# Beyond Average Safety: Chance-Constrained LLM Fine-tuning

arXiv: https://arxiv.org/abs/2609.29960 · HTML: https://mlsanity.com/paper/2609.29960/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 36 references that are in the map.
- First posted on arXiv 24 Sep 2026.

## Builds on (most cited first, 29 of 29)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [BeaverTails: Towards Improved Safety Alignment of LLM via a Human-Preference Dataset](https://mlsanity.com/paper/2307.04657/) (2023)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [Responsive Safety in Reinforcement Learning by PID Lagrangian Methods](https://mlsanity.com/paper/2007.03964/) (2020)
- [Shadow Alignment: The Ease of Subverting Safely-Aligned Language Models](https://mlsanity.com/paper/2310.02949/) (2023)
- [Projection-Based Constrained Policy Optimization](https://mlsanity.com/paper/2010.03152/) (2020)
- [LoRA Fine-tuning Efficiently Undoes Safety Training in Llama 2-Chat 70B](https://mlsanity.com/paper/2310.20624/) (2023)
- [Removing RLHF Protections in GPT-4 via Fine-Tuning](https://mlsanity.com/paper/2311.05553/) (2023)
- [Constrained Reinforcement Learning Has Zero Duality Gap](https://mlsanity.com/paper/1910.13393/) (2019)
- [Safe LoRA: the Silver Lining of Reducing Safety Risks when Fine-tuning Large Language Models](https://mlsanity.com/paper/2405.16833/) (2024)
- [Vaccine: Perturbation-aware Alignment for Large Language Models against Harmful Fine-tuning Attack](https://mlsanity.com/paper/2402.01109/) (2024)
- [Representation Noising: A Defence Mechanism Against Harmful Finetuning](https://mlsanity.com/paper/2405.14577/) (2024)
- [Lisa: Lazy Safety Alignment for Large Language Models against Harmful Fine-tuning Attack](https://mlsanity.com/paper/2405.18641/) (2024)
- [Booster: Tackling Harmful Fine-tuning for Large Language Models via Attenuating Harmful Perturbation](https://mlsanity.com/paper/2409.01586/) (2024)
- [Covert Malicious Finetuning: Challenges in Safeguarding LLM Adaptation](https://mlsanity.com/paper/2406.20053/) (2024)
- [SaLoRA: Safety-Alignment Preserved Low-Rank Adaptation](https://mlsanity.com/paper/2501.01765/) (2025)
- [AsFT: Anchoring Safety During LLM Fine-Tuning Within Narrow Safety Basin](https://mlsanity.com/paper/2506.08473/) (2025)
- [Gradient Surgery for Safe LLM Fine-Tuning](https://mlsanity.com/paper/2508.07172/) (2025)
- [Constrained Entropic Unlearning: A Primal-Dual Framework for Large Language Models](https://mlsanity.com/paper/2506.05314/) (2025)
- [Antibody: Strengthening Defense Against Harmful Fine-Tuning for Large Language Models via Attenuating Harmful Gradient Influence](https://mlsanity.com/paper/2603.00498/) (2026)

## Abstract (arXiv)

Fine-tuning large language models on new objectives can improve helpfulness, instruction following, or domain-specific performance, but it can also induce regressions on safety-critical prompts. Existing safety-preserving fine-tuning methods typically control average safety loss or use weighted auxiliary penalties, which can obscure rare but severe failures. We propose a chance-constrained formulation for safety-preserving fine-tuning that limits the fraction of safety examples whose degradation relative to a reference model exceeds a prescribed threshold. Because the resulting empirical chance constraint contains a discontinuous indicator, we introduce a differentiable majorization of the violation rate, yielding a tractable conservative constraint. We then develop a constraint-aware gradient descent method that treats the majorized constraint as a safe set in parameter space and minimally modifies the fine-tuning direction to preserve feasibility. The resulting update admits a closed form and produces a tail-aware safety correction that emphasizes examples near or above the degradation threshold. We conduct an extensive set of experiments on harmful fine-tuning across three different tasks and three models and show that our approach consistently outperforms the baselines that exist in the literature. These results suggest that safety preservation in LLM fine-tuning is better viewed as a reliability-constrained optimization problem than as average-risk regularization.