The {\alpha}-Law of Observable Belief Revision in Large Language Model Inference

arXiv:2603.19262v1 Announce Type: cross Abstract: Large language models (LLMs) that iteratively revise their outputs through mechanisms such as chain-of-thought reasoning, self-reflection, or multi-agent debate lack principled guarantees regarding the stability of their probability updates. We identify a consistent multiplicative scaling law that governs how instruction-tuned LLMs revise probability assignments over candidate answers, expressed as a belief revision exponent that controls how pri