Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization (2109.02934v3)

Abstract: Learning robust models that generalize well under changes in the data distribution is critical for real-world applications. To this end, there has been a growing surge of interest to learn simultaneously from multiple training domains - while enforcing different types of invariance across those domains. Yet, all existing approaches fail to show systematic benefits under controlled evaluation protocols. In this paper, we introduce a new regularization - named Fishr - that enforces domain invariance in the space of the gradients of the loss: specifically, the domain-level variances of gradients are matched across training domains. Our approach is based on the close relations between the gradient covariance, the Fisher Information and the Hessian of the loss: in particular, we show that Fishr eventually aligns the domain-level loss landscapes locally around the final weights. Extensive experiments demonstrate the effectiveness of Fishr for out-of-distribution generalization. Notably, Fishr improves the state of the art on the DomainBed benchmark and performs consistently better than Empirical Risk Minimization. Our code is available at https://github.com/alexrame/fishr.

• The paper’s main contribution is introducing a gradient variance matching method that improves out-of-distribution generalization.
• It leverages theoretical insights from the Fisher Information Matrix and Hessian to align loss landscapes across domains.
• Empirical results on benchmarks like Colored MNIST and PACS demonstrate Fishr's superior performance over ERM and IRM methods.

Fishr: Invariant Gradient Variances for Out-of-Distribution Generalization

In the domain of machine learning, the challenge of creating models that can generalize across various data distributions is of paramount importance. This paper introduces Fishr, a novel approach aimed at improving out-of-distribution (OOD) generalization by leveraging invariant gradient variances across different domains. The main innovation lies in the regularization technique which emphasizes the consistency in the variance of gradient updates, rather than just focusing on loss minimization across domains.

Key Contributions and Methodology

1. Gradient Variance Matching: Fishr takes an innovative approach by ensuring domain invariance in the gradient space. Rather than focusing solely on aligning feature distributions or ensuring invariant risk minimization across domains, Fishr matches the domain-level variances of gradients. This is proposed as more effective than merely aligning the average gradients, which can miss critical variance information that affects generalization.
2. Theoretical Justification: The research builds on the insight that the gradient variance is closely related to the Fisher Information Matrix and the Hessian of the loss. The matching of gradient variances across domains indirectly controls these matrices' properties, promoting more consistent alignments of domain-level loss landscapes. This theoretically reduces inconsistencies in loss landscapes, thereby fostering better generalization performance across unseen domains.
3. Empirical Validation: The experimental setup includes extensive evaluation on both synthetic and real-world datasets. Fishr is tested on the DomainBed benchmark, which includes datasets like Colored MNIST and PACS, among others. Fishr consistently outperforms baseline approaches like Empirical Risk Minimization (ERM) and other competing methods, achieving better generalization on diverse datasets. Notably, it consistently improves test accuracy on tasks like Colored MNIST, which are designed to highlight the weaknesses of models relying on spurious correlations.
4. Comparison with Related Work: By capitalizing on the gradient variance, Fishr offers a complementary perspective to existing methods like Invariant Risk Minimization (IRM) and Risk Extrapolation (V-REx). Unlike these methods, which suffer under certain conditions or require complex training schema, Fishr demonstrates robustness across a range of hyperparameters and does not require intricate scheduling strategies.

Implications and Future Directions

Fishr contributes to the understanding and development of OOD generalization by presenting a computationally efficient and empirically robust method that can be easily integrated into existing models. The theoretical insights into the role of gradient variances extend the current understanding of generalization in neural networks and suggest new paths for improving model robustness.

Looking ahead, future work could focus on:

• Exploring the integration of Fishr with other regularization techniques, potentially enhancing its performance.
• Adapting the Fishr regularization for more complex tasks beyond classification, such as regression and reinforcement learning.
• Investigating the potential of Fishr in adversarial settings, where robustness against distribution shifts is crucial.

In sum, Fishr stands as a significant advancement in the quest for developing models capable of robust OOD generalization by affirmatively addressing the invariant properties of gradient updates across diverse training environments.