When a language model reasons through a problem step by step, its uncertainty at each step can be measured by the entropy of its next-token distribution. The total entropy reduction between the first step and the last seems like the natural predictor of correctness: more total uncertainty reduction should mean more decisive reasoning.
It does not. Total entropy reduction has a correlation of -0.06 with correctness. Essentially zero.
What predicts correctness is whether entropy decreases monotonically at every step — no reversals, no wavering. This monotonicity criterion achieves 68.8% accuracy in predicting whether the final answer is right, compared to 46.8% for total reduction. The shape of the uncertainty curve matters; its magnitude does not.
The structural insight is clean. A reasoning chain that wavers — where uncertainty at step 5 exceeds uncertainty at step 4 — is one that has introduced confusion. The model considered something at step 5 that undermined what it had established by step 4. This reversal need not be large. Even a small entropy increase signals that the reasoning path has encountered an internal contradiction, a bifurcation, or a distraction. The subsequent steps may recover, driving entropy back down, but the damage is done. The recovery compensates for the detour rather than advancing toward the answer.
Total reduction misses this because it compares only endpoints. A chain that drops from 5 to 1 with a smooth decline and a chain that drops from 5 to 1 after spiking to 8 in the middle both show the same total reduction. But the second chain wavered, and wavering predicts failure.
This generalizes beyond language models. In any sequential decision process — medical diagnosis through a series of tests, engineering design through iterative refinement, legal reasoning through a chain of precedents — the monotonicity of the confidence trajectory may be a more reliable diagnostic than the final confidence level. A system that never hesitates is more likely right than one that hesitates and then catches itself. The catching feels like robustness. The data says otherwise.