Oops, Wait: Token-Level Signals as a Lens into LLM Reasoning

TL;DR

This paper introduces a token-probability lens to study LLM reasoning by examining next-token probabilities after a double-newline separator across models trained with different recipes and scales. It shows that certain tokens reliably signal correct reasoning (e.g., progression tokens like "therefore"), while others accompany incorrect reasoning (e.g., "wait"), and that these patterns are more dependent on training strategy than model capacity. A focused analysis of the "wait" token reveals its dual role as a trigger for probability jumps and as a post-jump self-check, with small-scale supervised fine-tuning only partially transferring these dynamics. The findings enable token-level steering, improved ensembling, and post-training approaches, offering a concrete path toward more controllable and effective reasoning in LLMs.

Abstract

The emergence of discourse-like tokens such as "wait" and "therefore" in large language models (LLMs) has offered a unique window into their reasoning processes. However, systematic analyses of how such signals vary across training strategies and model scales remain lacking. In this paper, we analyze token-level signals through token probabilities across various models. We find that specific tokens strongly correlate with reasoning correctness, varying with training strategies while remaining stable across model scales. A closer look at the "wait" token in relation to answer probability demonstrates that models fine-tuned on small-scale datasets acquire reasoning ability through such signals but exploit them only partially. This work provides a systematic lens to observe and understand the dynamics of LLM reasoning.

Figures (5)

• Figure 1: Overview of how token probabilities are collected. We extract next-token probability distributions specifically after "\\n\\n", which serve as natural segmentation points in the trajectories. This enables us to capture latent token-level signals beyond simple frequency counts, reflecting how strongly the model intends to generate particular tokens even when they are not actually selected during generation. Such token-probability measures enable a fine-grained comparison of token-level signals across models.
• Figure 2: Changes in answer probabilities and emergence of "wait" and its subsequent tokens along the thinking trajectory. Horizontal dashed lines indicate where "wait" is generated, and the probability jump region is highlighted, with the red dashed line marking the point of maximum increase. Expressions following "wait" differ depending on whether they occur before or after the probability jump, with earlier instances more often extending the reasoning and later instances serving as re-checks. Note that answer probabilities are computed at the token level, although the figure is visualized in a line-based format.
• Figure 3: Distribution of the relative positions of the nearest rethink and recall "wait" token to the probability jump. For each reasoning trajectory, exactly one rethink and one recall token are selected, which might cause or follow the probability jump. An asymmetric Gaussian curve is fitted to each distribution.
• Figure 4: Difference in answer probability increase distributions following rethink "wait" tokens between DeepSeek-R1-distill-Qwen-32B and s1.1-32B.
• Figure 5: Statistics of rethink and recall "wait" tokens across DeepSeek-R1-distill-Qwen-32B and s1.1-32B. (a)–(d) show the number of rethink "wait" and recall "wait" tokens, the ratio of rethink "wait" tokens followed by a significant probability increase, and the total number of "wait" tokens in incorrect trajectories, respectively.