# RSRA: Training-Free Probing of Representation Sensitivity for Efficient LoRA Rank Allocation

arXiv: https://arxiv.org/abs/2607.09757 · HTML: https://mlsanity.com/paper/2607.09757/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Beyond Low-Rank Tuning: Model Prior-Guided Rank Allocation for Effective Transfer in Low-Data and Large-Gap Regimes](https://mlsanity.com/paper/2507.00327/) (2025)

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

- [Not All Layers Need Tuning: Diagnosing and Directing Adaptation in Vision-Language-Action Models](https://mlsanity.com/paper/2609.18084/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning enables large language models to adapt to downstream tasks with substantially lower computational and storage cost, and Low-Rank Adaptation (LoRA) is among its most widely used techniques. However, vanilla LoRA assigns a uniform rank to all adapted modules, while existing adaptive methods either incur additional optimization overhead or rely on static weights and local gradients that do not capture task-conditioned representation changes. We propose RSRA, a training-free rank allocator that estimates where adaptation capacity is most needed through forward-only representation sensitivity probing on a small calibration set. Specifically, RSRA uses Spectral Effective Rank to allocate capacity across layers, measures module-wise hidden-state displacement under standardized virtual low-rank updates with the Frechet Distance, and combines both signals through hierarchical normalization to produce a task-aware rank configuration before fine-tuning. Across commonsense reasoning and natural language understanding benchmarks with Qwen3-4B and Mistral-7B, RSRA achieves the highest average performance in all three reported model-benchmark settings and a 1.48x-1.93x speedup in allocation time over the fastest competing pre-allocation method. When integrated with DoRA, LoRA-FA, and PiSSA, RSRA improves 15 of the 18 evaluated combinations and increases the average performance of all three PEFT methods.