Applying STP at consecutive semantic reasoning steps achieves 168x more accurate multi-step latent prediction on ProcessBench than frozen baselines, with trajectories forming smooth curves best captured by non-linear predictors.
Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability
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abstract
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 benchmarks. Crucially, TRACED bridges geometry and cognition by mapping high curvature to ''Hesitation Loops'' and displacement to ''Certainty Accumulation'', offering a physical lens to decode the internal dynamics of machine thought.
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2026 1verdicts
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Semantic Step Prediction: Multi-Step Latent Forecasting in LLM Reasoning Trajectories via Step Sampling
Applying STP at consecutive semantic reasoning steps achieves 168x more accurate multi-step latent prediction on ProcessBench than frozen baselines, with trajectories forming smooth curves best captured by non-linear predictors.