The Valley of Interrupted Thought: Non-Monotone Budget Curves in Small Reasoning Models, and When They Vanish

Budget forcing caps a reasoning model's chain of thought at a fixed token budget and forces an answer, and is now widely used to control test-time compute. Prior work has observed that truncated reasoning can underperform direct answering, but whether apparent low-budget non-monotonicity survives a calibrated test that accounts for selection over budgets remains unclear. Studying an open ladder of reasoning models on MATH-500, we find that increasing the budget can first reduce and then restore accuracy, producing an interior valley. We distinguish two claims using two statistics: a maximum in-grid drawdown that detects any interior descent, and a stricter valley statistic that requires both a descent and a subsequent recovery. We fit an isotonic monotone-null curve, recenter a problem-clustered paired bootstrap, and apply Holm correction to a primary family of tests. Pronounced valleys occur in the evaluated DeepSeek-R1-Distill-Qwen-1.5B and 7B models, with depths of 0.137 and 0.060, respectively; both statistics remain significant at $p<0.001$. No valley is detected in the evaluated Qwen3 or Nemotron models. These cross-family differences are associated with model family, post-training recipe, and scale, but do not identify a causal training mechanism. The drawdown shrinks along the R1-distill scale ladder and is not statistically detected at 32B. At 1.5B and 7B, the truncated curve can also fall below a matched NOTHINK baseline; matching the answer cap reduces the 7B gap to an approximately three-point residual, while the 1.5B gap remains substantial. Budget-forcing evaluations should therefore report the full low-budget curve, or risk ranking a model at an unfavorable point inside its valley.