Contribution-Aware Bandwidth Allocation for Multimodal Split Learning

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 $66\times$.

Efficient multimodal inference is increasingly constrained not only by model quality or FLOP count, but also by the cost of preserving, moving, routing, caching, and quantizing multimodal representations under latency, memory, and energy constraints. This paper reviews recent advances in efficient vision-language and multimodal large language models, covering visual token compression, video token management, KV-cache optimization, Mixture-of-Experts (MoE) routing, low-bit quantization, edge deployment, and hardware-aware benchmarking. We argue that these techniques cannot be treated as independent optimizations. Visual token compression alters downstream feature distributions and MoE routing decisions, routing behavior affects expert utilization and quantization sensitivity, quantized router logits influence expert assignment, KV-cache policies determine retained multimodal evidence, and hardware constraints often transform computational savings into memory and communication bottlenecks. We organize the literature around these interactions and identify key design trade-offs, including accuracy versus token budget, static versus adaptive compression, sparse routing efficiency versus expert collapse, and low-bit inference versus modality-specific degradation. Finally, we introduce Temporal Routing Consistency as a diagnostic for video MoE models and highlight open research directions in routing-aware compression, cross-modal cache management, hardware-aware co-design, and unified benchmarking for multimodal edge intelligence.

Centralized multimodal learning commonly compresses language, acoustic, and visual signals into a single fused representation for prediction. While effective, this paradigm suffers from two limitations: modality dominance, where optimization gravitates towards the path of least resistance, ignoring weaker but informative modalities, and spurious modality coupling, where models overfit to incidental cross-modal correlations. To address these, we propose Group Cognition Learning (GCL), a governed collaboration paradigm that applies a two-stage protocol after modality-specific encoding. In Stage 1 (Selective Interaction), a Routing Agent proposes directed interaction routes, and an Auditing Agent assigns sample-wise gates to emphasize exchanges that yield positive marginal predictive gain while suppressing redundant coupling. In Stage 2 (Consensus Formation), a Public-Factor Agent maintains an explicit shared factor, and an Aggregation Agent produces the final prediction through contribution-aware weighting while keeping each modality representation as a specialization channel. Extensive experiments on CMU-MOSI, CMU-MOSEI, and MIntRec demonstrate that GCL mitigates dominance and coupling, establishing state-of-the-art results across both regression and classification benchmarks. Analysis experiments further demonstrate the effectiveness of the design.