Counting on Thinking: Tracing Evidence Integration in Language Models

Jingming Xue, Robert C. Wilson, Huadong Xiong

Finite computational resources force a tradeoff between automatic System 1 processes and costly System 2 thinking. Large language models (LLMs) can spend extra computation on hard problems, yet direct answers struggle even with counting, an elementary operation humans and animals perform automatically. We ask why this requires thinking in LLMs. Evidence integration has long been used in psychology and neuroscience to probe decision-making. Our evidence-integration task presents one letter per conversational turn and asks which of two target letters appeared more often. A running count difference solves the task optimally by weighting every letter equally; tokens at each turn could represent and update this difference. Direct responses instead weighted evidence unevenly, with strong recency effects, and assigned less probability to the correct answer as difficulty increased. Thinking improved performance and made integration weights nearly uniform, yet final-query attention remained concentrated on the sequence ends in both modes. Reasoning trajectories showed models revisiting input, recounting letters, and checking intermediate counts that informed the answer, suggesting that…