[Paper Review] Learning explanations that are hard to vary

Giambattista Parascandolo, Alexander Neitz+3 more|arXiv (Cornell University)|Sep 1, 2020

Neural Networks and ApplicationsComputer Science44 references73 citations

TL;DR

The paper formalizes Invariant Learning Consistency (ILC) and introduces an AND-mask gradient method to encourage learning invariant explanations across environments, reducing memorization and improving out-of-distribution generalization.

ABSTRACT

In this paper, we investigate the principle that `good explanations are hard to vary' in the context of deep learning. We show that averaging gradients across examples -- akin to a logical OR of patterns -- can favor memorization and `patchwork' solutions that sew together different strategies, instead of identifying invariances. To inspect this, we first formalize a notion of consistency for minima of the loss surface, which measures to what extent a minimum appears only when examples are pooled. We then propose and experimentally validate a simple alternative algorithm based on a logical AND, that focuses on invariances and prevents memorization in a set of real-world tasks. Finally, using a synthetic dataset with a clear distinction between invariant and spurious mechanisms, we dissect learning signals and compare this approach to well-established regularizers.

Motivation & Objective

• Motivate the need for invariant explanations that generalize across environments rather than memorizing spurious patterns.
• Formalize a consistency measure to evaluate how robust a model's minima are across environments.
• Propose and validate an alternative gradient aggregation method (AND-mask) to emphasize invariances.
• Demonstrate through synthetic and real-world tasks that ILC can improve o.o.d. generalization and resist memorization.
• Compare the proposed approach with established regularizers and domain adaptation methods.

Proposed method

• Define a formal consistency score I^ε(θ*) that measures how loss landscapes differ across environments near a minimum.
• Introduce Invariant Learning Consistency (ILC) as the expected consistency of the algorithm's convergent solution across environments.
• Propose the AND-mask: mask gradient components whose signs disagree across environments, enabling an implicit logical AND between environments.
• Explain how the AND-mask can be implemented with a threshold τ and show it preserves computational efficiency comparable to standard GD.
• Relate the method to the geometric mean of Hessians to conceptually justify reduced inconsistency in gradient directions.

Experimental results

Research questions

• RQ1 Can a consistency measure be defined to identify minima that generalize across environments?
• RQ2 Does gradient aggregation via an AND-like operation promote invariances and reduce memorization?
• RQ3 How does ILC with the AND-mask perform on synthetic tasks with invariant mechanisms and shortcuts compared to standard regularizers?
• RQ4 Does the approach improve out-of-distribution generalization in real tasks like CIFAR-10 with random labels and CoinRun behavioral cloning?

Key findings

• An AND-mask gradient method increases consistency by masking inconsistent gradient components across environments.
• The AND-mask can prevent memorization on synthetic tasks that rely on environment-specific shortcuts.
• On CIFAR-10 with random labels, the AND-mask prevents memorization while preserving performance on normally labeled data.
• In a CoinRun behavioral cloning setup, the AND-mask improves generalization to unseen levels.
• Standard training tends to maximize training speed, which can sacrifice invariant learning, whereas ILC trade-offs learning speed for invariances.