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DOTS: Learning to Reason Dynamically in LLMs via Optimal Reasoning Trajectories Search
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Proposes DOTS, which searches for per-question optimal trajectories of atomic reasoning actions (rewriting, decomposition, CoT/PoT, self-verification) for a given solver LLM and fine-tunes either an external planner or the solver itself to predict them.
Problem
Static, predefined prompting strategies (CoT, PoT, decomposition, self-verification) are applied uniformly to all questions and ignore both question characteristics and the capability of the task-solving LLM.
Approach
Treat reasoning actions (query rewriting/decomposition, CoT/PoT, self-verification) as atomic modules; search for the best-performing and shortest action trajectory per training question using the specific solver LLM, then SFT a planner (external) or the solver itself (internalized) to predict the trajectory with an explanation before solving.
Key results
- External planner (Llama-3-8B-Instruct) with GPT-4o-mini solver reaches 66.5% average over MATH, BBH, Game of 24, and TheoremQA, versus 63.0% for the best baseline Self-Refine.
- Internalized planner tuning on Llama-3-8B-Instruct reaches 35.5% average versus 33.6% for Vanilla SFT, with +8.7 points on BBH (69.7 vs 61.0).
- On OOD tasks with the internalized planner, average accuracy is 53.0% versus 50.2% for Vanilla SFT, and DOTS uses 409.1 output tokens versus 527.6 for Self-Refine.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use dynamic trajectory planning instead of the strongest static baseline | External planner with Llama-3-70B-Instruct solver · BBH | accuracy (%): 73.8 -> 77.3 | Helped |
| Use dynamic trajectory planning instead of the strongest static baseline | External planner with GPT-4o-mini solver · MATH | accuracy (%): 73.7 -> 75.4 | Helped |
| Use dynamic trajectory planning instead of the strongest static baseline | External planner with GPT-4o-mini solver · Game of 24 | accuracy (%): 68.7 -> 65.2 | Hurt |
| Use internalized trajectory planning instead of Vanilla SFT | Llama-3-8B-Instruct · BBH | accuracy (%): 61.0 -> 69.7 | Helped |
| Use dynamic trajectory planning instead of the strongest static baseline | External planner with GPT-4o-mini solver · OOD average | accuracy (%): 73.7 -> 75.4 | Helped |
| Search for optimal trajectories instead of using randomly selected trajectories (ablation) | DOTS external planner with GPT-4o-mini solver · MATH, BBH, Game24, and TheoremQA | accuracy (%): 69.2 -> 75.4; 78.6 -> 84.2; 28.9 -> 65.2; 40.2 -> 42.4 | Helped |
| Include explanations of optimal trajectories during planner training (ablation) | DOTS external planner with GPT-4o-mini solver · MATH, BBH, Game24, and TheoremQA | accuracy (%): 68.2 -> 75.4; 81.3 -> 84.2; 57.4 -> 65.2; 36.4 -> 42.4 | Helped |
| Search for optimal trajectories instead of using randomly selected trajectories (ablation) | DOTS internalized Llama-3-8B-Instruct · MATH, BBH, Game24, and TheoremQA | accuracy (%): 31.4 -> 34.4; 55.8 -> 69.7; 19.6 -> 21.9; 15.1 -> 16.1 | Helped |
| Include explanations of optimal trajectories during planner training (ablation) | DOTS internalized Llama-3-8B-Instruct · MATH, BBH, Game24, and TheoremQA | accuracy (%): 33.8 -> 34.4; 65.8 -> 69.7; 18.6 -> 21.9; 15.7 -> 16.1 | Helped |
Surprising findings
- Adding few-shot demonstrations to static prompting methods does not consistently improve performance, except on BBH.
- Without search (random trajectories), Game of 24 accuracy with the external planner drops sharply from 65.2 to 28.9.
Limitations
- Searching and explanation generation depend on GPT-4o, and the search is costly relative to a single trajectory.
- Action set is limited to rewriting, decomposition, CoT, PoT, and self-verification; some datasets (e.g., date understanding) show PoT failures from output-format errors.
- Reported results show mixed performance on some tasks (e.g., Game of 24 vs Self-Refine for external planner; MMLU-Pro and StrategyQA vs CoT for some solvers).
Experimental setup
Datasets: MATH BBH Game of 24 TheoremQA
Benchmarks: MATH BBH Game of 24 TheoremQA DeepMind Math MMLU-Pro StrategyQA DROP
Metrics: accuracy average output tokens
Baselines: CoT PoT Least-to-most Self-Refine PromptAgent Vanilla SFT
Builds on: Chain-of-Thought Program-of-Thought Least-to-most prompting Self-Refine PromptAgent
Closest papers by meaning
- GPO: Learning from Critical Steps to Improve LLM Reasoning (NeurIPS 2025 · similarity 0.90)
- Don’t Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models (NeurIPS 2025 · similarity 0.90)
- StrategyLLM: Large Language Models as Strategy Generators, Executors, Optimizers, and Evaluators for Problem Solving (NeurIPS 2024 · similarity 0.90)
- Bag of Tricks for Inference-time Computation of LLM Reasoning (NeurIPS 2025 · similarity 0.90)
- MILES: Modular Instruction Memory with Learnable Selection for Self-Improving LLM Reasoning (NeurIPS 2026 · similarity 0.89)
- ReGenesis: LLMs can Grow into Reasoning Generalists via Self-Improvement (ICLR 2025 · similarity 0.89)
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