# Stabilizing LLM Supervised Fine-Tuning via Explicit Distributional Control

arXiv: https://arxiv.org/abs/2605.04468 · HTML: https://mlsanity.com/paper/2605.04468/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 18 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 16 of 16)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Instruction-Following Evaluation for Large Language Models](https://mlsanity.com/paper/2311.07911/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [BioMistral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains](https://mlsanity.com/paper/2402.10373/) (2024)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [On the Generalization of SFT: A Reinforcement Learning Perspective with Reward Rectification](https://mlsanity.com/paper/2508.05629/) (2025)
- [Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process](https://mlsanity.com/paper/2407.20311/) (2024)
- [Self-Distillation Bridges Distribution Gap in Language Model Fine-Tuning](https://mlsanity.com/paper/2402.13669/) (2024)
- [Retaining by Doing: The Role of On-Policy Data in Mitigating Forgetting](https://mlsanity.com/paper/2510.18874/) (2025)
- [MedCalc-Bench: Evaluating Large Language Models for Medical Calculations](https://mlsanity.com/paper/2406.12036/) (2024)
- [Unveiling the Secret Recipe: A Guide For Supervised Fine-Tuning Small LLMs](https://mlsanity.com/paper/2412.13337/) (2024)
- [SFT Doesn't Always Hurt General Capabilities: Revisiting Domain-Specific Fine-Tuning in LLMs](https://mlsanity.com/paper/2509.20758/) (2025)
- [Mitigating Forgetting in LLM Fine-Tuning via Low-Perplexity Token Learning](https://mlsanity.com/paper/2501.14315/) (2025)

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

- [SoFT: Soft Targets for Generalizable LLM Fine-Tuning](https://mlsanity.com/paper/2609.32493/) (2026)

## Abstract (arXiv)

Post-training large language models (LLMs) often suffers from catastrophic forgetting, where improvements on a target objective degrade previously acquired capabilities. Recent evidence suggests that this phenomenon is primarily driven by excessive distributional drift during optimization. Motivated by this perspective, we propose Anchored Learning, a simple framework that explicitly controls distributional updates during offline fine-tuning via a dynamically evolving moving anchor. Instead of matching a fixed reference distribution, the anchor interpolates between the current model and a frozen reference to construct an intermediate target that the model distills toward, transforming global fine-tuning into a sequence of local trust-region updates in distribution space. Theoretically, we prove this anchor-based update admits a linear KL-divergence upper bound per iteration, ensuring a stable transition between model distributions. Extensive experiments on iGSM, MedCalc, and IFEval show that Anchored Learning consistently lies on the Pareto frontier of gain-stability trade-offs, achieving near-optimal performance improvements while substantially reducing degradation compared to strong baselines. For example, while standard SFT suffers from over 53% performance degradation on iGSM and MedCalc, Anchored Learning slashes this drop to under 5% while maintaining near-optimal gains (e.g., 75.2% on iGSM).