Geometry-Guided Constraint Learning for LLM Safety Classification

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arXiv:2607.19366v1 Announce Type: new Abstract: Safety as Polytope (SaP) learns linear half-space constraints in LLM hidden space but requires per-category tuning of the constraint count K. We show that sparse autoencoder (SAE) feature extraction resolves this: K=2 becomes optimal for 12/14 categories on Qwen3.5-9B, achieving 96-99% accuracy per category on our BeaverTails classification benchmark, largely eliminating the need for exhaustive sweeps (K=4-25 with random initialization). This conv