Entropy-Guided Tensor Compression for Multimodal Federated Learning on Edge Devices

2026-07-07

AI Summary

This work addresses the challenge in multimodal federated learning where device heterogeneity and structural disparities in cross-modal updates render existing compression methods ineffective at balancing efficiency and model performance. To overcome this, the authors propose MESH-FL, a novel framework that, for the first time, links the spectral entropy of layer-wise updates to the matrix product state (MPS) compression rank. By formulating a convex surrogate problem, MESH-FL adaptively allocates compression ranks across layers, modalities, and devices, enabling differentiated compression under client resource constraints while providing theoretical guarantees on compression error and convergence. Experiments on a heterogeneous cluster of 15 Raspberry Pi nodes demonstrate that the method achieves up to 56.8× compression ratio, improves accuracy by 2.01% over uncompressed FedAvg, and reduces communication overhead by as much as 66×.

Abstract

Federated learning (FL) over mobile and edge devices increasingly involves multimodal models in which clients differ in both sensing capability and computational capacity. Existing update compression schemes typically apply uniform policies across layers and devices, without accounting for modality-specific differences in spectral structure and compressibility. We propose MESH-FL, an entropy-guided matrix product state (MPS) update-compression framework for modality-heterogeneous FL on resource-constrained devices. MESH-FL estimates the spectral entropy of each layer-wise update via truncated singular value decomposition and allocates MPS compression ranks adaptively across layers, modalities, and devices under per-client payload budgets. We show that higher spectral entropy necessitates a higher reconstruction rank under the majorization order on singular-value energy distributions. Building on this result, we prove that the proposed entropy-guided allocation solves a convex surrogate rank-allocation problem, preserves monotonicity under the exact payload model, and achieves convergence with an explicit compression-dependent error term. Experiments on a 15-node heterogeneous Raspberry Pi~4/5 cluster with modality-heterogeneous clients show that MESH-FL achieves up to $56.8\times$ compression while surpassing the uncompressed FedAvg baseline in final accuracy by up to 2.01%, and reduces total transmitted data to reach convergence by up to $66\times$.

Problem

• multimodal federated learning
• update compression
• modality heterogeneity
• edge devices
• spectral entropy

Innovation

• entropy-guided compression
• matrix product state
• multimodal federated learning
• spectral entropy
• adaptive rank allocation