# Graph-Regularized Sparse Autoencoders for LLM Safety Steering

arXiv: https://arxiv.org/abs/2512.06655 · HTML: https://mlsanity.com/paper/2512.06655/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Safety alignment, refusal and guardrails, one of 12 directions in LLM safety and security.
- Builds on 45 of its 56 references that are in the map.
- First posted on arXiv 7 Dec 2025.

## Placed in

- LLM safety and security / [Safety alignment, refusal and guardrails](https://mlsanity.com/safety/safety-alignment-refusal-and-guardrails/)
- Mechanistic interpretability / [Steering and probing for LLM safety](https://mlsanity.com/mechinterp/steering-and-probing-for-llm-safety/)

## Builds on (most cited first, 30 of 45)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [HarmBench: A Standardized Evaluation Framework for Automated Red Teaming and Robust Refusal](https://mlsanity.com/paper/2402.04249/) (2024)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Refusal in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2406.11717/) (2024)
- [Revisiting Semi-Supervised Learning with Graph Embeddings](https://mlsanity.com/paper/1603.08861/) (2016)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [AutoDAN: Generating Stealthy Jailbreak Prompts on Aligned Large Language Models](https://mlsanity.com/paper/2310.04451/) (2023)
- [Phi-4 Technical Report](https://mlsanity.com/paper/2412.08905/) (2024)
- [Tree of Attacks: Jailbreaking Black-Box LLMs Automatically](https://mlsanity.com/paper/2312.02119/) (2023)
- [JailbreakBench: An Open Robustness Benchmark for Jailbreaking Large Language Models](https://mlsanity.com/paper/2404.01318/) (2024)
- [Jailbreaking Leading Safety-Aligned LLMs with Simple Adaptive Attacks](https://mlsanity.com/paper/2404.02151/) (2024)
- [Not All Language Model Features Are One-Dimensionally Linear](https://mlsanity.com/paper/2405.14860/) (2024)
- [Programming Refusal with Conditional Activation Steering](https://mlsanity.com/paper/2409.05907/) (2024)
- [The Geometry of Refusal in Large Language Models: Concept Cones and Representational Independence](https://mlsanity.com/paper/2502.17420/) (2025)
- [How Alignment and Jailbreak Work: Explain LLM Safety through Intermediate Hidden States](https://mlsanity.com/paper/2406.05644/) (2024)
- [Steering Language Model Refusal with Sparse Autoencoders](https://mlsanity.com/paper/2411.11296/) (2024)
- [Sparse Autoencoders Trained on the Same Data Learn Different Features](https://mlsanity.com/paper/2501.16615/) (2025)
- [Gradient Cuff: Detecting Jailbreak Attacks on Large Language Models by Exploring Refusal Loss Landscapes](https://mlsanity.com/paper/2403.00867/) (2024)
- [Uncovering Safety Risks of Large Language Models through Concept Activation Vector](https://mlsanity.com/paper/2404.12038/) (2024)
- [The Geometry of Concepts: Sparse Autoencoder Feature Structure](https://mlsanity.com/paper/2410.19750/) (2024)

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

- [When Safety Speaks a Language: A Mechanistic Analysis of Safety-Language Identity Entanglement in LLMs](https://mlsanity.com/paper/2608.29936/) (2026)

## Abstract (arXiv)

Sparse autoencoders (SAEs) are increasingly used to extract activation directions for inference-time steering, but their standard sparsity objective treats latent features as independent. This prior can be poorly matched to high-level safety behaviors, where refusal and harmful compliance appear to depend on distributed structure in activation space. We introduce Graph-Regularized Sparse Autoencoders (GSAE), a dictionary-learning method that learns safety-steering directions by smoothing SAE decoder vectors over a neuron co-activation graph and applying the resulting direction bank through a two-gate runtime controller. Empirically, GSAE improves selective refusal across JailbreakBench, HarmBench, and XSTest, increasing harmful-request refusal while keeping benign-prompt refusals low. On Llama-3-8B, replacing the standard SAE with GSAE in an otherwise identical pipeline improves Deltas by 20.1 points on JailbreakBench and 16.8 points on HarmBench. GSAE outperforms activation-steering baselines and black-box guardrails, preserves benign-task performance, generalizes across Llama-3, Mistral, Qwen 2.5, and Phi-4, and remains strong under black-box and gray-box jailbreak attacks.