mlsanityData to 14 Oct 2026

Budget Boundary Effects in Test-Time Mathematical Reasoning

arXiv 2609.38699 ↗First posted 30 Sep 2026cs.AIcited by 0

On the map: LLM reasoning → Test-time compute and efficient thinking also fits: Mathematical reasoning

Abstract (arXiv)

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. Second, comparisons along realized cost differ from same-cap comparisons: advisory 4k in low has higher accuracy than strict 8k at comparable mean completion cost, while in high its observed accuracy is 0.42 points below strict 32k using 59% of its mean tokens. These aggregate comparisons do not establish equal-compute superiority or accuracy equivalence. Third, increased candidate coverage does not guarantee higher answer accuracy: a log-probability selector loses accuracy while coverage rises, including after a source-grade consistency repair. Same-cap majority-accuracy differences shrink below 1.3 percentage points at 32k. Budget curves should jointly state the cap, realized cost, eligible candidates, stopping rule and selector information.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 20 of its 22 references that are in the map. First posted on arXiv 30 Sep 2026.

Builds on

20 of 22 references.

Closest ancestors · 12

Same direction, newest first

  1. 2026Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility4 Aug
  2. 2026Oracle Gap and Signal Fidelity: A Fixed-Pool Diagnostic for Test-Time Collaboration20 Jul
  3. 2026Beyond the Frontier: Stochastic Backtracking for Efficient Test-Time Scaling24 May
  4. 2025Stop When Enough: Adaptive Early-Stopping for Chain-of-Thought Reasoning11 Oct
  5. 2025Dynamic Early Exit in Reasoning Models22 Apr
  6. 2025Reasoning Models Can Be Effective Without Thinking14 Apr
  7. 2025When To Solve, When To Verify: Compute-Optimal Problem Solving and Generative Verification for LLM Reasoning1 Apr
  8. 2025L1: Controlling How Long A Reasoning Model Thinks With Reinforcement Learning6 Mar
  9. 2025s1: Simple test-time scaling31 Jan
  10. 2024Token-Budget-Aware LLM Reasoning24 Dec
  11. 2024Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models1 Aug
  12. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May

Other references · 8

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  3. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  4. 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
  5. 2023Let's Verify Step by Stepcited by 3,789
  6. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  7. 2026When Does Deep RL Beat Calibrated Baselines? A Benchmark Study on Adaptive Resource Controlcited by 3
  8. 2026Winning by Peeking: Unenforced Budgets and Test-Set Selection Inflate Short-Budget AutoML Comparisonscited by 1

Built on by

Not cited yet.

Similar, not cited

Close in wording, no citation either way

  1. 2026It's the Problem, Not the Path: Budget and Difficulty Confounds in LLM Reasoning Trajectories
  2. 2026Thinking Hard, Not Smart: Reasoning Models Fail to Ration Test-Time Compute Across Questions
  3. 2025Mitigating Strategy-Selection Bias in Reasoning for More Effective Test-Time Scaling
  4. 2026Shorter Reasoning, Earlier Answers? An Evaluation of Reasoning Interfaces
  5. 2025Test-Time Scaling in Reasoning Models Is Not Effective for Knowledge-Intensive Tasks Yet
  6. 2026How Much Can Language Models Gain from Test-Time Computation?
  7. 2026Reasoning Concentrates Errors, and Self-Consistency Never Notices
  8. 2025Rethinking Fine-Tuning when Scaling Test-Time Compute: Limiting Confidence Improves Mathematical Reasoning