Yaming Guo  
(郭 亚明)

Out-of-distribution generalization is challenging for non-participating clients of federated learning under distribution shifts. A proven strategy is to explore those invariant relationships between input and target variables, working equally well for non-participating clients. However, learning invariant relationships is often in an explicit manner from data, representation, and distribution, which violates the federated principles of privacy-preserving and limited communication. In this paper, we propose \textscFedIIR, which implicitly learns invariant relationships from parameter for out-of-distribution generalization, adhering to the above principles. Specifically, we utilize the prediction disagreement to quantify invariant relationships and implicitly reduce it through inter-client gradient alignment. Theoretically, we demonstrate the range of non-participating clients to which \textscFedIIR is expected to generalize and present the convergence results for \textscFedIIR in the massively distributed with limited communication. Extensive experiments show that \textscFedIIR significantly outperforms relevant baselines in terms of out-of-distribution generalization of federated learning.

Optimization over permutations is typically an NP-hard problem that arises extensively in sorting, matching, tracking, etc. Birkhoff polytope-based relaxation methods have made significant advancements, particularly in penalty-free optimization and probabilistic inference. Relaxation onto the orthogonal group offers unique potential advantages such as a lower representation dimension and preservation of inner products; however, equally effective approaches remain unexplored. To bridge the gap, we present a temperature-controlled differentiable transformation that maps unconstrained vector space to the orthogonal group, where the temperature, in the limit, concentrates orthogonal matrices near permutation matrices. This transformation naturally implements a parameterization for the relaxation of permutation matrices, allowing for gradient-based optimization of problems involving permutations. Additionally, by deriving a re-parameterized gradient estimator, this transformation also provides efficient stochastic optimization over the latent permutations. Extensive experiments involving the optimization over permutation matrices validate the effectiveness of the proposed method.