Invariance Principle Meets Information Bottleneck for Out-of-Distribution Generalization

TL;DR

This paper investigates the limitations of the invariance principle in out-of-distribution generalization for classification tasks and proposes combining it with an information bottleneck constraint to improve robustness.

Contribution

It reveals the insufficiency of invariance alone in classification OOD tasks and introduces a combined approach with information bottleneck to enhance generalization.

Findings

Invariance alone is insufficient for OOD generalization in classification.

Stronger restrictions on distribution shifts are needed for invariance-based methods.

Combining invariance with an information bottleneck improves OOD robustness.

Abstract

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.