Range Penalization: Theoretical Insights with Applications in Federated Learning

This paper introduces range regularization for federated learning with linear systematic components to enhance statistical accuracy and induce cross-client regularity conducive to quantization, coding, and resource efficiency. Our approach identifies features with shared weights across different clients and adaptively clusters the weights of personalized features at extreme values, a process we refer to as polar clustering. Theoretical analysis of the associated estimators poses significant challenges due to the seminorm nature and non-decomposability of the regularizer. We develop new proof techniques for the nonasymptotic analysis of statistical accuracy and faithful pattern recovery. Moreover, a fast optimization algorithm that leverages varying degrees of local strong convexity is proposed to reduce iteration complexity. Experiments support the efficacy and efficiency of the proposed approach.

H2Tune: Federated Foundation Model Fine-Tuning with Hybrid Heterogeneity

Different from existing federated fine-tuning (FFT) methods for foundation models, hybrid heterogeneous federated fine-tuning (HHFFT) is an under-explored scenario where clients exhibit double heterogeneity in model architectures and downstream tasks. This hybrid heterogeneity introduces two significant challenges: 1) heterogeneous matrix aggregation, where clients adopt different large-scale foundation models based on their task requirements and resource limitations, leading to dimensional mismatches during LoRA parameter aggregation; and 2) multi-task knowledge interference, where local shared parameters, trained with both task-shared and task-specific knowledge, cannot ensure only task-shared knowledge is transferred between clients. To address these challenges, we propose H2Tune, a federated foundation model fine-tuning with hybrid heterogeneity. Our framework H2Tune consists of three key components: (i) sparsified triple matrix decomposition to align hidden dimensions across clients through constructing rank-consistent middle matrices, with adaptive sparsification based on client resources; (ii) relation-guided matrix layer alignment to handle heterogeneous layer structures and representation capabilities; and (iii) alternating task-knowledge disentanglement mechanism to decouple shared and specific knowledge of local model parameters through alternating optimization. Theoretical analysis proves a convergence rate of O(1/\sqrt{T}). Extensive experiments show our method achieves up to 15.4% accuracy improvement compared to state-of-the-art baselines. Our code is available at https://anonymous.4open.science/r/H2Tune-1407.

Proto-EVFL: Enhanced Vertical Federated Learning via Dual Prototype with Extremely Unaligned Data

In vertical federated learning (VFL), multiple enterprises address aligned sample scarcity by leveraging massive locally unaligned samples to facilitate collaborative learning. However, unaligned samples across different parties in VFL can be extremely class-imbalanced, leading to insufficient feature representation and limited model prediction space. Specifically, class-imbalanced problems consist of intra-party class imbalance and inter-party class imbalance, which can further cause local model bias and feature contribution inconsistency issues, respectively. To address the above challenges, we propose Proto-EVFL, an enhanced VFL framework via dual prototypes. We first introduce class prototypes for each party to learn relationships between classes in the latent space, allowing the active party to predict unseen classes. We further design a probabilistic dual prototype learning scheme to dynamically select unaligned samples by conditional optimal transport cost with class prior probability. Moreover, a mixed prior guided module guides this selection process by combining local and global class prior probabilities. Finally, we adopt an \textit{adaptive gated feature aggregation strategy} to mitigate feature contribution inconsistency by dynamically weighting and aggregating local features across different parties. We proved that Proto-EVFL, as the first bi-level optimization framework in VFL, has a convergence rate of 1/\sqrt T. Extensive experiments on various datasets validate the superiority of our Proto-EVFL. Even in a zero-shot scenario with one unseen class, it outperforms baselines by at least 6.97%