# DOTS: Learning to Reason Dynamically in LLMs via Optimal Reasoning Trajectories Search

arXiv: https://arxiv.org/abs/2410.03864 · HTML: https://mlsanity.com/paper/2410.03864/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 26 of 26)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Super-NaturalInstructions: Generalization via Declarative Instructions on 1600+ NLP Tasks](https://mlsanity.com/paper/2204.07705/) (2022)
- [AGIEval: A Human-Centric Benchmark for Evaluating Foundation Models](https://mlsanity.com/paper/2304.06364/) (2023)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [Improve Mathematical Reasoning in Language Models by Automated Process Supervision](https://mlsanity.com/paper/2406.06592/) (2024)
- [Scaling Synthetic Data Creation with 1,000,000,000 Personas](https://mlsanity.com/paper/2406.20094/) (2024)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Monte Carlo Tree Search Boosts Reasoning via Iterative Preference Learning](https://mlsanity.com/paper/2405.00451/) (2024)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [PromptAgent: Strategic Planning with Language Models Enables Expert-level Prompt Optimization](https://mlsanity.com/paper/2310.16427/) (2023)
- [MAmmoTH2: Scaling Instructions from the Web](https://mlsanity.com/paper/2405.03548/) (2024)
- [MathScale: Scaling Instruction Tuning for Mathematical Reasoning](https://mlsanity.com/paper/2403.02884/) (2024)
- [Mutual Reasoning Makes Smaller LLMs Stronger Problem-Solvers](https://mlsanity.com/paper/2408.06195/) (2024)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [Self-Discover: Large Language Models Self-Compose Reasoning Structures](https://mlsanity.com/paper/2402.03620/) (2024)
- [Question Decomposition Improves the Faithfulness of Model-Generated Reasoning](https://mlsanity.com/paper/2307.11768/) (2023)
- [Automatic Model Selection with Large Language Models for Reasoning](https://mlsanity.com/paper/2305.14333/) (2023)

## Built on by (most cited first, 17 of 17)

- [DeepResearcher: Scaling Deep Research via Reinforcement Learning in Real-world Environments](https://mlsanity.com/paper/2504.03160/) (2025)
- [ReMA: Learning to Meta-think for LLMs with Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2503.09501/) (2025)
- [ReasonFlux-PRM: Trajectory-Aware PRMs for Long Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2506.18896/) (2025)
- [Route to Reason: Adaptive Routing for LLM and Reasoning Strategy Selection](https://mlsanity.com/paper/2505.19435/) (2025)
- [A Survey on LLM Test-Time Compute via Search: Tasks, LLM Profiling, Search Algorithms, and Relevant Frameworks](https://mlsanity.com/paper/2501.10069/) (2025)
- [PresentAgent: Multimodal Agent for Presentation Video Generation](https://mlsanity.com/paper/2507.04036/) (2025)
- [A Survey on Large Language Models for Automated Planning](https://mlsanity.com/paper/2502.12435/) (2025)
- [Causal Sufficiency and Necessity Improves Chain-of-Thought Reasoning](https://mlsanity.com/paper/2506.09853/) (2025)
- [Using LLMs for Late Multimodal Sensor Fusion for Activity Recognition](https://mlsanity.com/paper/2509.10729/) (2025)
- [ToolLibGen: Scalable Automatic Tool Creation and Aggregation for LLM Reasoning](https://mlsanity.com/paper/2510.07768/) (2025)
- [Teaching LLMs According to Their Aptitude: Adaptive Reasoning for Mathematical Problem Solving](https://mlsanity.com/paper/2502.12022/) (2025)
- [LETToT: Label-Free Evaluation of Large Language Models On Tourism Using Expert Tree-of-Thought](https://mlsanity.com/paper/2508.11280/) (2025)
- [TIME: Temporally Intelligent Meta-reasoning Engine for Context-Triggered Explicit Reasoning](https://mlsanity.com/paper/2601.05300/) (2026)
- [Automatic Slide Updating with User-Defined Dynamic Templates and Natural Language Instructions](https://mlsanity.com/paper/2604.17894/) (2026)
- [STRIDE: Learnable Stepwise Language Feedback for LLM Reasoning](https://mlsanity.com/paper/2605.18851/) (2026)
- [Spatial Reasoning via Modality Switching Between Language and Symbolic Representations](https://mlsanity.com/paper/2606.31285/) (2026)
- [MedAlign: A Synergistic Framework of Multimodal Preference Optimization and Federated Meta-Cognitive Reasoning](https://mlsanity.com/paper/2510.21093/) (2025)

## Abstract (arXiv)

Enhancing the capability of large language models (LLMs) in reasoning has gained significant attention in recent years. Previous studies have demonstrated the effectiveness of various prompting strategies in aiding LLMs in reasoning (called "reasoning actions"), such as step-by-step thinking, reflecting before answering, solving with programs, and their combinations. However, these approaches often applied static, predefined reasoning actions uniformly to all questions, without considering the specific characteristics of each question or the capability of the task-solving LLM. In this paper, we propose DOTS, an approach enabling LLMs to reason dynamically via optimal reasoning trajectory search, tailored to the specific characteristics of each question and the inherent capability of the task-solving LLM. Our approach involves three key steps: i) defining atomic reasoning action modules that can be composed into various reasoning action trajectories; ii) searching for the optimal action trajectory for each training question through iterative exploration and evaluation for the specific task-solving LLM; and iii) using the collected optimal trajectories to train an LLM to plan for the reasoning trajectories of unseen questions. In particular, we propose two learning paradigms, i.e., fine-tuning an external LLM as a planner to guide the task-solving LLM, or directly fine-tuning the task-solving LLM with an internalized capability for reasoning actions planning. Our experiments across eight reasoning tasks show that our method consistently outperforms static reasoning techniques and the vanilla instruction tuning approach. Further analysis reveals that our method enables LLMs to adjust their computation based on problem complexity, allocating deeper thinking and reasoning to harder problems.