Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability
This provides a novel geometric approach to understanding and evaluating LLM reasoning dynamics, which is an incremental advancement in interpretability for AI researchers and practitioners.
The paper tackles the problem of evaluating LLM reliability by moving beyond scalar probabilities to analyze reasoning structural dynamics, introducing the TRACED framework that uses geometric kinematics to distinguish correct reasoning (high-progress, stable trajectories) from hallucinations (low-progress, unstable patterns) and achieves competitive performance and superior robustness across benchmarks.
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.