arXiv 2610.05114
Belief-Trajectory Energy: Measuring the Path to a Prediction
AI15 upvotes
Authors: Jiahao Ying, Wei Tang, Boxian Ai, Yaoning Wang, Haotian Chen, Wenhe Sun, Caijun Xu, Haozhan Cai +2
Overview
The authors introduce Belief-Trajectory Energy (BTE), which scores an input by the layer-by-layer predictive revisions it induces in an LLM after mapping intermediate states into a shared predictive space. BTE can be summarized as a scalar or as a structured depth profile, and locally it corresponds to predictive revision under Fisher-Rao geometry.
Introduction
LLMs revise their predictions across Transformer layers, but usually only the final output is observed, so the trajectory that formed it is lost.
Results
Richer BTE representations reach up to 0.998 macro-AUROC for human-LLM review detection. They also reach 95.6% eight-way generator attribution accuracy, while scalar BTE serves as a model-relative difficulty signal across reasoning tasks.
Conclusion
Belief trajectories offer a principled, model-grounded signal, suggesting that learned models can themselves serve as instruments for characterizing the data they process.