犹豫具有几何结构：基于熵训练的双曲探针用于稀疏激活引导
Hesitation Has a Geometry: Entropy-Trained Hyperbolic Probes for Sparse Activation Steering
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中文总结 AI 辅助
提出双曲熵引导（HEST），利用基于熵训练的双曲探针在稀疏令牌处沿测地线引导激活，提升数学推理准确率，最高达1.8个百分点。
中文摘要 AI 辅助
当大型语言模型解决数学问题时，其推理过程在很大程度上是层次化的，并且解决方案常常在少数几个令牌处产生分支，这些令牌的下一个令牌熵较高。这种树状结构嵌入双曲空间时，其畸变远低于欧几里得空间。然而，激活引导通常通过在每个令牌处添加一个固定的欧几里得向量来编辑预训练模型的隐藏状态，尽管解决方案的大多数令牌已经由上下文确定。我们提出了双曲熵引导（HEST），该方法使用一个轻量级探针将隐藏状态嵌入庞加莱球，该探针的唯一标签是模型自身的下一个令牌熵。当熵超过阈值时，HEST 沿着探针读出值的陡峭下降测地线移动嵌入状态，并将变化映射回隐藏状态。对于学习到的理想点的 Busemann 读出，我们证明固定长度的步长在每个状态下都会使其降低相同的量。在来自 Qwen2.5-Math 和 Llama-3.1 系列的三个指令微调模型上，使用 Busemann 读出的 HEST 在 MATH-500 和 GSM8K 上的贪婪准确率在六种设置中的五种中有所提高，最高提升 1.8 个百分点，而在每个令牌处添加对比引导向量则会降低准确率。使用以相同方式训练的欧几里得探针时，这种增益在 Qwen2.5-Math-1.5B-Instruct 上消失。增益在模型经常犹豫的问题上最大，而其余问题的准确率几乎不变。
英文摘要
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 entropy exceeds a threshold, HEST moves the embedded state along the geodesic of steepest descent of a readout of the probe and maps the change back to the hidden state. For the Busemann readout of a learned ideal point, we prove that a step of fixed length lowers it by the same amount at every state. On three instruction-tuned models from the Qwen2.5-Math and Llama-3.1 families, HEST with the Busemann readout improves greedy accuracy on MATH-500 and GSM8K in five of six settings, by up to 1.8 points, whereas a contrastive steering vector added at every token lowers accuracy. With a Euclidean probe trained in the same way, this gain disappears on Qwen2.5-Math-1.5B-Instruct. The gains are largest on problems where the model hesitates often, and accuracy on the remaining problems is almost unchanged.
发表机构
- New Jersey Institute of Technology（新泽西理工学院）
- University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
- Stony Brook University（石溪大学）
机构由 AI 辅助整理，请以论文原文为准。
