# Verbalized Algorithms: Classical Algorithms are All You Need (Mostly)

arXiv: https://arxiv.org/abs/2509.08150 · HTML: https://mlsanity.com/paper/2509.08150/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 56 references that are in the map.
- First posted on arXiv 9 Sep 2025.

## Builds on (most cited first, 30 of 34)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [MTEB: Massive Text Embedding Benchmark](https://mlsanity.com/paper/2210.07316/) (2022)
- [GoEmotions: A Dataset of Fine-Grained Emotions](https://mlsanity.com/paper/2005.00547/) (2020)
- [Is ChatGPT Good at Search? Investigating Large Language Models as Re-Ranking Agents](https://mlsanity.com/paper/2304.09542/) (2023)
- [Large Language Models are Effective Text Rankers with Pairwise Ranking Prompting](https://mlsanity.com/paper/2306.17563/) (2023)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [CUAD: An Expert-Annotated NLP Dataset for Legal Contract Review](https://mlsanity.com/paper/2103.06268/) (2021)
- [Leveraging Pre-trained Large Language Models to Construct and Utilize World Models for Model-based Task Planning](https://mlsanity.com/paper/2305.14909/) (2023)
- [Efficient Guided Generation for Large Language Models](https://mlsanity.com/paper/2307.09702/) (2023)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Improving Passage Retrieval with Zero-Shot Question Generation](https://mlsanity.com/paper/2204.07496/) (2022)
- [Algorithms with Predictions](https://mlsanity.com/paper/2006.09123/) (2020)
- [Translating Natural Language to Planning Goals with Large-Language Models](https://mlsanity.com/paper/2302.05128/) (2023)
- [Zero-Shot Listwise Document Reranking with a Large Language Model](https://mlsanity.com/paper/2305.02156/) (2023)
- [XGrammar: Flexible and Efficient Structured Generation Engine for Large Language Models](https://mlsanity.com/paper/2411.15100/) (2024)
- [Large Language Models Enable Few-Shot Clustering](https://mlsanity.com/paper/2307.00524/) (2023)
- [ClusterLLM: Large Language Models as a Guide for Text Clustering](https://mlsanity.com/paper/2305.14871/) (2023)
- [Planning Anything with Rigor: General-Purpose Zero-Shot Planning with LLM-based Formalized Programming](https://mlsanity.com/paper/2410.12112/) (2024)
- [Thought of Search: Planning with Language Models Through The Lens of Efficiency](https://mlsanity.com/paper/2404.11833/) (2024)
- [HouseExpo: A Large-scale 2D Indoor Layout Dataset for Learning-based Algorithms on Mobile Robots](https://mlsanity.com/paper/1903.09845/) (2019)
- [Parallel Correlation Clustering on Big Graphs](https://mlsanity.com/paper/1507.05086/) (2015)
- [MD3: The Multi-Dialect Dataset of Dialogues](https://mlsanity.com/paper/2305.11355/) (2023)
- [Can Large Language Models Reason? A Characterization via 3-SAT](https://mlsanity.com/paper/2408.07215/) (2024)

## Abstract (arXiv)

Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we should not treat them as general-purpose reasoners, and as an alternative, we propose a paradigm we call verbalized algorithms (VAs), which combines LLMs and various algorithms with established guarantees. Instead of betting on LLM's ability to solve a reasoning task, VAs limit their scope by decomposing the task down to simple elementary operations on strings that they can answer reliably. For example, sorting a list of natural language strings could be done by using an LLM as a binary comparison oracle in a parallel or approximate sorting algorithm. We push the accuracy-runtime Pareto front with verbalized maximum, sorting, clustering, and submodular maximization, for numerical reasoning, topic clustering, Wi-Fi access point optimization, and multi-hop Q&A RAG task. These results suggest improving LLM-based reasoning through standard algorithmic analysis is a feasible and better grounded research direction.