Hesitation Has a Geometry: Entropy-Trained Hyperbolic Probes for Sparse Activation Steering
When a large language model solves a mathematical problem, its reasoning is largely hierarchical, and the solution often branches at a few tokens where the next-token entropy is high. Such tree-like structure embeds in hyperbolic space with far lower distortion than in Euclidean space. Activation steering, however, usually edits the hidden states of a pretrained model by adding one fixed Euclidean vector at every token, even though most tokens of a solution are already determined by the context. We propose Hyperbolic Entropy Steering (HEST), which embeds the hidden states in the Poincaré ball with a lightweight probe whose only label is the model's own next-token entropy. Where this entro...
| Authors | Zeyong Zhang, Tung Sum Thomas Kwok, Tengfei Ma et al. |
|---|---|
| Primary category | cs.LG |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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