Cliff Tokens: Identifying Single-Token Failure Triggers in LLM Mathematical Reasoning

Large language models reach high accuracy in mathematical reasoning, but individual traces on the same problem diverge — some arrive at the correct answer while others fail. Prior work analyzes failure at the step, chunk, or sentence level, or at tokens where failure has already occurred, but none identifies the precise trigger that causes the shift toward failure. A paper posted on arXiv on June 25 introduces the cliff token — a token where the token-wise potential drops significantly, marking the critical transition point from a correct path toward failure. This is akin to finding the key signal in the black box flight recorder of LLM reasoning. The paper is available under arXiv ID 2606.25524 in the cs.AI category and offers a new granularity for analyzing and improving LLM reasoning reliability.