Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability
Evaluating LLM reliability via scalar probabilities often fails to capture the structural dynamics of reasoning. We introduce TRACED, a framework that assesses reasoning quality through theoretically grounded geometric kinematics. By decomposing reasoning traces into Progress (displacement) and Stability (curvature), we reveal a distinct topological divergence: correct reasoning manifests as high-progress, stable trajectories, whereas hallucinations are characterized by low-progress, unstable patterns (stalled displacement with high curvature fluctuations). Leveraging these signatures, our probabilistic framework achieves competitive performance and superior robustness across diverse benc...
| Authors | Xinyan Jiang, Ninghao Liu, Di Wang et al. |
|---|---|
| Primary category | cs.AI |
| Published | 11 March 2026 |
| Last updated at source | 14 June 2026 |
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