Harmful Intent as a Geometrically Recoverable Feature of LLM Residual Streams

Abstract

Aligned language models refuse harmful instructions, but the representations through which they recognise such instructions are less well characterised than the behaviours they produce. Harmful intent is linearly separable from residual-stream activations across 12 models spanning four architectural families (Qwen2.5, Qwen3.5, Llama-3.2, Gemma-3) and three alignment variants (base, instruction-tuned, abliterated), with parameter scales from 0.5B to 1.3B and a within-family scale extension to 9B on Qwen3.5. A direction fitted from 100 labelled examples per class via Soft-AUC optimisation reaches mean effective AUROC 0.982 and TPR@1\%FPR 0.797, generalises to three held-out harm benchmarks and a hard-benign control, and matches its instruction-tuned counterpart within $\pm 0.003$ AUROC in abliterated variants from which the refusal mechanism has been removed. The supervised strategies all exceed AUROC 0.96, but their TPR@1\%FPR varies by more than ten times the AUROC gap; a deployed 9B safety classifier shows the same pattern at AUROC 0.94 and TPR 0.30, motivating low-FPR reporting as a default in safety-adjacent detection evaluation. Geometric measurements refine the picture. The recovered direction is concentrated within each extraction protocol but protocol-dependent across them: two pooling choices applied to the same chat-templated activations at the same residual-stream layer (max-pool over content tokens versus last-token at the post-instruction position) recover harm directions $73^\circ$ apart, and projecting one out leaves detection under either max-pool extraction essentially intact. Probing identifies a protocol-specific direction rather than a unique computational feature.