AGOPNs: Null-Space Activation Steering for Jailbreak Defense via Average Gradient Outer Product Concept Extraction

Minh-Nguyen Bui, Binh-Phuong Phan, Thanh-Khang Doan, Bao Huynh-Gia, Phung-Anh Nguyen


Abstract
Activation steering offers a training-free path to defending large language models (LLMs) against jailbreak attacks, but existing methods fail to resolve the tension between safety and utility. We identify two root causes: safety concept vectors derived from difference-in-means are fragile under diverse attack geometries, and steering transformations lack a principled guarantee of leaving benign prompts unaffected. We propose AGOPNs (Average Gradient Outer Product with Null-space steering), which addresses both issues by extracting a safety concept vector via the Recursive Feature Machine, a feature-learning estimator grounded in the Average Gradient Outer Product, and confining the resulting steering matrix to the null space of benign activations, guaranteeing near-zero perturbation of benign prompts by construction. Experiments on Llama-3.1-8B-Instruct, Llama-3.1-70B-Instruct, and Llama-3.3-70B-Instruct across seven jailbreak attack families show that AGOPNs consistently achieves strong defense success rates while preserving near-baseline utility on AlpacaEval, XSTest, GSM8K, and MATH500.
Anthology ID:
2026.findings-aacl.91
Volume:
Findings of the Association for Computational Linguistics: IJCNLP-AACL 2026
Month:
November
Year:
2026
Address:
Hengqin, China
Editors:
Yue Zhang, Ruifeng Xu, Ayu Purwarianti, Tong Rong, Jun Suzuki
Venue:
Findings
SIG:
Publisher:
Association for Computational Linguistics
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Pages:
1832–1849
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URL:
https://aclanthology.org/2026.findings-aacl.91/
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Cite (ACL):
Minh-Nguyen Bui, Binh-Phuong Phan, Thanh-Khang Doan, Bao Huynh-Gia, and Phung-Anh Nguyen. 2026. AGOPNs: Null-Space Activation Steering for Jailbreak Defense via Average Gradient Outer Product Concept Extraction. In Findings of the Association for Computational Linguistics: IJCNLP-AACL 2026, pages 1832–1849, Hengqin, China. Association for Computational Linguistics.
Cite (Informal):
AGOPNs: Null-Space Activation Steering for Jailbreak Defense via Average Gradient Outer Product Concept Extraction (Bui et al., Findings 2026)
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https://aclanthology.org/2026.findings-aacl.91.pdf