Budget Boundary Effects in Test-Time Mathematical Reasoning
A cumulative token cap can fall inside a mathematical derivation, forcing a test-time controller to choose between stopping at the cap (strict) and allowing the current attempt to finish (advisory). We measure this boundary choice with paired offline replays of 19,200 public traces: 120 AIME, BrUMO and HMMT problems and two archive configurations of one model. Candidate order and a 16-attempt cap are fixed, and answer selection is blind to reference answers and correctness labels. Three findings emerge. First, at the 4k cap, most advisory accuracy gains replace abstention with a correct answer; strict stopping pays for an unfinished prefix that the completed-only selector cannot use. Seco...
| Authors | Guilin Zhang, Ziqi Tan, Wulan Guo et al. |
|---|---|
| Primary category | cs.AI |
| Published | 30 September 2026 |
| Last updated at source | 30 September 2026 |
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