# Mitigating Reasoning-Induced Misalignment via Safety-Direction Penalty

arXiv: https://arxiv.org/abs/2608.23497 · HTML: https://mlsanity.com/paper/2608.23497/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning for agents, planning and code, one of 17 directions in LLM reasoning.
- Builds on 19 of its 19 references that are in the map.
- First posted on arXiv 24 Aug 2026.

## Placed in

- LLM reasoning / [Reasoning for agents, planning and code](https://mlsanity.com/lr/reasoning-for-agents-planning-and-code/)
- LLM safety and security / [Safety alignment, refusal and guardrails](https://mlsanity.com/safety/safety-alignment-refusal-and-guardrails/)

## Builds on (most cited first, 19 of 19)

- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [Fine-tuning Aligned Language Models Compromises Safety, Even When Users Do Not Intend To!](https://mlsanity.com/paper/2310.03693/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Safety-Tuned LLaMAs: Lessons From Improving the Safety of Large Language Models that Follow Instructions](https://mlsanity.com/paper/2309.07875/) (2023)
- [LoRA Fine-tuning Efficiently Undoes Safety Training in Llama 2-Chat 70B](https://mlsanity.com/paper/2310.20624/) (2023)
- [Emergent Misalignment: Narrow finetuning can produce broadly misaligned LLMs](https://mlsanity.com/paper/2502.17424/) (2025)
- [Safe LoRA: the Silver Lining of Reducing Safety Risks when Fine-tuning Large Language Models](https://mlsanity.com/paper/2405.16833/) (2024)
- [Representation Noising: A Defence Mechanism Against Harmful Finetuning](https://mlsanity.com/paper/2405.14577/) (2024)
- [Booster: Tackling Harmful Fine-tuning for Large Language Models via Attenuating Harmful Perturbation](https://mlsanity.com/paper/2409.01586/) (2024)
- [Convergent Linear Representations of Emergent Misalignment](https://mlsanity.com/paper/2506.11618/) (2025)
- [1.4 Million Open-Source Distilled Reasoning Dataset to Empower Large Language Model Training](https://mlsanity.com/paper/2503.19633/) (2025)
- [Self-Jailbreaking: Language Models Can Reason Themselves Out of Safety Alignment After Benign Reasoning Training](https://mlsanity.com/paper/2510.20956/) (2025)
- [Putnam-AXIOM: A Functional and Static Benchmark for Measuring Higher Level Mathematical Reasoning in LLMs](https://mlsanity.com/paper/2508.08292/) (2025)

## Abstract (arXiv)

Reasoning-Induced Misalignment, where fine-tuning on reasoning data containing no harmful content, including mathematics, code, and problem-solving with chain-of-thought traces can induce harmful behaviors of LLM, posing a serious challenge to the safety of LLM reasoning. Cross-architecture, cross-scale, and cross-dataset checks show that RIM does not always emerge. Previous work attributed RIM to neuron-level entanglement, but did not identify the geometry of the representation space underlying this entanglement or propose a training-time fix. We provide both: a representation-space analysis of RIM and the Safety-Direction Penalty (SDP), which penalizes movement along a learned safety direction during reasoning fine-tuning. The analysis extracts two activation-space directions, one encoding reasoning ability and the other safety behavior. These directions are coupled: fine-tuning that improves reasoning shifts safety representations, and prompts with larger shifts show larger safety degradation. CKA distance ratios and probes locate the safety-decision layers where this shift is most relevant. These findings guide the design of SDP: the coupling motivates penalizing displacement along the safety direction, and the layer localization sets the initial scope. When the initial scope leaves compensatory shifts beyond the penalized layers, the same diagnostics guide iterative expansion. On Qwen2.5-3B and 7B, SDP restores safety while preserving benchmark reasoning performance.