On held-out MATH-500, a 1.5-billion-parameter reasoning model learned to choose how much text to generate for each problem. It averaged 2,810 tokens of generated text per response, compared with 4,743 for the base model, while exact-answer accuracy was 78.2% versus 79.6%. That was a 41% reduction in tokens, with the figures reported as means over three seeds.
A budget chosen at the start
The approach makes the budget choice part of the answer itself. The first response token is NoThink, Short or Long, and that token selects the mode. The main model learns this decision end to end with a reward-based training method called GRPO, without a separate router.
Default caps were 1,024 tokens for NoThink and 3,000 for Short; Long was uncapped. A response that ran beyond its mode's cap was scored incorrect. The training included a 45-step forced-routing warmup and a balance term aimed at preventing a single mode from taking over.
The experiment used one model, DeepSeek-R1-Distill-Qwen-1.5B. Training used MATH-lighteval and held out MATH-500 for evaluation. Fixed NoThink-only, Short-only and Long-only versions were trained with the same data and hyperparameters, giving the study single-mode comparisons.
Out-of-distribution tests covered GSM8K's 1,319 problems and AIME 2024 and 2025, with 30 problems in each year. Exact final answers determined correctness; GSM8K scores used avg@5 and AIME scores avg@16, both at temperature 0.6.
The model learned to vary its effort
Near step 90, free rollouts settled into a roughly 20% NoThink, 32% Short and 47% Long split. Routing entropy, a measure of how evenly the choices were distributed, was about 1.04 against a three-mode maximum of about 1.10. All three choices remained active rather than collapsing into one.
On MATH-500, the model's choices also tracked difficulty. The paper's five-level scale ran from 1, the easiest, to 5, the hardest: NoThink was used most on level 1, Short at intermediate levels and Long on level 5. The mode-accuracy ranking inverted around training step 50, although this figure-based pattern was not formally tested.
Learning the split was not smooth. MATH validation accuracy fell from 0.807 at step 0 to 0.727 at step 30, then recovered to 0.764 at step 60 and 0.783 at step 90.
On MATH-500, free routing also sat above the fixed single-mode accuracy-versus-length frontier. A fixed mode needed 27% more tokens to reach the router's accuracy, according to the reported comparison.
Savings depended on the benchmark
The largest token saving came on GSM8K. Free routing used 459 tokens on average versus 1,930 for the base, a 76% reduction, or a 4.2-fold difference in token use. Accuracy was 78.1% versus 83.1%, so the reported comparison paired fewer tokens with lower accuracy.
On the harder AIME tests, the reduction was much smaller. Combined mean length was 10,716 tokens for free routing versus 12,266 for the base, a 13% reduction. Accuracy was 27.6% versus 26.5% on AIME 2024 and 22.2% versus 23.1% on AIME 2025. The study used avg@16 on each 30-problem set.
Where the method broke down
A preliminary two-mode test on Countdown exposed a failure. The router collapsed within 30 to 50 training steps in every configuration. Correct solutions were about 300 tokens, and giving the model more tokens did not rescue instances it could not solve.
Even so, the evidence is narrow. It covers three seeds of one 1.5B model trained on one mathematical distribution. The mode caps are task-specific, and validation generation was uncapped, which may make brief-mode accuracy marginally optimistic.
Taken together, the preprint reports a benchmark-specific efficiency pattern: shorter modes were favored for easier MATH problems, while the harder AIME tests used most of the available reasoning budget. The Countdown result shows that this pattern did not hold across every tested task.
Paper data and sources
Original title: Learning When to Think: Adaptive Reasoning for Test-Time Compute Allocation
Authors: Gijs Kassenaar, Zhao Yang, Vincent François-Lavet
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text