Is Token Confidence Just Chain Length? A Signal-Processing Audit of Reasoning Traces

Pragna Mallappa

Reasoning language models answer math problems by writing long chains of thought, and sampling many chains per problem and taking a majority vote raises accuracy at a large cost in generated text. A popular way to cut that cost scores each chain by the model's confidence in each token it writes, where a token is a word or part of a word. The method averages this confidence over a sliding window of 2048 tokens and keeps or stops chains based on the lowest average. We treat the confidence, recorded token by token, as a signal in the sense of audio or radio, and examine the method with standard signal-processing tools such as spectral analysis and statistical tests for detecting a sudden change. We sampled 16 chains for each of 500 problems from two math benchmarks with a small open reasoning model. The windowed-minimum score turns out to measure mostly how long a chain is. Ranking chains by length alone does as well as or better than the confidence score, and once length is accounted for the score carries no information about correctness. Signal processing explains why: the minimum of a longer stretch of a slowly drifting signal is lower by chance alone, and the confidence signal…