Reasoning about Reasoning: BAPO Bounds on Chain-of-Thought Token Complexity in LLMs 文章

arXiv:2602.02909v2 Announce Type: replace Abstract: Inference-time scaling via chain-of-thought (CoT) reasoning is a major driver of state-of-the-art LLM performance, but it comes with substantial latency and compute costs. We address a fundamental theoretical question: how many reasoning tokens are required to solve a problem as input size grows? By extending the bounded attention prefix oracle (BAPO) model--an abstraction of LLMs that quantifies the information flow required to solve a task--we prove lower bounds on the CoT tokens required for three canonical BAPO-hard tasks: binary majority, triplet matching, and graph reachability. We show that each requires $\Omega(n)$ reasoning tokens when the input size is $n$. We complement these results with matching or near-matching upper bounds via explicit constructions.