A 1.5-billion-parameter AI model trained to choose how much reasoning to use on each maths problem stayed close to its base model’s accuracy on MATH-500 while generating 41% fewer response tokens, according to an arXiv preprint dated 20 August 2026. The routed model averaged 78.2% accuracy, compared with 79.6% for the base model, while its responses averaged 2,810 tokens rather than 4,743.
The study asks whether a model can decide at test time—when it is answering a new prompt—whether to use no, short or long reasoning. Its first response token selects NoThink, Short or Long, and the main model is trained end to end with GRPO without a separate router.
The model made the choice itself
The design included hard caps for the three modes, an advantage-level balance term and a forced-rollout warm-up to address mode collapse, the problem of a routing system settling on one option. The study also compared free routing with forced NoThink-only, Short-only and Long-only versions trained with the same data and hyperparameters.
Training used MATH-lighteval, with evaluation on held-out MATH-500, GSM8K and AIME 2024 and 2025. The model was DeepSeek-R1-Distill-Qwen-1.5B; GSM8K contained 1,319 problems, while each AIME set contained 30. Training ran for 90 steps, and the router and each single-mode baseline were tested with three seeds.
Longer thinking appeared on harder items
By step 90, free rollouts still used all three modes: about 20% NoThink, 32% Short and 47% Long. Routing entropy—a measure of how evenly choices are spread—was about 1.04, close to the three-way maximum of roughly 1.10. Long was the most common choice, but no single mode took over.
The routing pattern also varied with problem difficulty. Around training step 50, the ordering of per-mode accuracy inverted; in validation, NoThink was used more on easier levels, Long more on harder ones, and Short was most common in between. That pattern is consistent with assigning less reasoning to easier problems and more to harder ones, although the routed subsets were not a randomized comparison of modes.
Savings varied across the tests
On MATH-500, free routing was reported above the accuracy–length frontier of the fixed modes—the best trade-offs those fixed choices produced—and reached its accuracy with 27% fewer tokens than that frontier required.
On GSM8K, free routing averaged 78.1% accuracy and 459 tokens, versus 83.1% and 1,930 tokens for the base model. At almost the same length as Short-only, which averaged 440 tokens, it scored higher than Short-only’s 75.6%. The reported reduction against the base was 76%.
On AIME 2024 and AIME 2025, free routing scored 27.6% and 22.2%, compared with 26.5% and 23.1% for the base model. Its combined mean response length was 10,716 tokens, against 12,266 for the base, a reported 13% reduction.
An early result with clear boundaries
Not every test produced a stable split. In a preliminary Countdown experiment, correct solutions were about 300 tokens, extra tokens did not rescue unsolved instances, and a binary router collapsed within 30 to 50 training steps.
The evidence covers one 1.5-billion-parameter model, one mathematical training distribution and three seeds. The mode caps were task-specific, and validation generation was uncapped, which may make brief-mode accuracy look better than it would under the capped training objective.
The results therefore show an association between routing and performance, not that selecting a particular mode caused the accuracy differences. They also do not establish that the approach will generalize beyond the mathematical benchmarks tested here.
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