Visual Representation Learning Does Not Generalize Strongly Within the Same Domain

1 INTRODUCTION . Humans excel at learning underlying physical mechanisms or inner workings of a system from observations ( Funke et al. , 2021 ; Barrett et al. , 2018 ; Santoro et al. , 2017 ; Villalobos et al. , 2020 ; Spelke , 1990 ) , which helps them generalize quickly to new situations and to learn efficiently from little data ( Battaglia et al. , 2013 ; Dehaene , 2020 ; Lake et al. , 2017 ; Téglás et al. , 2011 ) . In contrast , machine learning systems typically require large amounts of curated data and still mostly fail to generalize to out-of-distribution ( OOD ) scenarios ( Schölkopf et al. , 2021 ; Hendrycks & Dietterich , 2019 ; Karahan et al. , 2016 ; Michaelis et al. , 2019 ; Roy et al. , 2018 ; Azulay & Weiss , 2019 ; Barbu et al. , 2019 ) . It has been hypothesized that this failure of machine learning systems is due to shortcut learning ( Kilbertus * et al. , 2018 ; Ilyas et al. , 2019 ; Geirhos et al. , 2020 ; Schölkopf et al. , 2021 ) . In essence , machines seemingly learn to solve the tasks they have been trained on using auxiliary and spurious statistical relationships in the data , rather than true mechanistic relationships . Pragmatically , models relying on statistical relationships tend to fail if tested outside their training distribution , while models relying on ( approximately ) the true underlying mechanisms tend to generalize well to novel scenarios ( Barrett et al. , 2018 ; Funke et al. , 2021 ; Wu et al. , 2019 ; Zhang et al. , 2018 ; Parascandolo et al. , 2018 ; Schölkopf et al. , 2021 ; Locatello et al. , 2020a ; b ) . To learn effective statistical relationships , the training data needs to cover most combinations of factors of variation ( like shape , size , color , viewpoint , etc. ) . Unfortunately , the number of combinations scales exponentially with the number of factors . In contrast , learning the underlying mechanisms behind the factors of variation should greatly reduce the need for training data and scale more gently with the number of factors ( Schölkopf et al. , 2021 ; Peters et al. , 2017 ; Besserve et al. , 2021 ) . Benchmark : Our goal is to quantify how well machine learning models already learn the mechanisms underlying a data generative process . To this end , we consider four image data sets where each image is described by a small number of independently controllable factors of variation such as scale , color , or size . We split the training and test data such that models that learned the underlying mechanisms should generalize to the test data . More precisely , we propose several systematic out-of-distribution ( OOD ) test splits like composition ( e.g. , train = small hearts , large squares → test = small squares , large hearts ) , interpolation ( e.g. , small hearts , large hearts → medium hearts ) and extrapolation ( e.g. , small hearts , medium hearts → large hearts ) . While the factors of variation are independently controllable ( e.g. , there may exist large and small hearts ) , the observations may exhibit spurious statistical dependencies ( e.g. , observed hearts are typically small , but size may not be predictive at test time ) . Based on this setup , we benchmark 17 representation learning approaches and study their inductive biases . The considered approaches stem from un-/weakly supervised disentanglement , supervised learning , and the transfer learning literature . Results : Our benchmark results indicate that the tested models mostly struggle to learn the underlying mechanisms regardless of supervision signal and architecture . As soon as a factor of variation is outside the training distribution , models consistently tend to predict a value in the previously observed range . On the other hand , these models can be fairly modular in the sense that predictions of in-distribution factors remain accurate , which is in part against common criticisms of deep neural networks ( Greff et al. , 2020 ; Csordás et al. , 2021 ; Marcus , 2018 ; Lake & Baroni , 2018 ) . New Dataset : Previous datasets with independent controllable factors such as dSprites , Shapes3D , and MPI3D ( Matthey et al. , 2017 ; Kim & Mnih , 2018 ; Gondal et al. , 2019 ) stem from highly structured environments . For these datasets , common factors of variations are scaling , rotation and simple geometrical shapes . We introduce a dataset derived from celebrity faces , named CelebGlow , with factors of variations such as smiling , age and hair-color . It also contains all possible factor combinations . It is based on latent traversals of a pretrained Glow network provided by Kingma et al . ( Kingma & Dhariwal , 2018 ) and the Celeb-HQ dataset ( Liu et al. , 2015 ) . We hope that this benchmark can guide future efforts to find machine learning models capable of understanding the true underlying mechanisms in the data . To this end , all data sets and evaluation scripts are released alongside a leaderboard on GitHub . 1 2 PROBLEM SETTING y1 . . . yn x s Figure 1 : Assumed graphical model connecting the factors of variations y = ( y1 , ... , yn ) to observations x = g ( y ) . The selection variable s ∈ { tr , te } leads to different train and test splits ps ( y ) , thereby inducing correlation between the FoVs . Assume that we render each observation or image x ∈ Rd using a “ computer graphic model ” which takes as input a set of independently controllable factors of variation ( FoVs ) y ∈ Rn like size or color . More formally , we assume a generative process of the form x = g ( y ) , where g : Rn 7→ Rd is an injective and smooth function . In the standard independently and identically distributed ( IID ) setting , we would generate the training and test data in the same way , i.e. , we would draw y from the same prior distribution p ( y ) and then generate the corresponding images x according to g ( · ) . Instead , we here consider an OOD setting where the prior distribution ptr ( y ) during training is different from the prior distribution pte ( y ) during testing . In fact , in all settings of our benchmark , the training and test distributions are completely disjoint , meaning that each point can only have non-zero probability mass in either ptr ( y ) or pte ( y ) . Crucially , however , the function g which maps between FoVs and observations is shared between training and testing , which is why we refer to it as an invariant mechanism . As shown in the causal graphical model in Fig . 1 , the factors of variations y are independently controllable to begin with , but the binary split variable s introduces spurious correlations between the FoVs that are different at training and test time as a result of selection bias ( Storkey , 2009 ; Bareinboim & Pearl , 2012 ) . In particular , we consider Random , Composition , Interpolation , and Extrapolation splits as illustrated in Fig . 2 . We refer to §4.2 for details on the implementation of these splits . The task for our machine learning models f is to estimate the factors of variations y that generated the sample x on both the training and test data . In other words , we want that ( ideally ) f = g−1 . The main challenge is that , during training , we only observe data from ptr but wish to generalize to pte . Hence , the learned function f should not only invert g locally on the training domain supp ( ptr ( y ) ) ⊆ Rn but ideally globally . In practice , let Dte = { ( yk , xk ) } be the test data with yk drawn from pte ( y ) and let f : Rd 7→ Rn be the model . Now , the goal is to design and optimize the 1https : //github.com/bethgelab/InDomainGeneralizationBenchmark model f on the training set Dtr such that it achieves a minimal R-squared distance between yk and f ( xk ) on the test set Dte . During training , models are allowed to sample the data from all non-zero probability regions supp ( ptr ( y ) ) in whatever way is optimal for its learning algorithm . This general formulation covers different scenarios and learning methods that could prove valuable for learning independent mechanisms . For example , supervised methods will sample an IID data set Dtr = { ( yk , xk ) } with yk ∼ ptr ( y ) , while self-supervised methods might sample a data set of unlabeled image pairs Dtr = { ( xk , x̃k ) } . We aim to understand what inductive biases help on these OOD settings and how to best leverage the training data to learn representations that generalize . 3 INDUCTIVE BIASES FOR GENERALIZATION IN VISUAL REPRESENTATION LEARNING . We now explore different types of assumptions , or inductive biases , on the representational format ( §3.1 ) , architecture ( §3.2 ) , and dataset ( §3.3 ) which have been proposed and used in the past to facilitate generalization . Inductive inference and the generalization of empirical findings is a fundamental problem of science that has a long-standing history in many disciplines . Notable examples include Occam ’ s razor , Solomonoff ’ s inductive inference ( Solomonoff , 1964 ) , Kolmogorov complexity ( Kolmogorov , 1998 ) , the bias-variance-tradeoff ( Kohavi et al. , 1996 ; Von Luxburg & Schölkopf , 2011 ) , and the no free lunch theorem ( Wolpert , 1996 ; Wolpert & Macready , 1997 ) . In the context of statistical learning , Vapnik and Chervonenkis ( Vapnik & Chervonenkis , 1982 ; Vapnik , 1995 ) showed that generalizing from a sample to its population ( i.e. , IID generalization ) requires restricting the capacity of the class of candidate functions—a type of inductive bias . Since shifts between train and test distributions violate the IID assumption , however , statistical learning theory does not directly apply to our types of OOD generalization . OOD generalization across different ( e.g. , observational and experimental ) conditions also bears connections to causal inference ( Pearl , 2009 ; Peters et al. , 2017 ; Hernán & Robins , 2020 ) . Typically , a causal graph encodes assumptions about the relation between different distributions and is used to decide how to “ transport ” a learned model ( Pearl & Bareinboim , 2011 ; Pearl et al. , 2014 ; Bareinboim & Pearl , 2016 ; von Kügelgen et al. , 2019 ) . Other approaches aim to learn a model which leads to invariant prediction across multiple environments ( Schölkopf et al. , 2012 ; Peters et al. , 2016 ; HeinzeDeml et al. , 2018 ; Rojas-Carulla et al. , 2018 ; Arjovsky et al. , 2019 ; Lu et al. , 2021 ) . However , these methods either consider a small number of causally meaningful variables in combination with domain knowledge , or assume access to data from multiple environments . In our setting , on the other hand , we aim to learn from higher-dimensional observations and to generalize from a single training set to a different test environment . Our work focuses on OOD generalization in the context of visual representation learning , where deep learning has excelled over traditional learning approaches ( Krizhevsky et al. , 2012 ; LeCun et al. , 2015 ; Schmidhuber , 2015 ; Goodfellow et al. , 2016 ) . In the following , we therefore concentrate on inductive biases specific to deep neural networks ( Goyal & Bengio , 2020 ) on visual data . For details regarding specific objective functions , architectures , and training , we refer to the supplement .

Summary: The paper introduces a new dataset: CelebGLOW which is a controllable environment generation dataset, which can be used in the same form as significantly less complex datasets, such as sprites. The paper evaluates over 3 key inductive biases using the dataset: "representational format" (using images in this paper), neural network architectural variants (MLPs/CNNs/ transformers, etc), and ability to perform transfer learning. The paper evalutes the models on 4 given modes of generalization: interpolation, extrapolation, compositional learning and "random", and finds extremely fascinating conclusions through extensive experimentation.