Research map / Large language models / Reasoning and chain of thought
Algorithm of Thoughts: Enhancing Exploration of Ideas in Large Language Models
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Proposes Algorithm of Thoughts (AoT), a single-prompt in-context method whose exemplars show DFS/BFS-style search traces so the LLM explores ideas within one generation, matching or beating tree-search ToT with far fewer queries.
Problem
Multi-query reasoning methods such as Tree of Thoughts require halting, evaluating, and resuming generation, which multiplies query count, latency, cost, and tokens for tasks needing extensive idea exploration.
Approach
Few-shot exemplars capture the full algorithmic search process (node selection, expansion, failed attempts, backtracking) rather than only solution steps, so the LLM internalizes tree search and generates the whole exploration in one uninterrupted sequence at temperature 0.
Key results
- Game of 24: AoT reaches 71% success with a single query versus 69% for ToT (b=5), which uses about 109 queries per example.
- Mini crosswords: AoT achieves 52% word success with 2 queries versus 46.5% for ToT, which uses over 200 queries.
- Fine-tuning GPT-3.5-Turbo on 900 examples raises Game of 24 accuracy from 3% to 63% with AoT versus 3% to 12% with CoT.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use AoT instead of ToT | GPT-4 · Game of 24 | success: 69% -> 71% | Helped |
| manually resolve the final answer after AoT finds a solution (ablation) | AoT · Game of 24 | success: 71% -> 78% | Helped |
| use shorter in-context examples with one or two steps (ablation) | AoT · Game of 24 | success: 71% -> 48% | Hurt |
| use AoT instead of ToT | GPT-4 · Mini Crosswords (5×5) | word success: 46.5% -> 52% | Helped |
| use AoT instead of ToT | GPT-4 · GSM8K | accuracy: 90% -> 89% | Hurt |
| use AoT instead of CoT | GPT-4 · GSM8K | accuracy: 86% -> 89% | Helped |
| use AoT instead of ToT | GPT-4 · StrategyQA | accuracy: 83% -> 84% | Helped |
| use AoT instead of CoT | GPT-4 · Coin Change | accuracy: 76% -> 96% | Helped |
| use AoT instead of CoT | GPT-4 · Edit Distance | accuracy: 64% -> 90% | Helped |
| use AoT instead of ToT | GPT-4 · Creative Writing | score: 7.56 -> 7.58 | No clear effect |
| fine-tune AoT prompts on 900 examples | GPT-3.5-Turbo · Game of 24 | success: 3% -> 63% | Helped |
| fine-tune CoT prompts on 900 examples | GPT-3.5-Turbo · Game of 24 | success: 3% -> 12% | Helped |
Surprising findings
- AoT with a DFS-style exemplar expands fewer nodes than the DFS algorithm it imitates, suggesting the LLM adds its own heuristic.
- Repeating correct in-context arithmetic examples with identical outputs sharply lowers text-davinci-003 accuracy on simple arithmetic.
Limitations
- Resource demand exceeds standard prompting and CoT due to long token generation.
- Experiments conducted only with GPT-4; weaker models may not benefit.
- Exemplar construction relies on manually written search traces, with some outputs requiring manual resolution to reach 78%.
Experimental setup
Datasets: 4nums.com game of 24 (indices 901-1000) goobix.com mini crosswords (20 test games) GSM8K (first 100 questions) StrategyQA (first 100 questions) Coin Change Edit Distance
Benchmarks: Game of 24 Mini Crosswords Creative Writing GSM8K StrategyQA Coin Change Edit Distance
Metrics: success rate word success rate number of queries prompt tokens completion tokens coherence score (1-10)
Baselines: standard prompting CoT CoT-SC Tree of Thoughts I/O + Refine DFS
Builds on: chain-of-thought tree of thoughts self-consistency least-to-most prompting
Closest papers by meaning
- Generating Chain-of-Thoughts with a Pairwise-Comparison Approach to Searching for the Most Promising Intermediate Thought (ICML 2024 · similarity 0.90)
- Accelerating Large Language Model Reasoning via Speculative Search (ICML 2025 · similarity 0.90)
- RATT: A Thought Structure for Coherent and Correct LLM Reasoning (AAAI 2025 · similarity 0.89)
- Reasoning Scaffolding: Distilling the Flow of Thought from LLMs (ICLR 2026 · similarity 0.89)
- Toward Adaptive Reasoning in Large Language Models with Thought Rollback (ICML 2024 · similarity 0.89)
- TSLM: Tree-Structured Language Modeling for Divergent Thinking (ICLR 2026 · similarity 0.89)
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