Optimal Hydra: Model Heterogeneous Federated Learning for LLMs using Data-Informed Hydra-Nets

Federated Split Learning has been identified as an efficient approach to address the computational resource constraints of clients in classical federated learning, while guaranteeing data privacy for distributed model training across data owners. However, it faces some critical challenges when such a training strategy meets large language models (LLMs) for fine-tuning. Such challenges include setting the cutlayer adaptively across different clients to address the data and device heterogeneity issues, which affect the system performance significantly. In addition, efficiently reducing the communication overhead during the fine-tuning procedure is also another challenge. No work tries to address these challenges. To bridge this gap, we propose SplitTF, an adaptive federated split learning system for LLMs fine-tuning. SplitFT enables different clients to set different cut layers according to their computation resources and trained model performance. SplitFT also proposes to reduce the LoRA rank in cutlayer to reduce the communication overhead. In addition to simulating the heterogeneous data in real-world applications for our proposed split federated learning system, we propose a length-based Dirichlet approach to divide the training data into different clients. Extensive experimental results show that our proposed approach outperforms the state-of-the-art approach for fine-tuning time efficiency and model performance based on various popular benchmarks.

Federated Learning (FL) with Low-Rank Adaptation (LoRA) has become a standard for privacy-preserving LLM fine-tuning. However, existing personalized methods predominantly operated under a restrictive Flat-Model Assumption: they addressed client-side statistical heterogeneity but treated the model as a monolithic block, ignoring the functional heterogeneity across LLM layers. We argue that these two statistical (horizontal) and functional (vertical) dimensions, are orthogonal in source yet coupled in interaction, implying that the optimal depth of parameter sharing is functionally dependent on client similarity. To address this, we propose FedTreeLoRA, a framework employing tree-structured aggregation for fine-grained, layer-wise alignment. By dynamically constructing an aggregation hierarchy, FedTreeLoRA allows clients to share broad consensus on shallow trunks' while progressively specializing on deep branches'. Experiments on NLU and NLG benchmarks demonstrate that FedTreeLoRA significantly outperforms state-of-the-art methods by effectively reconciling generalization and personalization.

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.