mlsanityData to 14 Oct 2026

The Safety Operator: Modulating the Expression of Safety Instructions via Spectral Optimization

arXiv 2609.36434 ↗First posted 29 Sep 2026cs.AIcited by 0

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Abstract (arXiv)

Context tokens in a transformer-based language model can be absorbed into the model's weights as a multiplicative operator. We study this operator in the setting of safety instructions and show that influencing its dominant eigenvalue modulates how strongly the instruction shapes generation. We derive a Contrastive Safety Loss with a suppression weight that controls the tradeoff between emphasizing the safety instruction on harmful queries while suppressing it on harmless queries. Varying the suppression weight maps a relationship between the attack success and the over-refusal rates, supporting the hypothesis that the operator's eigenvalue acts as a continuous dial for the instruction's influence. Moreover, this relationship holds relatively independently of how the Safety Loss is parameterized, yielding Pareto-improved safety instructions for appropriate values of suppression weight.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 24 of its 54 references that are in the map. First posted on arXiv 29 Sep 2026.

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24 of 54 references.

References · 24

  1. 2023Universal and Transferable Adversarial Attacks on Aligned Language Modelscited by 3,104
  2. 2025Gemma 3 Technical Reportcited by 1,824
  3. 2023Jailbreaking Black Box Large Language Models in Twenty Queriescited by 1,420
  4. 2021A General Language Assistant as a Laboratory for Alignmentcited by 1,055
  5. 2023Steering Language Models With Activation Engineeringcited by 922
  6. 2023SmoothLLM: Defending Large Language Models Against Jailbreaking Attackscited by 469
  7. 2024Great, Now Write an Article About That: The Crescendo Multi-Turn LLM Jailbreak Attackcited by 390
  8. 2020AutoPrompt: Eliciting Knowledge from Language Models with Automatically Generated Promptscited by 249
  9. 2024Programming Refusal with Conditional Activation Steeringcited by 206
  10. 2023Defending Large Language Models Against Jailbreaking Attacks Through Goal Prioritizationcited by 170
  11. 2024On Prompt-Driven Safeguarding for Large Language Modelscited by 116
  12. 2023Tell Your Model Where to Attend: Post-hoc Attention Steering for LLMscited by 91
12 more
  1. 2024SCANS: Mitigating the Exaggerated Safety for LLMs via Safety-Conscious Activation Steeringcited by 50
  2. 2026Building Production-Ready Probes For Geminicited by 47
  3. 2025Learning without training: The implicit dynamics of in-context learningcited by 43
  4. 2026Constitutional Classifiers++: Efficient Production-Grade Defenses against Universal Jailbreakscited by 41
  5. 2025Defending Against Prompt Injection with DataFiltercited by 35
  6. 2025Spotlight Your Instructions: Instruction-following with Dynamic Attention Steeringcited by 21
  7. 2025RepIt: Steering Language Models with Concept-Specific Refusal Vectorscited by 12
  8. 2025Instruction Following by Principled Boosting Attention of Large Language Modelscited by 9
  9. 2026Spectral Attention Steering for Prompt Highlightingcited by 8
  10. 2025Refusal Steering: Fine-grained Control over LLM Refusal Behaviour for Sensitive Topicscited by 6
  11. 2026Enhancing Instruction Following of LLMs via Activation Steering with Dynamic Rejectioncited by 6
  12. 2025Mitigating Over-Refusal in Aligned Large Language Models via Inference-Time Activation Energycited by 5

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  3. 2026Beyond Routine Compliance: Cunning Data Cultivates Safety Vigilance in Large Language Models
  4. 2026The Geometry of Refusal: Why Post-Hoc Safety Is Fragile and Pretraining-Time Safety Persists
  5. 2026Discovering Agentic Safety Specifications from 1-Bit Danger Signals
  6. 2026Safety Paradox: How Enhanced Safety Awareness Leaves LLMs Vulnerable to Posterior Attack
  7. 2026When Safety Routing Breaks: Understanding Alignment Fragility under Benign Fine-Tuning
  8. 2025MetaSC: Test-Time Safety Specification Optimization for Language Models