Spectral Transformation for Layer-wise Global Rank Discovery in Federated LoRA for Vision Transformers

Fine-tuning Vision Transformers (ViTs) with low-rank adapters (LoRA) promises better communication efficiency under federated setup, yet existing aggregation strategies face fundamental limitations. Independently averaging these LoRA factors is mathematically inconsistent, introducing cross-term aggregation error. In contrast, approaches that preserve heterogeneous client ranks by concatenating local adapters on the server substantially increase download cost and often require merging global LoRA updates into pretrained weights on the clients, causing reinitialization lag and unstable convergence. Other approaches further increase server-side overhead by reconstructing dense weight updates or training auxiliary models to refine aggregation error. In this work, we propose SpecTraL, spectral transformation for layer-wise global rank discovery, that resolves these challenges within a unified design. SpecTraL stacks local LoRA modules from clients and performs orthonormal Householder Transformation of the stacked adapters directly in the low-rank latent space, eliminating dense reconstruction of the global update and any auxiliary refinement on the server. By leveraging the Spiked Covariance Model from Random Matrix Theory, SpecTraL analytically separates the global consensus signal from non-IID noise, discovering optimal layer-wise global ranks without manual hyperparameter tuning. To match local ranks in subsequent rounds, we introduce a padding-aware initialization framework that lets clients incorporate residual LoRA dimensions without re-merging them into the pre-trained base model. Experiments on federated fine-tuning of ViT-B/16 and ViT-L/16 over DomainNet and NICO++ demonstrate improved accuracy-communication trade-offs, reduced server computation, and elimination of hyperparameter search for rank selection. Our code is available at https://github.com/DASS-Lab-Group/SpecTraL

FLoRIST: Singular Value Thresholding for Efficient and Accurate Federated Fine-Tuning of Large Language Models

Integrating Low-Rank Adaptation (LoRA) into federated learning offers a promising solution for parameter-efficient fine-tuning of Large Language Models (LLMs) without sharing local data. However, several methods designed for federated LoRA present significant challenges in balancing communication efficiency, model accuracy, and computational cost, particularly among heterogeneous clients. These methods either rely on simplistic averaging of local adapters, which introduces aggregation noise, require transmitting large stacked local adapters, leading to poor communication efficiency, or necessitate reconstructing memory-dense global weight-update matrix and performing computationally expensive decomposition to design client-specific low-rank adapters. In this work, we propose FLoRIST, a federated fine-tuning framework that achieves mathematically accurate aggregation without incurring high communication or computational overhead. Instead of constructing the full global weight-update matrix at the server, FLoRIST employs an efficient decomposition pipeline by performing singular value decomposition on stacked local adapters separately. This approach operates within a compact intermediate space to represent the accumulated information from local LoRAs. We introduce tunable singular value thresholding for server-side optimal rank selection to construct a pair of global low-rank adapters shared by all clients. Extensive empirical evaluations across multiple datasets and LLMs demonstrate that FLoRIST consistently strikes the best balance between superior communication efficiency and competitive performance in both homogeneous and heterogeneous setups.