Haozhe Si

Haoxiang Wang, Gargi Balasubramaniam, Haozhe Si et al.

Domain generalization asks for models trained over a set of training environments to generalize well in unseen test environments. Recently, a series of algorithms such as Invariant Risk Minimization (IRM) have been proposed for domain generalization. However, Rosenfeld et al. (2021) shows that in a simple linear data model, even if non-convexity issues are ignored, IRM and its extensions cannot generalize to unseen environments with less than $d_s+1$ training environments, where $d_s$ is the dimension of the spurious-feature subspace. In this work, we propose Invariant-feature Subspace Recovery (ISR): a new class of algorithms to achieve provable domain generalization across the settings of classification and regression problems. First, in the binary classification setup of Rosenfeld et al. (2021), we show that our first algorithm, ISR-Mean, can identify the subspace spanned by invariant features from the first-order moments of the class-conditional distributions, and achieve provable domain generalization with $d_s+1$ training environments. Our second algorithm, ISR-Cov, further reduces the required number of training environments to $O(1)$ using the information of second-order moments. Notably, unlike IRM, our algorithms bypass non-convexity issues and enjoy global convergence guarantees. Next, we extend ISR-Mean to the more general setting of multi-class classification and propose ISR-Multiclass, which leverages class information and provably recovers the invariant-feature subspace with $\lceil d_s/k\rceil+1$ training environments for $k$-class classification. Finally, for regression problems, we propose ISR-Regression that can identify the invariant-feature subspace with $d_s+1$ training environments. Empirically, we demonstrate the superior performance of our ISRs on synthetic benchmarks. Further, ISR can be used as post-processing methods for feature extractors such as neural nets.

Haoxiang Wang, Haozhe Si, Huajie Shao et al.

Real-world applications of machine learning models often confront data distribution shifts, wherein discrepancies exist between the training and test data distributions. In the common multi-domain multi-class setup, as the number of classes and domains scales up, it becomes infeasible to gather training data for every domain-class combination. This challenge naturally leads the quest for models with Compositional Generalization (CG) ability, where models can generalize to unseen domain-class combinations. To delve into the CG challenge, we develop CG-Bench, a suite of CG benchmarks derived from existing real-world image datasets, and observe that the prevalent pretraining-finetuning paradigm on foundational models, such as CLIP and DINOv2, struggles with the challenge. To address this challenge, we propose Compositional Feature Alignment (CFA), a simple two-stage finetuning technique that i) learns two orthogonal linear heads on a pretrained encoder with respect to class and domain labels, and ii) fine-tunes the encoder with the newly learned head frozen. We theoretically and empirically justify that CFA encourages compositional feature learning of pretrained models. We further conduct extensive experiments on CG-Bench for CLIP and DINOv2, two powerful pretrained vision foundation models. Experiment results show that CFA outperforms common finetuning techniques in compositional generalization, corroborating CFA's efficacy in compositional feature learning.

Yuen Chen, Haozhe Si, Guojun Zhang et al.

Domain generalization (DG) seeks to develop models that generalize well to unseen target domains, addressing the prevalent issue of distribution shifts in real-world applications. One line of research in DG focuses on aligning domain-level gradients and Hessians to enhance generalization. However, existing methods are computationally inefficient and the underlying principles of these approaches are not well understood. In this paper, we develop the theory of moment alignment for DG. Grounded in \textit{transfer measure}, a principled framework for quantifying generalizability between two domains, we first extend the definition of transfer measure to domain generalization that includes multiple source domains and establish a target error bound. Then, we prove that aligning derivatives across domains improves transfer measure both when the feature extractor induces an invariant optimal predictor across domains and when it does not. Notably, moment alignment provides a unifying understanding of Invariant Risk Minimization, gradient matching, and Hessian matching, three previously disconnected approaches to DG. We further connect feature moments and derivatives of the classifier head, and establish the duality between feature learning and classifier fitting. Building upon our theory, we introduce \textbf{C}losed-Form \textbf{M}oment \textbf{A}lignment (CMA), a novel DG algorithm that aligns domain-level gradients and Hessians in closed-form. Our method overcomes the computational inefficiencies of existing gradient and Hessian-based techniques by eliminating the need for repeated backpropagation or sampling-based Hessian estimation. We validate the efficacy of our approach through two sets of experiments: linear probing and full fine-tuning. CMA demonstrates superior performance in both settings compared to Empirical Risk Minimization and state-of-the-art algorithms.

Haoxiang Wang, Haozhe Si, Bo Li et al.

Domain generalization asks for models trained over a set of training environments to perform well in unseen test environments. Recently, a series of algorithms such as Invariant Risk Minimization (IRM) has been proposed for domain generalization. However, Rosenfeld et al. (2021) shows that in a simple linear data model, even if non-convexity issues are ignored, IRM and its extensions cannot generalize to unseen environments with less than $d_s+1$ training environments, where $d_s$ is the dimension of the spurious-feature subspace. In this paper, we propose to achieve domain generalization with Invariant-feature Subspace Recovery (ISR). Our first algorithm, ISR-Mean, can identify the subspace spanned by invariant features from the first-order moments of the class-conditional distributions, and achieve provable domain generalization with $d_s+1$ training environments under the data model of Rosenfeld et al. (2021). Our second algorithm, ISR-Cov, further reduces the required number of training environments to $O(1)$ using the information of second-order moments. Notably, unlike IRM, our algorithms bypass non-convexity issues and enjoy global convergence guarantees. Empirically, our ISRs can obtain superior performance compared with IRM on synthetic benchmarks. In addition, on three real-world image and text datasets, we show that both ISRs can be used as simple yet effective post-processing methods to improve the worst-case accuracy of (pre-)trained models against spurious correlations and group shifts.