# Frozen Cores Need Task Signal: Fisher-Whitened Cross-Covariance for Low-Resource LLM Adaptation

arXiv: https://arxiv.org/abs/2609.00762 · HTML: https://mlsanity.com/paper/2609.00762/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 1 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (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)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [LoRA-GA: Low-Rank Adaptation with Gradient Approximation](https://mlsanity.com/paper/2407.05000/) (2024)
- [Flora: Low-Rank Adapters Are Secretly Gradient Compressors](https://mlsanity.com/paper/2402.03293/) (2024)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [LoRA-XS: Low-Rank Adaptation with Extremely Small Number of Parameters](https://mlsanity.com/paper/2405.17604/) (2024)
- [Parameter Efficient Fine-tuning via Explained Variance Adaptation](https://mlsanity.com/paper/2410.07170/) (2024)

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

- [Adaptive Fisher-Whitened Cross-Covariance for Low-Resource Speech Recognition](https://mlsanity.com/paper/2609.29800/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning is usually framed as a question of how many parameters to update. Under a severe trainable-state budget, however, where those coefficients act is equally consequential. We study this choice through frozen-core adaptation: a calibration pass fixes left and right bases for each weight matrix, and fine-tuning optimizes only an r× r core. This removes the ability of trainable factors to repair a poor initial span and makes subspace quality directly observable. We introduce FCCA, which estimates the signed input--error cross-covariance, whitens it with diagonal Fisher moments, truncates it in the resulting local metric, maps the selected directions back, and applies thin QR to obtain stable core coordinates. Under a matched r2 budget, we compare eight basis constructors on 11 tasks, four model settings, and three seeds. On Qwen2.5-3B, FCCA reaches an 83.0 macro-average, 2.3 points above the next-best matched-budget constructor, and exceeds its unwhitened RawGrad control on all 11 tasks. It ranks first at all three Qwen scales and finishes within 0.13 points of the best method on Llama-3.2-1B. Controlled ablations show gains of 2.7--17.2 points from whitening and identify QR as necessary for stable core optimization in the tested regime. Finally, FCCA comes within 0.32 and 0.23 average points of LoRA and DoRA while optimizing 36.9K rather than roughly 7.4M parameters. These results show that a carefully selected fixed span can recover most of the benefit of movable low-rank factors at a much smaller trainable and optimizer-state cost.