Beyond Scalars: Evaluating and Understanding LLM Reasoning via Geometric Progress and Stability
arXiv:2603.10384v3 Announce Type: replace 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
The paper introduces a novel framework (TRACED) for evaluating LLM reasoning, filling a critical gap in current assessment methods that often oversimplify complex cognitive processes.
This framework offers a more robust and granular way to understand and mitigate LLM hallucinations, which is crucial for advancing AI reliability and deployment in sensitive applications.
The ability to geometrically analyze LLM reasoning opens new pathways for debugging, improving, and fundamentally understanding AI models beyond scalar metrics, potentially leading to more robust and trustworthy AI.
- · AI researchers
- · LLM developers
- · AI application providers
- · Companies seeking reliable AI solutions
- · Developers relying solely on scalar evaluation metrics
- · Applications vulnerable to LLM hallucinations
- · Methods for LLM evaluation that only use scalar output
More accurate and reliable LLMs will emerge due to improved diagnostic tools.
Increased trust in AI systems will accelerate their integration into critical domains like finance, healthcare, and infrastructure.
The geometric approach could inspire new architectures for LLMs designed to inherently produce more stable and higher-progress reasoning trajectories.
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Read at arXiv cs.AI