Federated domain generalization addresses the crucial challenge of developing models that can generalize across diverse domains while maintaining data privacy in federated learning settings. Current approaches either compromise privacy constraints or focus narrowly on specific aspects of model invariance, often incurring significant computational overhead. We propose a novel approach FedDIM, which leverages the concept of “insight matrix” - a fine-grained representation of the model's decision-making process derived from element-wise products between feature vectors and classifier weights. By introducing a regularization term that promotes consistency between individual sample insight matrices and their class-wise mean representations, our method effectively captures both feature and classifier invariance. This approach not only maintains strict privacy requirements but also introduces minimal computational overhead as it utilizes intermediate computations already present in the forward pass. Extensive experiments demonstrate that our method achieves superior out-of-distribution generalization compared to existing federated learning approaches while being simple to implement. Our work provides a new perspective on achieving robust generalization in federated learning settings through the lens of decision-making processes.

Domain generalization is a critical challenge for machine learning systems. Prior domain generalization methods focus on extracting domain-invariant features across several stationary domains to enable generalization to new domains. However, in non-stationary tasks where new domains evolve in an underlying continuous structure, such as time, merely extracting the invariant features is insufficient for generalization to the evolving new domains. Nevertheless, it is non-trivial to learn both evolving and invariant features within a single model due to their conflicts. To bridge this gap, we build causal models to characterize the distribution shifts concerning the two patterns, and propose to learn both dynamic and invariant features via a new framework called Mutual Information-Based Sequential Autoencoders (MISTS). MISTS adopts information theoretic constraints onto sequential autoencoders to disentangle the dynamic and invariant features, and leverage an adaptive classifier to make predictions based on both evolving and invariant information. Our experimental results on both synthetic and real-world datasets demonstrate that MISTS succeeds in capturing both evolving and invariant information, and present promising results in evolving domain generalization tasks.

Learning neural subset selection tasks, such as compound selection in AI-aided drug discovery, have become increasingly pivotal across diverse applications. The existing methodologies in the field primarily concentrate on constructing models that capture the relationship between utility function values and subsets within their respective supersets. However, these approaches tend to overlook the valuable information contained within the superset when utilizing neural networks to model set functions. In this work, we address this oversight by adopting a probabilistic perspective. Our theoretical findings demonstrate that when the target value is conditioned on both the input set and subset, it is essential to incorporate an invariant sufficient statistic of the superset into the subset of interest for effective learning. This ensures that the output value remains invariant to permutations of the subset and its corresponding superset, enabling identification of the specific superset from which the subset originated. Motivated by these insights, we propose a simple yet effective information aggregation module designed to merge the representations of subsets and supersets from a permutation invariance perspective. Comprehensive empirical evaluations across diverse tasks and datasets validate the enhanced efficacy of our approach over conventional methods, underscoring the practicality and potency of our proposed strategies in real-world contexts.

Subset selection tasks, such as anomaly detection and compound selection in AI-assisted drug discovery, are crucial for a wide range of applications. Learning subset-valued functions with neural networks has achieved great success by incorporating permutation invariance symmetry into the architecture. However, existing neural set architectures often struggle to either capture comprehensive information from the superset or address complex interactions within the input. Additionally, they often fail to perform in scenarios where superset sizes surpass available memory capacity. To address these challenges, we introduce the novel concept of the Identity Property, which requires models to integrate information from the originating set, resulting in the development of neural networks that excel at performing effective subset selection from large supersets. Moreover, we present the Hierarchical Representation of Neural Subset Selection (HORSE), an attention-based method that learns complex interactions and retains information from both the input set and the optimal subset supervision signal. Specifically, HORSE enables the partitioning of the input ground set into manageable chunks that can be processed independently and then aggregated, ensuring consistent outcomes across different partitions. Through extensive experimentation, we demonstrate that HORSE significantly enhances neural subset selection performance by capturing more complex information and surpasses state-of-the-art methods in handling large-scale inputs by a margin of up to 20%.

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. We then propose a new framework Graph invAriant Learning Assistant (GALA). GALA incorporates an assistant model that needs to be sensitive to graph environment changes or distribution shifts. The correctness of the proxy predictions by the assistant model hence can differentiate the variations in spurious subgraphs. We show that extracting the maximally invariant subgraph to the proxy predictions provably identifies the underlying invariant subgraph for successful OOD generalization under the established minimal assumptions. Extensive experiments on datasets including DrugOOD with various graph distribution shifts confirm the effectiveness of GALA.

The AutoAttack (AA) has been the most reliable method to evaluate adversarial robustness when considerable computational resources are available. However, the high computational cost (e.g., 100 times more than that of the project gradient descent attack) makes AA infeasible for practitioners with limited computational resources, and also hinders applications of AA in the adversarial training (AT). In this paper, we propose a novel method, minimum-margin (MM) attack, to fast and reliably evaluate adversarial robustness. Compared with AA, our method achieves comparable performance but only costs 3% of the computational time in extensive experiments. The reliability of our method lies in that we evaluate the quality of adversarial examples using the margin between two targets that can precisely identify the most adversarial example. The computational efficiency of our method lies in an effective Sequential TArget Ranking Selection (STARS) method, ensuring that the cost of the MM attack is independent of the number of classes. The MM attack opens a new way for evaluating adversarial robustness and provides a feasible and reliable way to generate high-quality adversarial examples in AT.

Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses unique challenges to adopting the invariance principle. In particular, distribution shifts on graphs can appear in a variety of forms such as attributes and structures, making it difficult to identify the invariance. Moreover, domain or environment partitions, which are often required by OOD methods on Euclidean data, could be highly expensive to obtain for graphs. To bridge this gap, we propose a new framework, called Causality Inspired Invariant Graph LeArning (CIGA), to capture the invariance of graphs for guaranteed OOD generalization under various distribution shifts. Specifically, we characterize potential distribution shifts on graphs with causal models, concluding that OOD generalization on graphs is achievable when models focus only on subgraphs containing the most information about the causes of labels. Accordingly, we propose an information-theoretic objective to extract the desired subgraphs that maximally preserve the invariant intra-class information. Learning with these subgraphs is immune to distribution shifts. Extensive experiments on 16 synthetic or real-world datasets, including a challenging setting -- DrugOOD, from AI-aided drug discovery, validate the superior OOD performance of CIGA.