Out-of-distribution (OOD) generalization deals with the prevalent learning scenario where test distribution shifts from training distribution. With rising application demands and inherent complexity, graph OOD problems call for specialized solutions. While data-centric methods exhibit performance enhancements on many generic machine learning tasks, there is a notable absence of data augmentation methods tailored for graph OOD generalization. In this work, we propose to achieve graph OOD generalization with the novel design of non-Euclidean-space linear extrapolation. The proposed augmentation strategy extrapolates both structure and feature spaces to generate OOD graph data. Our design tailors OOD samples for specific shifts without corrupting underlying causal mechanisms. Theoretical analysis and empirical results evidence the effectiveness of our method in solving target shifts, showing substantial and constant improvements across various graph OOD tasks.
Covariate shifts are a common problem in predictive modeling on real-world problems. This paper proposes addressing the covariate shift problem by minimizing Maximum Mean Discrepancy (MMD) statistics between the training and test sets in either feature input space, feature representation space, or both. We designed three techniques that we call MMD Representation, MMD Mask, and MMD Hybrid to deal with the scenarios where only a distribution shift exists, only a missingness shift exists, or both types of shift exist, respectively. We find that integrating an MMD loss component helps models use …
Mila（米拉研究所）；University of Montreal（蒙特利尔大学）；Vector（Vector研究所）；University of Toronto（多伦多大学）；McGill University（麦吉尔大学）；Facebook AI Research（脸书人工智能研究院）
Distributional shift is one of the major obstacles when transferring machine learning prediction systems from the lab to the real world. To tackle this problem, we assume that variation across training domains is representative of the variation we might encounter at test time, but also that shifts at test time may be more extreme in magnitude. In particular, we show that reducing differences in risk across training domains can reduce a model's sensitivity to a wide range of extreme distributional shifts, including the challenging setting where the input contains both causal and anti-causal ele…
Diversified Outlier Exposure for Out-of-Distribution Detection via Informative Extrapolation
CMIC, Shanghai Jiao Tong University（上海交通大学CMIC）；Shanghai AI Laboratory（上海人工智能实验室）；Sydney AI Centre, The University of Sydney（悉尼大学悉尼AI中心）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能研究中心）；The University of Tokyo（东京大学）；Hong Kong Baptist University（香港浸会大学）
In general, graph representation learning methods assume that the train and test data come from the same distribution. In this work we consider an underexplored area of an otherwise rapidly developing field of graph representation learning: The task of out-of-distribution (OOD) graph classification, where train and test data have different distributions, with test data unavailable during training. Our work shows it is possible to use a causal model to learn approximately invariant representations that better extrapolate between train and test data. Finally, we conclude with synthetic and real-…
Yale Center for Medical Informatics, Yale University（耶鲁大学耶鲁医学信息学中心）；VA Connecticut Healthcare System（康涅狄格州退伍军人医疗保健系统）；Yale School of Medicine（耶鲁大学医学院）
We study the functional task of deep learning image classification models and show that image classification requires extrapolation capabilities. This suggests that new theories have to be developed for the understanding of deep learning as the current theory assumes models are solely interpolating, leaving many questions about them unanswered. We investigate the pixel space and also the feature spaces extracted from images by trained models (in their hidden layers, including the 64-dimensional feature space in the last hidden layer of pre-trained residual neural networks), and also the featur…
Universitat Politècnica de Catalunya-Barcelona Tech（加泰罗尼亚理工大学-巴塞罗那理工）；University of Minnesota（明尼苏达大学）
Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable algorithms. This paper analyzes the generalization error of such approaches, and presents numerical tests confirming the theoretical results.
Yale Center for Medical Informatics（耶鲁医学信息学中心）；VA Connecticut Healthcare System（康涅狄格州退伍军人医疗系统）
We study the generalization of over-parameterized deep networks (for image classification) in relation to the convex hull of their training sets. Despite their great success, generalization of deep networks is considered a mystery. These models have orders of magnitude more parameters than their training samples, and they can achieve perfect accuracy on their training sets, even when training images are randomly labeled, or the contents of images are replaced with random noise. The training loss function of these models has infinite number of near zero minimizers, where only a small subset of …
A popular assumption for out-of-distribution generalization is that the training data comprises sub-datasets, each drawn from a distinct distribution; the goal is then to "interpolate" these distributions and "extrapolate" beyond them -- this objective is broadly known as domain generalization. A common belief is that ERM can interpolate but not extrapolate and that the latter is considerably more difficult, but these claims are vague and lack formal justification. In this work, we recast generalization over sub-groups as an online game between a player minimizing risk and an adversary present…
Rule Extrapolation in Language Models: A Study of Compositional Generalization on OOD Prompts
University of Cambridge（剑桥大学）；AI Center, UCL（伦敦大学学院人工智能中心）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；ELLIS Institute Tübingen（蒂宾根ELLIS研究所）；Tübingen AI Center（蒂宾根人工智能中心）
Understanding how agents learn to generalize -- and, in particular, to extrapolate -- in high-dimensional, naturalistic environments remains a challenge for both machine learning and the study of biological agents. One approach to this has been the use of function learning paradigms, which allow peoples' empirical patterns of generalization for smooth scalar functions to be described precisely. However, to date, such work has not succeeded in identifying mechanisms that acquire the kinds of general purpose representations over which function learning can operate to exhibit the patterns of gene…
Centre d’Analyse et de Mathématique Sociales（社会分析与数学中心）；École des Hautes Études en Sciences Sociales（社会科学高等学院）
There has been a long history of works showing that neural networks have hard time extrapolating beyond the training set. A recent study by Balestriero et al. (2021) challenges this view: defining interpolation as the state of belonging to the convex hull of the training set, they show that the test set, either in input or neural space, cannot lie for the most part in this convex hull, due to the high dimensionality of the data, invoking the well known curse of dimensionality. Neural networks are then assumed to necessarily work in extrapolative mode. We here study the neural activities of the…
Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when increasing the batch size to a substantial fraction of the training data for improving training time is the persistent degradation in performance (generalization gap). To address this issue, recent work propose to add small perturbations to the model parameters when computing the stochastic gradients and report improved generalization performance due to smoothi…
Blavatnik School of Computer Science（布拉瓦特尼克计算机科学学院）；Tel Aviv University（特拉维夫大学）
When using recurrent neural networks (RNNs) it is common practice to apply trained models to sequences longer than those seen in training. This "extrapolating" usage deviates from the traditional statistical learning setup where guarantees are provided under the assumption that train and test distributions are identical. Here we set out to understand when RNNs can extrapolate, focusing on a simple case where the data generating distribution is memoryless. We first show that even with infinite training data, there exist RNN models that interpolate perfectly (i.e., they fit the training data) ye…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Boston University（波士顿大学）
Flexible neural sequence models outperform grammar- and automaton-based counterparts on a variety of tasks. However, neural models perform poorly in settings requiring compositional generalization beyond the training data -- particularly to rare or unseen subsequences. Past work has found symbolic scaffolding (e.g. grammars or automata) essential in these settings. We describe R&R, a learned data augmentation scheme that enables a large category of compositional generalizations without appeal to latent symbolic structure. R&R has two components: recombination of original training examples via …
National University of Defense Technology（国防科技大学）；International Digital Economy Academy（国际数字经济研究院）
In the last few years, the solution to Knowledge Graph (KG) completion via learning embeddings of entities and relations has attracted a surge of interest. Temporal KGs(TKGs) extend traditional Knowledge Graphs (KGs) by associating static triples with timestamps forming quadruples. Different from KGs and TKGs in the transductive setting, constantly emerging entities and relations in incomplete TKGs create demand to predict missing facts with unseen components, which is the extrapolation setting. Traditional temporal knowledge graph embedding (TKGE) methods are limited in the extrapolation sett…
When applying machine learning/statistical methods to the environmental sciences, nonlinear regression (NLR) models often perform only slightly better and occasionally worse than linear regression (LR). The proposed reason for this conundrum is that NLR models can give predictions much worse than LR when given input data which lie outside the domain used in model training. Continuous unbounded variables are widely used in environmental sciences, whence not uncommon for new input data to lie far outside the training domain. For six environmental datasets, inputs in the test data were classified…
Gaussian processes are rich distributions over functions, with generalization properties determined by a kernel function. When used for long-range extrapolation, predictions are particularly sensitive to the choice of kernel parameters. It is therefore critical to account for kernel uncertainty in our predictive distributions. We propose a distribution over kernels formed by modelling a spectral mixture density with a Lévy process. The resulting distribution has support for all stationary covariances--including the popular RBF, periodic, and Matérn kernels--combined with inductive biases which…
