This paper presents Sheaf-DMFL, a novel decentralized multimodal federated learning framework leveraging sheaf theory to enhance collaborative learning among clients with diverse modalities. By framing the multimodal federated learning problem as multitask learning, Sheaf-DMFL leverages learnable restriction maps to capture relationships between clients’ models. Specifically, each client has a set of local feature encoders for its different modalities, whose outputs are concatenated before passing through a task-specific layer. Encoders corresponding to the same modality are shared among clients, while the intrinsic correlation among their task-specific layers is captured by using the sheaf structure. Numerical experiments in a mmWave beamforming prediction scenario show that the proposed algorithm surpasses baseline methods, delivering improved convergence rates and test accuracy.

In this letter, we formulate a compositional distributed learning framework for multi-view perception by leveraging the maximal coding rate reduction principle combined with subspace basis fusion. In the proposed algorithm, each agent conducts a periodic singular value decomposition on its learned subspaces and exchanges truncated basis matrices, based on which the fused subspaces are obtained. By introducing a projection matrix and minimizing the distance between the outputs and its projection, the learned representations are enforced towards the fused subspaces. It is proved that the trace on the coding-rate change is bounded and the consistency of basis fusion is guaranteed theoretically. Numerical simulations validate that the proposed algorithm achieves high classification accuracy while maintaining representations' diversity, compared to baselines showing correlated subspaces and coupled representations.

The distributed alternating direction method of multipliers (ADMM) is an efficient distributed optimization algorithm, which however shows poor convergence in time-varying network topologies. To solve the challenge, we propose TV-ADMM, a novel distributed ADMM algorithm for time-varying communication networks. More specifically, importance weight parameters are introduced in message fusion, with the purpose of mitigating the potential error brought by the network topology dynamics. Based on that, the updating rules are designed with the first-order approximation and a Bregman divergence term, which can reduce the variance caused by the randomness and enhance the robustness. Moreover, we consider two different practical scenarios with time-varying communication network. In Scenario One, the communication between two nodes succeeds with certain probabilities, based on which the importance weight parameters are designed. Scenario Two considers mobile agents, where the communication link is determined by the distance between two agents. We derive the connectivity probability in this scenario and get the corresponding importance weight. Numerical simulations validate the effectiveness of the proposed algorithm in both scenarios, in comparison with the subgradient-based method.

In this article, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the system. Explicitly, in the proposed algorithm, each node interacts with only part of its neighboring nodes, the number of which is progressively determined according to a heuristic searching procedure, which takes into account both the predicted convergence rate and the communication and computation costs at each iteration, resulting in a trade-off between communication and computation. Then the node chooses its neighboring nodes according to an importance sampling distribution derived theoretically to minimize the variance with the latest information it locally stores. Finally, the node updates its local information with a new update rule which adapts to the number of communication nodes. We prove the convergence of the proposed algorithm and provide an upper bound of the convergence variance brought by randomness. Extensive simulations validate the excellent performances of the proposed algorithm in terms of convergence rate and variance, the overall communication and computation cost, the impact of network topology as well as the time for evaluation, in comparison with the traditional counterparts.