From Task Mixtures to Specialized Experts

Federated learning of foundation models faces a fundamental resource-asymmetry challenge: the institutions holding the most valuable domain-specific data cannot host billion-parameter models. Existing heterogeneous federated approaches attempt to bridge this gap through parameter-efficient tuning, model pruning, or knowledge distillation, yet each trades away a critical property, whether full-model memory reduction, architectural self-containedness, or representational fidelity, leaving the core tension unresolved. We propose FedSLM, a parameter-centric framework for federated fine-tuning with heterogeneous compressed clients. FedSLM uses SVD-based decomposition to produce self-contained client models, whose low-rank subspaces form nested manifolds that are structurally compatible for aggregation. It then applies a two-stage protocol that synchronizes lightweight adapters within compression groups and fuses full-rank reconstructions across groups via structural alignment. Finally, a weak-to-strong elicitation step with auxiliary confidence loss transfers the aggregated knowledge to the full-scale server, while an explicit bias--variance trade-off mitigates compression artifacts. We provide theoretical guarantees for adapter-level aggregation, subspace-alignment bounds for cross-group fusion, and a characterization of how the confidence loss mitigates weak-supervision noise. Experiments on natural language and vision--language benchmarks show that FedSLM outperforms existing federated baselines under both IID and non-IID partitions, while client models operate at roughly 50% of the GPU memory required by the full model.

Federated PEFT enables LLMs to collaboratively adapt to decentralized private data without sharing raw examples. However, task heterogeneity across clients can cause cross-task interference and gradient conflicts during aggregation. Federated MoE-LoRA addresses this challenge through specialized LoRA experts and conditional routing. Yet existing methods typically specialize at client granularity, implicitly assuming task-coherent clients. Our core insight is that experts need purity, namely pattern-coherent updates that preserve specialization, whereas routers need contrast, namely mixed-task observations that support expert comparison. We propose FedWeave, a framework that adopts asymmetric aggregation, separating expert aggregation from router optimization to meet these two requirements. FedWeave uses unsupervised prototype discovery to form local buckets and align them across clients, enabling prototype-level expert aggregation while retaining mixed-task client trajectories for router training. At inference, FedWeave performs sparse inference with one active expert while preserving nearly all soft-routing performance. Our theoretical analysis explains why asymmetric aggregation is advantageous: it controls expert convergence in stationarity through off-pattern contamination, identifies the consensus error induced by fragmented router trajectories, and bounds sparse-inference risk. On a heterogeneous multi-task benchmark with mainstream LLM backbones, FedWeave consistently outperforms strong baselines, while ablations verify the effectiveness of our design.

Heterogeneous LoRA-rank methods address system heterogeneity in federated fine-tuning of foundation models by assigning client-specific ranks based on computational capabilities. However, these methods achieve only marginal computational savings, as dense feed-forward computations dominate. Sparse Mixture-of-Experts (SMoE) provides a promising alternative through conditional computation, yet we identify that its naive application to heterogeneous federated settings introduces two critical discordances: (i) expert utilization imbalance and (ii) non-differentiability of Top-K routing. Our convergence analysis demonstrates that these discordances lead to degraded convergence, particularly for resource-constrained clients. To address these challenges, we propose Universally Balanced Sparse Mixture-of-Experts (UB-SMoE), which introduces Dynamic Modulated Routing (DMR) to rebalance expert utilization, and Universal Pseudo-Gradient (PG) to reconstruct learning signals for non-activated experts. These mechanisms form a self-reinforcing cycle that maintains expert viability across heterogeneous clients. Experiments on benchmarks show that UB-SMoE achieves up to $45.0\%$ computational reduction on low-resource clients while improving their performance by $8.7 \times$ compared to existing heterogeneous LoRA-rank methods.