How Hard Does It Think? Analyzing Step-Aware Reasoning Energy in LLM Chain-of-Thought Trajectories

它思考得有多努力？分析大语言模型思维链轨迹中的“步级推理能量”

Abstract: Understanding how computational effort is allocated across individual chain-of-thought (CoT) reasoning steps remains an open challenge: existing interpretability methods rely on output-level signals or collapse processing depth into a single trajectory-level scalar, leaving step-wise effort opaque.

摘要： 理解计算工作量如何在思维链（CoT）的各个推理步骤中分配，仍然是一个未解的挑战：现有的可解释性方法要么依赖于输出层面的信号，要么将处理深度压缩为单一的轨迹级标量，导致步级（step-wise）的努力程度变得模糊不清。

We propose Step-Aware Reasoning Energy (SARE), a geometric framework that quantifies effort at the granularity of individual CoT steps via Centered Kernel Alignment (CKA) between Gram matrices of token hidden states across adjacent transformer layers, capturing inter-token relational structure without requiring eigenvector alignment or cluster correspondence.

我们提出了“步级推理能量”（Step-Aware Reasoning Energy, SARE），这是一个几何框架，通过计算相邻 Transformer 层之间 Token 隐藏状态的 Gram 矩阵的中心核对齐（CKA），在单个 CoT 步骤的粒度上量化计算努力。该方法无需特征向量对齐或聚类对应，即可捕捉 Token 间的关系结构。

SARE further contextualizes this energy within reasoning’s semantic progression by modeling CoT trajectories as transitions among latent semantic states.

SARE 通过将 CoT 轨迹建模为潜在语义状态之间的转换，进一步将这种能量置于推理的语义演进背景中进行分析。

Across six reasoning benchmarks and three open-weight LLMs, we find that reasoning energy is highly non-uniform across step types, exhibiting phase-like transitions invisible to trajectory-level metrics; incorrect trajectories show systematically lower energy at critical reasoning junctions; and SARE-based features match or outperform output-based confidence baselines in most settings, indicating that internal geometric dynamics encode predictive information beyond surface-level signals.

通过在六个推理基准测试和三个开源权重的大语言模型上进行实验，我们发现推理能量在不同类型的步骤中表现出高度的不均匀性，并呈现出轨迹级指标无法察觉的“相变”特征；错误的推理轨迹在关键推理节点上表现出系统性的能量偏低；此外，在大多数设置下，基于 SARE 的特征能够匹配甚至超越基于输出的置信度基准，这表明内部的几何动态编码了超越表面信号的预测信息。