# Algorithm of Thoughts: Enhancing Exploration of Ideas in Large Language Models

arXiv: https://arxiv.org/abs/2308.10379 · HTML: https://mlsanity.com/paper/2308.10379/

## Key facts

- Cited by 92 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 29 of its 38 references that are in the map.
- First posted on arXiv 20 Aug 2023.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [LaMDA: Language Models for Dialog Applications](https://mlsanity.com/paper/2201.08239/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance](https://mlsanity.com/paper/2305.05176/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Automatic Chain of Thought Prompting in Large Language Models](https://mlsanity.com/paper/2210.03493/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [DeepSpeed Inference: Enabling Efficient Inference of Transformer Models at Unprecedented Scale](https://mlsanity.com/paper/2207.00032/) (2022)
- [Augmented Language Models: a Survey](https://mlsanity.com/paper/2302.07842/) (2023)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Sustainable AI: Environmental Implications, Challenges and Opportunities](https://mlsanity.com/paper/2111.00364/) (2021)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [Leveraging Large Language Models for Multiple Choice Question Answering](https://mlsanity.com/paper/2210.12353/) (2022)
- [Compositional Semantic Parsing with Large Language Models](https://mlsanity.com/paper/2209.15003/) (2022)
- [Synthetic Prompting: Generating Chain-of-Thought Demonstrations for Large Language Models](https://mlsanity.com/paper/2302.00618/) (2023)

## Built on by (most cited first, 30 of 92)

- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models](https://mlsanity.com/paper/2501.09686/) (2025)
- [Evolution of Heuristics: Towards Efficient Automatic Algorithm Design Using Large Language Model](https://mlsanity.com/paper/2401.02051/) (2024)
- [Data Interpreter: An LLM Agent For Data Science](https://mlsanity.com/paper/2402.18679/) (2024)
- [Navigate through Enigmatic Labyrinth A Survey of Chain of Thought Reasoning: Advances, Frontiers and Future](https://mlsanity.com/paper/2309.15402/) (2023)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [Stream of Search (SoS): Learning to Search in Language](https://mlsanity.com/paper/2404.03683/) (2024)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [Forest-of-Thought: Scaling Test-Time Compute for Enhancing LLM Reasoning](https://mlsanity.com/paper/2412.09078/) (2024)
- [Towards System 2 Reasoning in LLMs: Learning How to Think With Meta Chain-of-Thought](https://mlsanity.com/paper/2501.04682/) (2025)
- [A Review of Large Language Models and Autonomous Agents in Chemistry](https://mlsanity.com/paper/2407.01603/) (2024)
- [On Generative Agents in Recommendation](https://mlsanity.com/paper/2310.10108/) (2023)
- [Language Agents as Optimizable Graphs](https://mlsanity.com/paper/2402.16823/) (2024)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [Tell Me More! Towards Implicit User Intention Understanding of Language Model Driven Agents](https://mlsanity.com/paper/2402.09205/) (2024)
- [Suspicion-Agent: Playing Imperfect Information Games with Theory of Mind Aware GPT-4](https://mlsanity.com/paper/2309.17277/) (2023)
- [StateFlow: Enhancing LLM Task-Solving through State-Driven Workflows](https://mlsanity.com/paper/2403.11322/) (2024)
- [Demystifying Chains, Trees, and Graphs of Thoughts](https://mlsanity.com/paper/2401.14295/) (2024)
- [Learning Adaptive Parallel Reasoning with Language Models](https://mlsanity.com/paper/2504.15466/) (2025)
- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiency](https://mlsanity.com/paper/2309.17382/) (2023)
- [Dualformer: Controllable Fast and Slow Thinking by Learning with Randomized Reasoning Traces](https://mlsanity.com/paper/2410.09918/) (2024)
- [LatEval: An Interactive LLMs Evaluation Benchmark with Incomplete Information from Lateral Thinking Puzzles](https://mlsanity.com/paper/2308.10855/) (2023)
- [Large Language Models for Planning: A Comprehensive and Systematic Survey](https://mlsanity.com/paper/2505.19683/) (2025)
- [System-1.x: Learning to Balance Fast and Slow Planning with Language Models](https://mlsanity.com/paper/2407.14414/) (2024)
- [DetermLR: Augmenting LLM-based Logical Reasoning from Indeterminacy to Determinacy](https://mlsanity.com/paper/2310.18659/) (2023)
- [PENCIL: Long Thoughts with Short Memory](https://mlsanity.com/paper/2503.14337/) (2025)
- [LongProc: Benchmarking Long-Context Language Models on Long Procedural Generation](https://mlsanity.com/paper/2501.05414/) (2025)
- [Chain-of-Reasoning: Towards Unified Mathematical Reasoning in Large Language Models via a Multi-Paradigm Perspective](https://mlsanity.com/paper/2501.11110/) (2025)

## Abstract (arXiv)

Current literature, aiming to surpass the "Chain-of-Thought" approach, often resorts to external modi operandi involving halting, modifying, and then resuming the generation process to boost Large Language Models' (LLMs) reasoning capacities. Due to their myopic perspective, they escalate the number of query requests, leading to increased costs, memory, and computational overheads. Addressing this, we propose the Algorithm of Thoughts -- a novel strategy that propels LLMs through algorithmic reasoning pathways. By employing algorithmic examples fully in-context, this overarching view of the whole process exploits the innate recurrence dynamics of LLMs, expanding their idea exploration with merely one or a few queries. Our technique outperforms earlier single-query methods and even more recent multi-query strategies that employ an extensive tree search algorithms while using significantly fewer tokens. Intriguingly, our results suggest that instructing an LLM using an algorithm can lead to performance surpassing that of the algorithm itself, hinting at LLM's inherent ability to weave its intuition into optimized searches. We probe into the underpinnings of our method's efficacy and its nuances in application. The code and related content can be found in: https://algorithm-of-thoughts.github.io.