# Learning in the Fisher Subspace: A Guided Initialization for LoRA Fine-Tuning

arXiv: https://arxiv.org/abs/2605.01046 · HTML: https://mlsanity.com/paper/2605.01046/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 25 of 25)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [Remote Sensing Image Scene Classification: Benchmark and State of the Art](https://mlsanity.com/paper/1703.00121/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [The E2E Dataset: New Challenges For End-to-End Generation](https://mlsanity.com/paper/1706.09254/) (2017)
- [Revisiting Natural Gradient for Deep Networks](https://mlsanity.com/paper/1301.3584/) (2013)
- [Pushing Mixture of Experts to the Limit: Extremely Parameter Efficient MoE for Instruction Tuning](https://mlsanity.com/paper/2309.05444/) (2023)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [HydraLoRA: An Asymmetric LoRA Architecture for Efficient Fine-Tuning](https://mlsanity.com/paper/2404.19245/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [CodeUltraFeedback: An LLM-as-a-Judge Dataset for Aligning Large Language Models to Coding Preferences](https://mlsanity.com/paper/2403.09032/) (2024)
- [Make LoRA Great Again: Boosting LoRA with Adaptive Singular Values and Mixture-of-Experts Optimization Alignment](https://mlsanity.com/paper/2502.16894/) (2025)
- [Efficient Learning With Sine-Activated Low-rank Matrices](https://mlsanity.com/paper/2403.19243/) (2024)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (2024)
- [MTL-LoRA: Low-Rank Adaptation for Multi-Task Learning](https://mlsanity.com/paper/2410.09437/) (2024)
- [UORA: Uniform Orthogonal Reinitialization Adaptation in Parameter-Efficient Fine-Tuning of Large Models](https://mlsanity.com/paper/2505.20154/) (2025)
- [Traffic Sign Classification Using Deep Inception Based Convolutional Networks](https://mlsanity.com/paper/1511.02992/) (2015)

## Built on by (most cited first, 2 of 2)

- [Behavior Quotient Learning for Low-Rank Adaptation of LLM Agents](https://mlsanity.com/paper/2609.12896/) (2026)
- [Reducing the Adaptation Gap Through Reachable Fisher Geometry](https://mlsanity.com/paper/2609.36329/) (2026)

## Abstract (arXiv)

LoRA adapts large language models (LLMs) by restricting updates to low-rank subspaces of pre-trained weights. While this substantially reduces training cost, the effectiveness of adaptation critically depends on which subspace is chosen at initialization: a poor initialization that allocates capacity to task-irrelevant directions can severely hinder downstream performance. Existing initialization strategies primarily rely on the intrinsic properties of pre-trained weights, implicitly assuming that weight geometry alone reflects task relevance. However, such criteria overlook how the model interacts with the downstream data distribution. In this work, we formulate LoRA initialization as identifying the degree of impact of directions in parameter space under the target data distribution. We argue that data-aware sensitivity, rather than weight-only magnitude, should govern the choice of adaptation subspaces. Building on this perspective, we propose a Fisher-guided framework that leverages curvature information induced by downstream data to characterize how parameter perturbations influence model predictions. This perspective yields a principled, task-dependent criterion for selecting LoRA directions that better align adaptation with the target objective. Empirical results across diverse tasks and modalities demonstrate that data-aware initialization consistently and significantly improves downstream performance over existing approaches.