# Where to Adapt Matters: Layer-Selective Fine-Tuning for Capability Retention

arXiv: https://arxiv.org/abs/2610.11620 · HTML: https://mlsanity.com/paper/2610.11620/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Builds on (most cited first, 6 of 6)

- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [Forgetting in Language Models: Capacity, Optimization, and Self-Generated Replay](https://mlsanity.com/paper/2605.26097/) (2026)
- [Layer-wise LoRA fine-tuning: a similarity metric approach](https://mlsanity.com/paper/2602.05988/) (2026)
- [PEFT-Arena: Understanding Parameter-Efficient Finetuning from a Stability-Plasticity Perspective](https://mlsanity.com/paper/2605.28819/) (2026)
- [Understanding and Guiding Layer Placement in Parameter-Efficient Fine-Tuning of Large Language Models](https://mlsanity.com/paper/2602.04019/) (2026)

## Abstract (arXiv)

Parameter-efficient fine-tuning (PEFT) enables large language models (LLMs) to adapt to specialized tasks, but often at the cost of degrading general capabilities acquired during pretraining. Existing approaches primarily mitigate this trade-off through data replay or regularization, relying on additional data or explicit optimization constraints. We instead focus on a different question: where should adaptation be applied? We find that fine-tuning different Transformer layers produces different target-task gains and degrees of capability degradation, suggesting that not all layers are equally suitable for adaptation. To characterize this difference, we use layer-wise empirical Fisher information to measure target-task sensitivity. However, computing Fisher scores requires backward computation and becomes increasingly expensive for large models. We therefore introduce input--output cosine similarity as a lightweight, forward-only proxy for ranking layer sensitivity. Across models and tasks, layers with lower input--output similarity consistently exhibit higher empirical Fisher scores. Building on this observation, we propose Layer-Selective LoRA (LS-LoRA), which places trainable LoRA adapters only in layers with low input--output similarity. Experiments on mathematical reasoning and code generation show that LS-LoRA improves average target-task performance while retaining substantially more commonsense reasoning capability than standard all-layer LoRA, demonstrating that carefully choosing where to adapt can provide a simple and effective way to balance target-task adaptation and general capability retention.