Jailbreaking the Matrix: Nullspace Steering for Controlled Model Subversion

Large language models remain vulnerable to jailbreak attacks, inputs crafted to bypass safety mechanisms and elicit harmful responses, despite advances in alignment and instruction tuning. Existing attacks often rely on prompt rewrites, dense optimization, or ad hoc heuristics, and lack interpretability and robustness. We propose Head-Masked Nullspace Steering (HMNS), a circuit-level intervention that (i) identifies attention heads most causally responsible for a model’s default behavior, (ii) suppresses their write paths via targeted column masking, and (iii) injects a perturbation constrained to the orthogonal complement of the muted subspace. This geometry-aware intervention preserves fluency while steering the model toward completions that differ from baseline routing. HMNS operates in a closed-loop detection–intervention cycle, re-identifying causal heads and reapplying interventions across multiple decoding attempts. Across multiple jailbreak benchmarks, strong safety defenses, and widely used language models, HMNS attains state-of-the-art attack success rates with fewer queries than prior methods. Ablations confirm that nullspace-constrained injection, residual norm scaling, and iterative re-identification are key to its effectiveness. To our knowledge, this is the first jailbreak method to leverage geometry-aware, interpretability-informed interventions, highlighting a new paradigm for controlled model steering and adversarial safety circumvention.