Geometry-Guided Constraint Learning for LLM Safety Classification
Fumiaki Uehara, Koo Imai, Masato Tsutsumi, Keigo Kansa, Sora Usui, Yuki Kobiyama
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 convergence to two planes is consistent with the Linear Representation Hypothesis, providing suggestive evidence that safety boundaries in this setting admit a low-dimensional linear description in the SAE feature space. Building on this geometric perspective, we introduce a cone constraint whose learnable aperture adapts to each category's cluster concentration, stabilized by a three-phase training
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Classified with taxonomy v2 on Sat, 5 Sept 2026.