# Fine-Tuning Without Forgetting via Loss-Adaptive Learning Rates

arXiv: https://arxiv.org/abs/2605.20005 · HTML: https://mlsanity.com/paper/2605.20005/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 62 of its 73 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 30 of 62)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [TOFU: A Task of Fictitious Unlearning for LLMs](https://mlsanity.com/paper/2401.06121/) (2024)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Measuring short-form factuality in large language models](https://mlsanity.com/paper/2411.04368/) (2024)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)

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

- [MIRROR: From Imitation to Internalization in LLM Personalization](https://mlsanity.com/paper/2610.09795/) (2026)

## Abstract (arXiv)

Fine-tuning large language models on new data improves task performance but degrades capabilities learned during pretraining, a phenomenon known as catastrophic forgetting. Existing methods mitigate this by modifying the fine-tuning objective to suppress high-loss tokens or sequences, but these tokens are essential for learning new tasks, especially those with poor pretraining coverage. In such settings, hard tokens should still contribute to learning, so forgetting must be controlled without suppressing them. We identify a simple mechanism for doing so: per-step forgetting is bounded by the product of the learning rate and the square root of the current training loss. This suggests that high-loss batches are especially prone to inducing forgetting. Motivated by this observation, we introduce FINCH, a loss-adaptive learning-rate schedule that reduces the learning rate on high-loss batches and increases it as the model converges, while leaving the fine-tuning objective unchanged. Across knowledge acquisition, science, and low-resource language adaptation benchmarks, FINCH reduces forgetting by 93% on average while matching the task performance of standard fine-tuning. On Qwen3-4B knowledge acquisition, FINCH cuts TruthfulQA degradation by 5x and reverses HaluEval degradation, while better preserving confidence calibration. Overall, our results show that learning-rate schedules are an effective tool to shape model behavior during fine-tuning, beyond just target-task optimization.