Several studies have compared the in-distribution (ID) and out-ofdistribution (OOD) performance of models in computer vision and NLP. They report a frequent positive correlation, but surprisingly, almost never an inverse correlation that would be indicative of a necessary trade-off. Such inverse patterns are possible theoretically, and their occurrence in practice is important to determine whether ID performance can serve as a proxy for OOD generalization.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning.

Invariant graph representation learning aims to learn the invariance among data from different environments for out-of-distribution generalization on graphs. As the graph environment partitions are usually expensive to obtain, augmenting the environment information has become the de facto approach. However, the usefulness of the augmented environment information has never been verified. In this work, we find that it is fundamentally impossible to learn invariant graph representations via environment augmentation without additional assumptions. Therefore, we develop a set of minimal assumptions, including variation sufficiency and variation consistency, for feasible invariant graph learning.

Out-of-distribution (OOD) detection and lossless compression constitute two problems that can be solved by the training of probabilistic models on a first dataset with subsequent likelihood evaluation on a second dataset, where data distributions differ. By defining the generalization of probabilistic models in terms of likelihood we show that, in the case of image models, the OOD generalization ability is dominated by local features.

The invariance principle from causality is at the heart of notable approaches such as invariant risk minimization (IRM) that seek to address out-of-distribution (OOD) generalization failures. Despite the promising theory, invariance principle-based approaches fail in common classification tasks, where invariant (causal) features capture all the information about the label. Are these failures due to the methods failing to capture the invariance? Or is the invariance principle itself insufficient? To answer these questions, we revisit the fundamental assumptions in linear regression tasks, where invariance-based approaches were shown to provably generalize OOD. In contrast to the linear regression tasks, we show that for linear classification tasks we need much stronger restrictions on the distribution shifts, or otherwise OOD generalization is impossible. Furthermore, even with appropriate restrictions on distribution shifts in place, we show that the invariance principle alone is insufficient. We prove that a form of the information bottleneck constraint along with invariance helps address key failures when invariant features capture all the information about the label and also retains the existing success when they do not. We propose an approach that incorporates both of these principles and demonstrate its effectiveness in several experiments.

Deep learning has advanced from fully connected architectures to structured models organized into components, e.g., the transformer composed of positional elements, modular architectures divided into slots, and graph neural nets made up of nodes. The nature of structured models is that communication among the components has a bottleneck, typically achieved by restricted connectivity and attention. In this work, we further tighten the bottleneck via discreteness of the representations transmitted between components. We hypothesize that this constraint serves as a useful form of inductive bias. Our hypothesis is motivated by past empirical work showing the benefits of discretization in non-structured architectures as well as our own theoretical results showing that discretization increases noise robustness and reduces the underlying dimensionality of the model.

While Vision Transformer (ViT) have achieved success across various machine learning tasks, deploying them in real-world scenarios faces a critical challenge: generalizing under Out-of-Distribution (OoD) shifts. A crucial research gap remains in understanding how to design ViT architectures - both manually and automatically - to excel in OoD generalization.

In the context of modern machine learning, models deployed in real-world scenarios often encounter diverse data shifts like covariate and semantic shifts, leading to challenges in both out-of-distribution (OOD) generalization and detection. Despite considerable attention to these issues separately, a unified framework for theoretical understanding and practical usage is lacking. To bridge the gap, we introduce a graph-theoretic framework to jointly tackle both OOD generalization and detection problems. By leveraging the graph formulation, data representations are obtained through the factorization of the graph's adjacency matrix, enabling us to derive provable error quantifying OOD generalization and detection performance.