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

arXiv: https://arxiv.org/abs/2607.21074 · HTML: https://mlsanity.com/paper/2607.21074/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 23 Jul 2026.

## Builds on (most cited first, 20 of 20)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [Moment Matching for Multi-Source Domain Adaptation](https://mlsanity.com/paper/1812.01754/) (2018)
- [Model-Contrastive Federated Learning](https://mlsanity.com/paper/2103.16257/) (2021)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [HeteroFL: Computation and Communication Efficient Federated Learning for Heterogeneous Clients](https://mlsanity.com/paper/2010.01264/) (2020)
- [Federated Learning with Buffered Asynchronous Aggregation](https://mlsanity.com/paper/2106.06639/) (2021)
- [Towards Building the Federated GPT: Federated Instruction Tuning](https://mlsanity.com/paper/2305.05644/) (2023)
- [Improving LoRA in Privacy-preserving Federated Learning](https://mlsanity.com/paper/2403.12313/) (2024)
- [FLoRA: Federated Fine-Tuning Large Language Models with Heterogeneous Low-Rank Adaptations](https://mlsanity.com/paper/2409.05976/) (2024)
- [Heterogeneous LoRA for Federated Fine-tuning of On-Device Foundation Models](https://mlsanity.com/paper/2401.06432/) (2024)
- [Federated Fine-tuning of Large Language Models under Heterogeneous Tasks and Client Resources](https://mlsanity.com/paper/2402.11505/) (2024)
- [LoRA-FAIR: Federated LoRA Fine-Tuning with Aggregation and Initialization Refinement](https://mlsanity.com/paper/2411.14961/) (2024)
- [ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise](https://mlsanity.com/paper/2009.12297/) (2020)
- [FLoRIST: Singular Value Thresholding for Efficient and Accurate Federated Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2506.09199/) (2025)

## Built on by (most cited first, 1 of 1)

- [FraQ: Efficient Coordinate-Space Recompression for Federated Low-Rank Adaptation](https://mlsanity.com/paper/2608.03605/) (2026)

## Abstract (arXiv)

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