# CPR for LLMs: Critical-Point Routing against Catastrophic Forgetting in Domain Adaptation

arXiv: https://arxiv.org/abs/2608.30158 · HTML: https://mlsanity.com/paper/2608.30158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 33 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 26 of 26)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [What Disease does this Patient Have? A Large-scale Open Domain Question Answering Dataset from Medical Exams](https://mlsanity.com/paper/2009.13081/) (2020)
- [PubMedQA: A Dataset for Biomedical Research Question Answering](https://mlsanity.com/paper/1909.06146/) (2019)
- [Length-Controlled AlpacaEval: A Simple Way to Debias Automatic Evaluators](https://mlsanity.com/paper/2404.04475/) (2024)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Contrastive Decoding: Open-ended Text Generation as Optimization](https://mlsanity.com/paper/2210.15097/) (2022)
- [FinQA: A Dataset of Numerical Reasoning over Financial Data](https://mlsanity.com/paper/2109.00122/) (2021)
- [Hybrid LLM: Cost-Efficient and Quality-Aware Query Routing](https://mlsanity.com/paper/2404.14618/) (2024)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [OpenMathInstruct-2: Accelerating AI for Math with Massive Open-Source Instruction Data](https://mlsanity.com/paper/2410.01560/) (2024)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [SFT Doesn't Always Hurt General Capabilities: Revisiting Domain-Specific Fine-Tuning in LLMs](https://mlsanity.com/paper/2509.20758/) (2025)
- [More Than Catastrophic Forgetting: Integrating General Capabilities For Domain-Specific LLMs](https://mlsanity.com/paper/2405.17830/) (2024)
- [Automatic Evaluation of Healthcare LLMs Beyond Question-Answering](https://mlsanity.com/paper/2502.06666/) (2025)
- [Entropy-Adaptive Fine-Tuning: Resolving Confident Conflicts to Mitigate Forgetting](https://mlsanity.com/paper/2601.02151/) (2026)
- [Don't Throw Away Your Pretrained Model](https://mlsanity.com/paper/2510.09913/) (2025)
- [Token-Level LLM Collaboration via FusionRoute](https://mlsanity.com/paper/2601.05106/) (2026)
- [Learning from the Undesirable: Robust Adaptation of Language Models without Forgetting](https://mlsanity.com/paper/2511.13052/) (2025)

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

- [SFT-as-Context Mitigates Forgetting in Supervised Fine-Tuning](https://mlsanity.com/paper/2610.11132/) (2026)

## Abstract (arXiv)

Supervised fine-tuning (SFT) is the de facto standard for adapting large language models (LLMs) to target domains, but it often degrades the model's general capabilities, a phenomenon known as catastrophic forgetting. Existing approaches typically modify the SFT loss to mitigate forgetting, but they inevitably operate along a domain-generality trade-off. In this work, we step outside this trade-off by decoupling the two capabilities at the model level: we keep the original base model for general capability, and selectively invoke the SFT expert only when domain-specific knowledge is required. Specifically, we propose CPR (Critical-Point Routing), a token-level routing framework between a base model and its expert derivative, based on critical tokens where the base model fails but the expert succeeds. We train a lightweight hierarchical router that estimates the expert-call probability per token, and pair it with a tailored inference procedure that combines momentum smoothing and threshold gating. Across diverse model-domain configurations, CPR achieves state-of-the-art across all settings, surpassing SFT expert by 1.4-5.5% in domain performance while recovering its general-capability drop from 3.4-14.5% to at most 0.5%, with minimal overhead from invoking the expert on only one-third of tokens.