# DART: Draft-Agreement Routing for Training-Free Adaptive Thinking Budgets in Hybrid Reasoning Models

Source: [DART: Draft-Agreement Routing for Training-Free Adaptive Thinking Budgets in Hybrid Reasoning Models](<https://www.sota2.com/research/paper/6a3a13b9206542251d7c78ca>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-06-24T05:00:31.418Z

Authors: Jungseob Lee, Seongtae Hong, Seungjun Lee, Jaehyung Seo, Junyoung Son, Sugyeong Eo, Chanjun Park, Hyeongju Park, Hyeonseok Moon, Heuiseok Lim

Published: 2026-06-22T11:24:59.000Z

## Abstract

Hybrid reasoning models can answer directly or spend extra tokens on extended thinking. A practical router should choose between these modes for each query, so easy problems avoid unnecessary reasoning and hard problems receive enough budget to finish the answer. Existing routers move in this direction, but they typically require labeled training data or fix thinking budgets up front, ignoring answer-level evidence from the model itself. We introduce DART, a training-free routing framework that samples two cheap no-think drafts, accepts direct answering when the drafts agree, and predicts a thinking budget from draft entropy when they disagree. Across the main comparisons, DART preserves or improves always-thinking accuracy in most settings while reducing thinking-token use. On math reasoning, accuracy improves by up to $+$9.0 points on Olympiad-level problems while thinking tokens drop 15-69%. On code reasoning under execution-based equivalence, accuracy improves by up to +22.5 points while thinking tokens drop 51-63%. The Stage~1 signal extends across model scales (0.6B-32B), model families, and API-only hosted settings, with no labeled data and no gradient updates required.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Code Generation on HumanEval (Accuracy and Thinking Token Usage)](<https://www.sota2.com/research/sota/code-generation-on-humaneval-accuracy-and-thinking-token-usage.md>): Code Generation; HumanEval; Accuracy: 95.1.

- [Code Generation on MBPP (Accuracy, Thinking Token Usage (%))](<https://www.sota2.com/research/sota/code-generation-on-mbpp-accuracy-thinking-token-usage-percent.md>): Code Generation; MBPP; Accuracy: 71.2.

- [Mathematical Reasoning on MATH 500 (Accuracy and Thinking Token Usage)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math-500-accuracy-and-thinking-token-usage.md>): Mathematical Reasoning; MATH 500; Accuracy: 88.5.

- [Mathematical Reasoning on MATH 500 (Accuracy, Think ↓, Route%)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-math-500-accuracy-think-route-percent.md>): Mathematical Reasoning; MATH 500; Accuracy: 92.6.

- [Mathematics on AIME 2025 (Accuracy, Thinking Token Reduction (%))](<https://www.sota2.com/research/sota/mathematics-on-aime-2025-accuracy-thinking-token-reduction-percent.md>): Mathematics; AIME 2025; Accuracy: 56.7.

- [Code Generation on HumanEval (held-out)](<https://www.sota2.com/research/sota/code-generation-on-humaneval-held-out.md>): Code Generation; HumanEval (held-out); Accuracy: 95.1.

- [Mathematical Reasoning on OlympiadBench (Accuracy, Thinking Token Usage (%))](<https://www.sota2.com/research/sota/mathematical-reasoning-on-olympiadbench-accuracy-thinking-token-usage-percent.md>): Mathematical Reasoning; OlympiadBench; Accuracy: 69.8.

- [Mathematics on AIME 2024 (Accuracy, Thinking Token Reduction %)](<https://www.sota2.com/research/sota/mathematics-on-aime-2024-accuracy-thinking-token-reduction-percent.md>): Mathematics; AIME 2024; Accuracy: 70.

- [Mathematical Reasoning on OlympiadBench (Accuracy, Think ↓, Route%)](<https://www.sota2.com/research/sota/mathematical-reasoning-on-olympiadbench-accuracy-think-route-percent.md>): Mathematical Reasoning; OlympiadBench; Accuracy: 69.8.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2606.23181>)

[PDF](<https://arxiv.org/pdf/2606.23181.pdf>)