned to second environment e2 when ^^ீ^ா^ ^^ଶ^ ^^^, ^^^ is less than^^ீ^ா^^^^^^^^, ^^^for the datapoint 12. While in this exemplary embodiment the difficultyscore 42 is based on the cross-entropy loss per datapoint 12, it may be understood that in other embodiments the difficulty score 42 may be based on metrics other than cross- entropy loss.

[0054] The invariant learning model 60 of system 1 applies the final environments e1’ and e2’ to an invariant learning predictor 62 configured to make predictions 72 regarding the presence of the target attribute in a given datapoint 12 contained in an input dataset 70 where the datapoints 12 of input dataset 70 may be different from or otherwise not contained in the training dataset 10. In some embodiments, sorting DLM 24 comprises an environmental sorting model configured to sort the training dataset 10 into final first and second environment sets e1 and e2 whereas DLM 60 comprises a predictive model configured to predict the presence of a target attribute in a given datapoint and which is trained using the training dataset 10 sorted into the final first and second environment sets e1 and e2 whereby the resulting trained predictive model may be at least less biased by one or more confounders present in the training dataset 10. Generally, the invariant learning predictor 62 comprises a predictor function (e.g., ^^: ^^ → ^^), where ^^ represents the input space and ^^ represents the label space) which generalizes across all possible environments. In some embodiments, invariant learning predictor 62 satisfies the environment invariance constraint (EIC).

[0055] As an illustrative example, the invariant learning predictor 62 may optimize a parameterized mapping or model (Φ) where (Φ:X ^H) with H representing a representation space. Generally, invariant62 is configured to learn a data representation function Φ(x) that performs simultaneously optimal for all environments (e.g., the data representation function Φ(x) has stable relationships with y across all environments. In some embodiments, for regular loss functions like cross- entropy and mean squared error, optimal classifiers may be expressed as conditional expectations of the output variable. Therefore, the data representation function Φ(x) additionally satisfies the Environment Invariance Constraint or Invariance Property.2483-14301

[0056] Not intending to be bound by any particular theory, the EIC may be expressed in accordance with Equation (4) presented below, where x, y, e represents observational data from multiple environments ^^ ∈ ^^ ^^ ^^ ^^^^^

[0057] To state learning model or predictorof outcomes given the predictor is invariant across all training environments. It may be understood that, in at least some embodiments, invariant learning predictor 62 satisfies the EIC with respect to a given dataset.

[0058] Referring to FIG.2, an embodiment of a computer-implemented method 100 for training a DLM to predict a presence of a target attribute (e.g., target attribute 14 shown in FIG.1) in a domain set is shown. Initially, at block 102, method 100 includes receiving a training dataset containing a set of datapoints and a corresponding set of target labels. For example, the training dataset may comprise the training dataset 10 shown in FIG.1 (e.g., or another training dataset comprising a plurality of images) with the corresponding set of target labels indicating the presence or absence of a target attribute in a corresponding datapoint.

[0059] At bock 104, method 100 comprises minimizing an expectation of CGE loss of a DLM (e.g., first sorting DLM 24 / 24’ shown in FIG.1) using the received training dataset as sorted into the first environment set and the second environment set. In this exemplary embodiment, block 104 includes, at block 108, assigning (e.g., reassigning) a datapoint of the training dataset to the first environment set in response to the CGE loss of the DLM, applying the datapoint and its corresponding target label, being less than the CGE loss of a second or dummy DLM (e.g., second sorting DLM 26 / 26’ shown in FIG.1) comprising, in this exemplary embodiment, an inverse of the DLM also applying the datapoint and its corresponding label.

[0060] Additionally, in this exemplary embodiment, block 104 includes at block 110 assigning (e.g., reassigning) a datapoint of the training dataset to the second environment set in response to the CGE loss of the DLM, applying the datapoint and its corresponding target label, being equal to or greater than the CGE loss of the dummy DLM also applying the datapoint and its corresponding label. In some embodiments,2483-14301 blocks 108 and 110 are performed iteratively (indicated by the dashed line 107 surrounding blocks 108 and 110 for each datapoint of the training dataset. At block 112, a final first environment set containing a first set of datapoints of the training dataset is determined. Similarly, at block 114, a final first environment set containing a first set of datapoints of the training dataset is determined. In some embodiments, the final first and second environment sets may be applied (e.g., used to train) a predictive model (e.g., a DLM such as predictive DLM 60 shown in FIG.1) for predicting the presence or absence of the target attribute in an input dataset that at least includes some datapoints not contained in the training dataset.

[0061] Referring to FIG.3, an embodiment of a computer-implemented method 150 for training a DLM to predict a presence of a target attribute (e.g., target attribute 14 shown in FIG.1) in a domain set is shown. At block 152, method 150 comprises training a first sorting DLM (e.g., first sorting DLM 24 shown in FIG. 1) of the DLM (e.g., invariant learning model 60 shown in FIG.1) using a training dataset (e.g., training dataset 10 shown in FIG.1) that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute (e.g., first environmental attribute 16 shown in FIG.1) in the first datapoint.

[0062] At block 154, method 150 comprises training a second sorting DLM (e.g., second sorting DLM 26 shown in FIG.1) of the DLM using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute in the second datapoint. At block 156, method 150 comprises comparing a first difficulty score (e.g., difficulty score 42 shown in FIG.1) of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints (e.g., datapoints 12 shown in FIG.1) of the training dataset with a second difficulty score (e.g., difficulty score 42 shown in FIG.1) of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset.

[0063] At block 158, method 150 comprises assigning the one or more datapoints to a first environment (e.g., first environment e1 shown in FIG. 1) in response to the first difficulty score being less than the second difficulty score for the one or more datapoints. At block 160, method 150 comprises assigning the one or more datapoints to a second environment (e.g., second environment e2 shown in FIG.1) that is different from the first environment in response to the first difficulty score being greater than the second2483-14301 difficulty score for the one or more datapoints.

[0064] Referring to FIG.4, an embodiment of a computer-implemented method 170 for training a DLM to predict a presence of a target attribute (e.g., target attribute 14 shown in FIG.1) in a domain set is shown. At block 172, method 170 comprises training a first sorting DLM (e.g., first sorting DLM 24 shown in FIG. 1) of the DLM (e.g., invariant learning model 60 shown in FIG.1) using a training dataset (e.g., training dataset 10 shown in FIG.1) that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute (e.g., first environmental attribute 16 shown in FIG.1) in the first datapoint.

[0065] At block 174, method 170 comprises training a second sorting DLM (e.g., second sorting DLM 26 shown in FIG. 1) of the DLM using the training dataset to predict a presence of the target attribute in a second datapoint of the training dataset based on the absence of the first environmental attribute from the second datapoint. At block 176, method 170 comprises assigning one or more datapoints (e.g., datapoints 12 shown in FIG. 1) of the training dataset to either a first environment (e.g., first environment e1 shown in FIG.1) or a second environment (e.g., second environment e2 shown in FIG. 1) that is different from the first environment based on which of the first sorting DLM and the second sorting DLM has a lesser cross-entropy loss for the one or more datapoints.

[0066] Referring now to Figure 5, a computer system 200 suitable for implementing one or more embodiments disclosed herein. For example, the system 1 for implementing the invariant learning model 60 using environment discovery described above may comprise the computer system 200 or at least some of the features of computer system 200. The computer system 200 includes a processor 202 (which may be referred to as a central processor unit or CPU) that is in communication with memory devices including secondary storage 204, read only memory (ROM) 206, random access memory (RAM) 208, input / output (I / O) devices 210, and network connectivity devices 212. The processor 202 may be implemented as one or more CPU chips. It is understood that by programming and / or loading executable instructions onto the computer system 200, at least one of the CPU 202, the RAM 208, and the ROM 206 are changed, transforming the computer system 200 in part into a particular machine or apparatus having the novel functionality taught by the present disclosure. Particularly, by programming and / or loading executable instructions onto the computer system 200, at least one of the CPU 202, the RAM 208, and the ROM 206 are changed, transforming the computer system2483-14301 200 in part into a particular machine or apparatus including, for example, the event portioning module 20, the environmentally sorted training dataset 50, the predictive DLM 60, and / or target attribute predictions 72 shown in FIG.1.

[0067] Additionally, after the system 200 is turned on or booted, the CPU 202 may execute a computer program or application. For example, the CPU 202 may execute software or firmware stored in the ROM 206 or stored in the RAM 208. In some cases, on boot and / or when the application is initiated, the CPU 202 may copy the application or portions of the application from the secondary storage 204 to the RAM 208 or to memory space within the CPU 202 itself, and the CPU 202 may then execute instructions that the application is comprised of. In some cases, the CPU 202 may copy the application or portions of the application from memory accessed via the network connectivity devices 212 or via the I / O devices 210 to the RAM 208 or to memory space within the CPU 202, and the CPU 202 may then execute instructions that the application is comprised of. During execution, an application may load instructions into the CPU 202, for example load some of the instructions of the application into a cache of the CPU 202. In some contexts, an application that is executed may be said to configure the CPU 202 to do something, e.g., to configure the CPU 202 to perform the function or functions promoted by the subject application. When the CPU 202 is configured in this way by the application, the CPU 202 becomes a specific purpose computer or a specific purpose machine.

[0068] Secondary storage 204 may be used to store programs which are loaded into RAM 208 when such programs are selected for execution. The ROM 206 is used to store instructions and perhaps data which are read during program execution. ROM 206 is a non-volatile memory device which typically has a small memory capacity relative to the larger memory capacity of secondary storage 204. The secondary storage 204, the RAM 208, and / or the ROM 206 may be referred to in some contexts as computer readable storage media and / or non-transitory computer readable media. I / O devices 210 may include printers, video monitors, liquid crystal displays (LCDs), touch screen displays, keyboards, keypads, switches, dials, mice, track balls, voice recognizers, card readers, paper tape readers, or other well-known input devices.

[0069] The network connectivity devices 212 may take the form of modems, modem banks, Ethernet cards, universal serial bus (USB) interface cards, wireless local area network (WLAN) cards, radio transceiver cards, and / or other well-known network devices. The network connectivity devices 212 may provide wired communication links2483-14301 and / or wireless communication links. These network connectivity devices 212 may enable the processor 202 to communicate with the Internet or one or more intranets. With such a network connection, it is contemplated that the processor 202 might receive information from the network, or might output information to the network. Such information, which may include data or instructions to be executed using processor 202 for example, may be received from and outputted to the network, for example, in the form of a computer data baseband signal or signal embodied in a carrier wave.

[0070] The processor 202 executes instructions, codes, computer programs, scripts which it accesses from hard disk, floppy disk, optical disk, flash drive, ROM 206, RAM 208, or the network connectivity devices 212. While only one processor 202 is shown, multiple processors may be present. Thus, while instructions may be discussed as executed by a processor, the instructions may be executed simultaneously, serially, or otherwise executed by one or multiple processors. Instructions, codes, computer programs, scripts, and / or data that may be accessed from the secondary storage 204, for example, hard drives, floppy disks, optical disks, and / or other device, the ROM 206, and / or the RAM 208 may be referred to in some contexts as non-transitory instructions and / or non-transitory information.

[0071] In an embodiment, the computer system 200 may comprise two or more computers in communication with each other that collaborate to perform a task. For example, but not by way of limitation, an application may be partitioned in such a way as to permit concurrent and / or parallel processing of the instructions of the application. Alternatively, the data processed by the application may be partitioned in such a way as to permit concurrent and / or parallel processing of different portions of a dataset by the two or more computers. In an embodiment, the functionality disclosed above may be provided by executing the application and / or applications in a cloud computing environment. Cloud computing may comprise providing computing services via a network connection using dynamically scalable computing resources.

[0072] In some embodiments, computer system 200 forms or defines a system for training a DLM to predict a presence of a target attribute (e.g., target attribute 14 shown in FIG.1) in a domain set. The system includes one or more applications stored in the ROM 206 that, when executed by the processor 202 train a first sorting DLM (e.g., first sorting DLM 24 shown in FIG.1) of the DLM (e.g., invariant learning model 60 shown in FIG. 1) using a training dataset (e.g., training dataset 10 shown in FIG. 1) that is a sample of the domain set to predict a presence of the target attribute in a first datapoint2483-14301 of the training dataset based on a presence of a first environmental attribute (e.g., first environmental attribute 16 shown in FIG. 1) in the first datapoint, and train a second sorting DLM (e.g., second sorting DLM 26 shown in FIG.1) of the DLM using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute in the second datapoint.

[0073] Additionally, the one or more applications, when executed by the processor 202 compare a first difficulty score (e.g., difficulty score 42 shown in FIG.1) of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints (e.g., datapoints 12 shown in FIG.1) of the training dataset with a second difficulty score (e.g., difficulty score 42 shown in FIG.1) of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset.

[0074] Further, the one or more applications, when executed by the processor 202 assign the one or more datapoints to a first environment (e.g., first environment e1 shown in FIG. 1) in response to the first difficulty score being less than the second difficulty score for the one or more datapoints, and assign the one or more datapoints to a second environment (e.g., second environment e2 shown in FIG.1) that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints.

[0075] Experiments were conducted pertaining to method for training a DLM to predict a presence of a target attribute in a domain set. It may be understood that the following experiments described herein are not intended to limit the scope of this disclosure and the embodiments described above and shown in FIGS. 1-4. Particularly, in an experimental study, it was demonstrated that the employment of environment discovery techniques (e.g., as described above with respect to system 1 shown in FIG. 1, and which are also referred to herein as frustratingly-easy event discovery (FEED)) can significantly improve worst-group performance for invariant learning algorithms compared to baseline conventional techniques. In addition, empirical analyses of FEED techniques were conducted.

[0076] Particularly, FEED techniques were compared with environment inference for invariant learning (EIIL) techniques, and the processes by which training environments created by FEED techniques and EIIL techniques assist invariant learning models (e.g., IRM and risk extrapolation (REx)) to improve generalization. In addition, environmental discovery techniques were compared with ERM, conditional variance at risk distributionally robust optimization (CVaR DRO), GEORGE, Fish, Spectral Decoupling2483-14301 (SD), CORAL, just train twice (JTT), and learning from failure (LfF) techniques. In this experimental study, group distributionally robust optimization (GroupDRO) was used as an upper bound given that GroupDRO uses training group annotations.

[0077] Table 1 presented above indicates average and worst-group accuracy for each of the approaches considered by this experimental study. Three main datasets for which prior works have observed poor generalization performance due to spurious correlations were studied: handwritten dataset colored MNIST (CMNIST), WaterBirds, and CelebA. The CMNIST dataset includes a binary classification of colored digit images of [0,4] vs. [5,9]. Two training environments were provided such that the color correlates with the target label with probabilities of 0.8 and 0.9. However, in the test dataset, this correlation dropped to 0.1. Also, the target label was generally noisy and matched the digit class with a probability of only 0.75. The WaterBirds dataset classified waterbirds versus landbirds. The label was spuriously correlated with the image environment, which was either land or water. The CelebA dataset classified the hair color of celebrities as blonde or not blonde. The label was spuriously correlated with gender, which was either male or female.

[0078] The worst group with respect to this experimental study refers to the group (e.g., CMNIST, WaterBirds, and CelebA) on which the model obtained the lowest test accuracy when tuned for average validation accuracy. It may be noted that for WaterBirds and CelebA, IRM and REx could not be directly applied as the environment assignments2483-14301 were originally unavailable. As seen from Table 1, ERM achieved a satisfactory average accuracy given that ERM minimizes the average risk over all training samples. However, the worst-group accuracy for ERM was relatively poor because there were fewer training samples for that group. Other methods, on the other hand, attempted to achieve a balanced performance across different environments or groups. Compared to the EIIL, using FEED to create environments for invariant learning algorithms substantially improved worst-group accuracy. Furthermore, it was found that using FEED+(invariant learning algorithms) could potentially outperform other approaches and achieve a comparable performance relative to GroupDRO, which relies on group annotations. In addition, it was found that for CMNIST, even though the training environment labels were available, FEED was able to create a set of new environments (given the combination of two available environments) with which invariant learning algorithms to achieve superior accuracy.

[0079] In this experimental study, how samples from different groups were distributed across the environments created by FEED was studied. Table 2 presented above indicates the distribution of each group in created environments. a=0 and a=1 corresponds to green and red for CMNIST, land and water environment in WaterBirds, female and male for CelebA, respectively. The numbers presented in Table 2 illustrate how each group is distributed in environments.

[0080] As shown in Table 2, the group annotations were used in each environment to closely examine what samples were assigned to each e1 and e2, although such group annotations were not used for FEED. In the experimental study, it was expected that e1 would contain samples where the shortcut (e.g., the spurious correlation prevalent in the training dataset) exists in the images. For instance, in CMNIST, it was observed that e1 only contained the samples where the label and color (spurious attribute) agreed. This2483-14301 property was reasonable because in this dataset, the digit color and the target attribute agreed for 85% of the training images on average. All other samples were assigned to e2 where this shortcut performed in reverse and the color and label disagreed. Thus, in the created environments, ^^^^^|ψ^(where ψ represents the spurious attribute) varied substantially. To state in other words, the correlation between color and the target attribute was unstableacross environments. However, the correlation between the digit shape and the target attribute remained invariant. Consequently, when an invariant learning algorithm was applied, the model could not satisfy the EIC unless it learned the digit shape. On the other hand, in the standard CMNIST training environment, there was still a slight chance of assuming an invariant association between the color and the target attribute across the environments (e.g., about 10%).

[0081] A similar behavior was observed for WaterBirds and CelebA. For example, in WaterBirds, only 56 training images from waterbirds on land were available, out of which 50 images were assigned to e2. Those remaining six images assigned to e1 were further analyzed. Particularly, most of these samples had environments resembling water, i.e., they were similar to waterbirds on water, which were mainly assigned to e1 (861 versus 195). This may explain why the remaining six images were assigned to e1. It may be noted that waterbirds on water were mostly assigned to e1 since it was intended to contain the samples with the prevalent shortcut.

[0082] Another way to explain the efficacy of the environments was by evaluating the group sufficiency gap g. Not intending to be bound by any particular theory, the group sufficiency gap g may be determined as indicated below in Equation (5) which is based on the EIC: ^^ ൌ | ^^^ ^^|ψ^ ^^^, ^^1^ െ ^^^ ^^|ψ^ ^^^, ^^2^| (5)

[0083] The groupwhich the environment assignments can violate the EIC. As part of this experimental study, it was intended to discover a partitioning strategy which maximized g given that a greater g means a corresponding greater variation in the environments which can lead to a tighter invariant set. In each of the environments that were created, the classifier could rely solely on the spurious attribute a to make predictions where ψ^ ^^^ ൌ ^^.

[0084] In this experimental study, in environment e1, each of digits [5,9] (y=1) were red (a=1) and each of digits [0,4] (y=0) were green (a=0), while in environment e2, each of digits [5,9] (y=1) were green (a=0) and each of digits [0,4] (y=0) were red (a=1). In this2483-14301 exemplary case, g=1, which was its maximum value. On the other hand, for the standard CMNIST environments, the gap was 0.1, and for the EIIL environments g equaled 0.83.

[0085] Overall, in this experimental study, FEED could create an optimal partitioning where the variation in environments was at its maximum. Also, using the pair of (e,y), (a,y) may be fully recovered, which is generally what GroupDRO uses to train a robust model. Therefore, FEED+GroupDRO was generally identical to GroupDRO.

[0086] Why ERM-based models are not sufficient?

[0087] EIIL assumes that the reference model, which is trained using ERM, is learning the shortcut that a spurious attribute can create in the training dataset. Techniques like JTT claim to achieve out-of-distribution generalization by discovering the errors of an ERM model and then upweighing the errors during the next steps of training. It may be questioned whether similar techniques like JTT, for example, can be used to partition the dataset and thereby create environments for invariant learning methods. Although this strategy may perform satisfactorily on datasets that were constructed to showcase out- of-distribution problems, assuming that the reference ERM model always learns the easy shortcuts is generally unrealistic. To illustrate this claim, a variant of the CMNIST dataset (the INVERSE-CMNIST dataset) was constructed where the robust feature (digit shape) was more predictive than the spurious feature (digit color) by decreasing the label noise level to 10%. Table 32483-14301

[0088] Table 3 presented above indicates the test accuracy for an INVERSE-CMNIST dataset. Although shortcuts existed in the dataset, ERM performed well. Hence, ERM- based models could not achieve a satisfactory generalization. On the other hand, FEED could create effective environment partitioning that helped invariant learning algorithms.

[0089] Particularly, Table 3 compares the performance of different methods on the INVERSE-CMNIST dataset. It was found that while the ERM method failed on standard CMNIST (e.g., as shown in Table 1), ERM performed well on INVERSE-CMNIST because relying on the most predictive features (digit shape) was an effective strategy for INVERSE-CMNIST. Other methods failed to achieve a satisfactory performance for INVERSE-CMNIST because the other methods assumed the ERM model was learning the shortcut. In addition, EIIL could not create useful environments in this case. In contrast, FEED utilized the GCE loss function to encourage the model to learn the shortcut and increase variation among environments. In this experimental study, FEED assigned environments similar to the standard CMNNIST, as shown in Table 2.

[0090] Referring now to Figures 5 and 6, Figure 5 illustrates a graph 250 comparing label noise to average accuracy (%) for ERM 251, IRM 252, EIIL 253, classification-enhanced iterative learning framework (CEIL) 254, and the optimum 255. In addition, Figure 6 illustrates a graph 260 comparing label noise to worst-group accuracy (%) for ERM 251, IRM 252, EIIL 253, and CEIL 254. As illustrated in graphs 250 and 260, in this experimental study, it was found that EIIL generalized better with sufficiently high label noise (greater than 25%) but poorly with low label noise. This experimental study highlights the limitations of EIIL and other ERM-based models in finding environments that emphasize the right invariances. Particularly, EIIL and other ERM-based models may leave open the question of how to effectively choose a reference ERM model in general. However, FEED encouraged learning the shortcut in a manner indicating promise in addressing this challenge.

[0091] Additionally, the effectiveness of FEED was evaluated to create useful environments when the spurious attribute creates a more challenging shortcut. A setting similar to the standard CMNIST and by creating grayscale images where the spurious attribute was a square randomly placed in the corners of the image was used. Although the square can serve as a shortcut for this task, it was not as straightforward as using the color in CMNIST or the environment in WaterBirds. This is because, in the feature space, the square is at a similar level as the digit strokes, making it more challenging to distinguish from the digits themselves.2483-14301Table 4

[0092] The results are shown in Table 4 presented above. Particularly, Table 4 indicates the test accuracy for SquareMNIST. Environments created by FEED enhanced the accuracy of the invariant learning algorithms. Additionally, using GCE in FEED assisted FEED in finding the respective shortcut in order to effectively partition the dataset.

[0093] In addition, the results presented in Table 4 indicate the ERM model learned a mix of the shortcut and the main task (e.g., predicting the presence of the target attribute). Therefore, similar to the INVERSE-CMNIST, ERM-based models like EIIL performed poorly in this task. Conversely, FEED effectively created useful environments. In this example, the updating step was initiated after a few training epochs (e.g., five training epochs) of training M1 and M2 with the initial random assignments. This gave the model sufficient time to learn the shortcut (which was challenging to learn in this example) before updating the partitioning. By repeating the partitioning ten times, the group sufficiency gap g for the environments created by FEED equaled 0.98 on average, while for EIIL g equaled only 0.74. In addition, the environments created by FEED improved the performance of the invariant learning algorithms. This experiment was repeated by replacing the GCE with standard cross-entropy (CE), as shown in Table 4. In this case, CE FEED was unable to identify the shortcut and instead partitioned the dataset based2483-14301 on the target attribute. As a result, the invariant learning algorithms could not learn a tight invariant set (e.g., g=0.5).

[0094] Referring to FIGS.8 and 9, FIG.8 includes a graph 300 illustrating training losses (a metric that measures how well a model fits the training dataset during the training phase) 302 and 304 as a function of the number of training epochs for a model trained using conventional ERM training techniques. Particularly, graph 300 illustrates training losses for a conventional ERM training technique when training with an aligned training dataset (aligned training loss 302) in which a shortcut or spurious predictor is aligned with the target attribute and a conflicting training dataset (conflicting training loss 304) in which the spurious predictor is not aligned or conflicts with the target attribute. As shown in graph 300, in this example, the conventional ERM technique produced substantially different degrees of training losses 302 and 304 depending on whether the underlying training dataset was aligned or conflicting. Particularly, for the aligned training dataset, aligned training losses 302 quickly trended towards zero whereas the conflicting training losses 304 initially trends upward only to decline after the completion of multiple early training epochs.

[0095] FIG.9 includes a graph 320 illustrating training losses 322 and 324 as a function of the number of training epochs for a model training using embodiments disclosed herein such as FEED described above, where training losses 322 comprises aligned training losses 322 associated with an aligned training dataset (e.g., the aligned training dataset used in the conventional ERM training technique referenced above with respect to FIG.8) while training losses 324 comprises conflicting training losses 324 associated with a conflicting training dataset (e.g., the conflicting training dataset used in the conventional ERM training technique referenced above with respect to FIG.8). Unlike conflicting training losses 304 of graph 300, the conflicting training losses 324 using the FEED technique showed no disparity with the aligned training losses 322 with each rapidly declining to zero in the initial or early training epochs.

[0096] Overall, this experimental study demonstrated the effectiveness of FEED in creating useful environments, even in challenging scenarios. This can have important implications for real-world applications where spurious attributes can create shortcuts that might be difficult to detect.

[0097] An embodiment of a computer-implemented method for training a deep learning model to predict a presence of a target attribute in a domain set comprises (a) training a first sorting deep learning model (DLM) using a training dataset that is a sample of the2483-14301 domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, (b) training a second sorting DLM using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute in the second datapoint, (c) comparing a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset, (d) assigning the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints, and (e) assigning the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints. In some embodiments, at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN). In some embodiments, the second sorting DLM corresponds to the inverse of the first sorting DLM. In certain embodiments, the method comprises (f) applying the first environment and the second environment to predictive DLM to form a prediction regarding a presence of the target attribute in one or more datapoints of a dataset of which the training dataset comprises a sample. In certain embodiments, the predictive DLM comprises an invariant learning predictor. In some embodiments, (f) comprises satisfying an environment invariance constraint (EIC) in forming the prediction regarding the presence of the target attribute in the one or more datapoints. In some embodiments, (c) comprises comparing a relative cross-entropy loss of the first sorting DLM and the second sorting DLM for the one or more datapoints. In certain embodiments, (c) comprises comparing a first generalized cross-entropy (GCE) loss of the first sorting DLM with a second GCE loss of the second sorting DLM across the one or more datapoints. In certain embodiments, (d) comprises assigning the one or more datapoints to the first environment in response to a first generalized cross- entropy (GCE) loss of the first sorting DLM being less than a second GCE loss of the second sorting DLM across the one or more datapoints, and (e) comprises assigning the one or more datapoints to the second environment in response to the second GCE loss of the first sorting DLM being less than a first GCE loss of the second sorting DLM across the one or more datapoints. In some embodiments, the method comprises (f) updating an earlier iteration of the first environment to define a later iteration of the first2483-14301 environment in response to (d), and (g) updating an earlier iteration of the second environment to define a later iteration of the second environment in response to (e).

[0098] An embodiment of a computer-implemented method for training a deep learning model to predict a presence of a target attribute in a domain set comprises (a) training a first sorting deep learning model (DLM) using a training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, (b) training a second sorting DLM using the training dataset to predict a presence of the target attribute in a second datapoint of the training dataset based on the absence of the first environmental attribute from the second datapoint, and (c) assigning one or more datapoints of the training dataset to either a first environment or a second environment that is different from the first environment based on which of the first sorting DLM and the second sorting DLM has a lesser cross-entropy loss for the one or more datapoints. In some embodiments, (c) comprises (c1) assigning at least one of the one or more datapoints of the training dataset to the first environment in response to the first sorting DLM having the lesser cross-entropy loss, and (c2) assigning another at least one of the one or more datapoints of the training dataset to the second environment in response to the second sorting DLM having the lesser cross-entropy loss. In certain embodiments, the method comprises (d) updating an earlier iteration of the first environment to define a later iteration of the first environment in response to (c1), and (e) updating an earlier iteration of the second environment to define a later iteration of the second environment in response to (c2). In certain embodiments, the method comprises (d) updating an earlier iteration of the first environment to define a later iteration of the first environment in response to (c1) for a plurality of distinct training epochs of the first sorting DLM, and (e) updating an earlier iteration of the second environment to define a later iteration of the second environment in response to (c2) for a plurality of distinct training epochs of the second sorting DLM. In some embodiments, the method comprises (d) defining a final first environment comprising a first plurality of datapoints of the training dataset, the final first environment being different from an initial first environment, and (e) defining a final second environment comprising a second plurality of datapoints of the training dataset, wherein the final second environment is different from both the final first environment and an initial second environment. In some embodiments, (c) comprises iteratively assigning the datapoints of the training dataset to the first environment and to the second environment based on which of the first sorting DLM and the second sorting2483-14301 DLM has the lesser cross-entropy loss for the datapoints to maximize a positive correlation between the first environmental attribute and the target attribute in the final first environment, and to maximize a negative correlation between the first environmental attribute and the target attribute in the final second environment. In certain embodiments, at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN). In certain embodiments, the method comprises (d) applying the first environment and the second environment to an invariant learning predictor to form a prediction regarding a presence of the target attribute in one or more datapoints of the domain set. In some embodiments, (c) comprises assigning the one or more datapoints of the training dataset to either the first environment or the second environment based on a relative cross-entropy loss of the first sorting DLM and the second sorting DLM for the one or more datapoints. In some embodiments, the second sorting DLM corresponds to the inverse of the first sorting DLM.

[0099] An embodiment of a system for training a deep learning model to predict a presence of a target attribute in a domain set comprises a processor, a non-transitory memory, and one or more applications stored in the non-transitory memory that, when executed by the processor: train a first sorting deep learning model (DLM) using a training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint, train a second sorting DLM using the training dataset to predict an absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute from the second datapoint, compare a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset, assign the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints, and assign the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints. In certain embodiments, at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN). In certain embodiments, the one or more applications stored in the non-transitory memory that, when executed by the processor apply the first environment and the second environment to an invariant2483-14301 learning predictor to form a prediction regarding a presence of the target attribute in one or more datapoints of the domain set. In some embodiments, the second sorting DLM corresponds to the inverse of the first sorting DLM.

[0100] While embodiments of the disclosure have been shown and described, modifications thereof can be made by one skilled in the art without departing from the scope or teachings herein. The embodiments described herein are exemplary only and are not limiting. Many variations and modifications of the systems, apparatus, and processes described herein are possible and are within the scope of the disclosure. For example, the relative dimensions of various parts, the materials from which the various parts are made, and other parameters can be varied. Accordingly, the scope of protection is not limited to the embodiments described herein, but is only limited by the claims that follow, the scope of which shall include all equivalents of the subject matter of the claims. Unless expressly stated otherwise, the steps in a method claim may be performed in any order. The recitation of identifiers such as (a), (b), (c) or (1), (2), (3) before steps in a method claim are not intended to and do not specify a particular order to the steps, but rather are used to simplify subsequent reference to such steps.

Claims

2483-14301 CLAIMS What is claimed is:

1. A computer-implemented method for training a deep learning model to predict a presence of a target attribute in a domain set, the method comprising: (a) training a first sorting deep learning model (DLM) using a training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint; (b) training a second sorting DLM using the training dataset to predict the absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute in the second datapoint; (c) comparing a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset; (d) assigning the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints; and (e) assigning the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints.

2. The method of claim 1, wherein at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN).

3. The method of claims 1 or 2, wherein the second sorting DLM corresponds to the inverse of the first sorting DLM.

4. The method of any of claims 1-3, further comprising: (f) applying the first environment and the second environment to predictive DLM to form a prediction regarding a presence of the target attribute in one or more datapoints of a dataset of which the training dataset comprises a sample.2483-14301 5. The method of claim 4, wherein the predictive DLM comprises an invariant learning predictor.

6. The method of claims 4 or 5, wherein (f) comprises satisfying an environment invariance constraint (EIC) in forming the prediction regarding the presence of the target attribute in the one or more datapoints.

7. The method of any of claims 1-6, wherein (c) comprises comparing a relative cross-entropy loss of the first sorting DLM and the second sorting DLM for the one or more datapoints.

8. The method of any of claims 1-7, wherein (c) comprises comparing a first generalized cross-entropy (GCE) loss of the first sorting DLM with a second GCE loss of the second sorting DLM across the one or more datapoints.

9. The method of any of claims 1-8, wherein: (d) comprises assigning the one or more datapoints to the first environment in response to a first generalized cross-entropy (GCE) loss of the first sorting DLM being less than a second GCE loss of the second sorting DLM across the one or more datapoints; and (e) comprises assigning the one or more datapoints to the second environment in response to the second GCE loss of the first sorting DLM being less than a first GCE loss of the second sorting DLM across the one or more datapoints.

10. The method of any of claims 1 -9, further comprising: (f) updating an earlier iteration of the first environment to define a later iteration of the first environment in response to (d); and (g) updating an earlier iteration of the second environment to define a later iteration of the second environment in response to (e).

11. A system for training a deep learning model to predict a presence of a target attribute in a domain set, the system comprising: a processor;2483-14301 a non-transitory memory; and one or more applications stored in the non-transitory memory that, when executed by the processor: train a first sorting deep learning model (DLM) using a training dataset that is a sample of the domain set to predict a presence of the target attribute in a first datapoint of the training dataset based on a presence of a first environmental attribute in the first datapoint; train a second sorting DLM using the training dataset to predict an absence of the target attribute in a second datapoint of the training dataset based on a presence of the first environmental attribute from the second datapoint; compare a first difficulty score of the first sorting DLM in predicting a presence of the target attribute in one or more datapoints of the training dataset with a second difficulty score of the second sorting DLM in predicting the presence of the target attribute in the one or more datapoints of the training dataset; assign the one or more datapoints to a first environment in response to the first difficulty score being less than the second difficulty score for the one or more datapoints; and assign the one or more datapoints to a second environment that is different from the first environment in response to the first difficulty score being greater than the second difficulty score for the one or more datapoints.

12. The system of claim 11, wherein at least one of the first sorting DLM and the second sorting DLM comprises a deep neural network (DNN).

13. The system of claim 11, wherein the one or more applications stored in the non- transitory memory that, when executed by the processor: apply the first environment and the second environment to a predictive DLM to form a prediction regarding a presence of the target attribute in one or more datapoints of the domain set.

14. The system of claim 13, wherein the predictive DLM comprises an invariant learning predictor.

15. The system of claim 11, wherein the second sorting DLM corresponds to the2483-14301 inverse of the first sorting DLM.

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