# Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation

arXiv: https://arxiv.org/abs/2310.02304 · HTML: https://mlsanity.com/paper/2310.02304/

## Key facts

- Cited by 148 papers in the map (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 54 of its 90 references that are in the map.
- First posted on arXiv 3 Oct 2023.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 30 of 54)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Voyager: An Open-Ended Embodied Agent with Large Language Models](https://mlsanity.com/paper/2305.16291/) (2023)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Large Language Models Are Human-Level Prompt Engineers](https://mlsanity.com/paper/2211.01910/) (2022)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [Are Emergent Abilities of Large Language Models a Mirage?](https://mlsanity.com/paper/2304.15004/) (2023)
- [Cognitive Architectures for Language Agents](https://mlsanity.com/paper/2309.02427/) (2023)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)

## Built on by (most cited first, 30 of 148)

- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [Cut the Crap: An Economical Communication Pipeline for LLM-based Multi-Agent Systems](https://mlsanity.com/paper/2410.02506/) (2024)
- [Advances and Challenges in Foundation Agents: From Brain-Inspired Intelligence to Evolutionary, Collaborative, and Safe Systems](https://mlsanity.com/paper/2504.01990/) (2025)
- [A Survey of Context Engineering for Large Language Models](https://mlsanity.com/paper/2507.13334/) (2025)
- [G-Designer: Architecting Multi-agent Communication Topologies via Graph Neural Networks](https://mlsanity.com/paper/2410.11782/) (2024)
- [Meta-Prompting: Enhancing Language Models with Task-Agnostic Scaffolding](https://mlsanity.com/paper/2401.12954/) (2024)
- [Self-Harness: Harnesses That Improve Themselves](https://mlsanity.com/paper/2606.09498/) (2026)
- [LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics](https://mlsanity.com/paper/2405.20132/) (2024)
- [A Survey on Self-Evolution of Large Language Models](https://mlsanity.com/paper/2404.14387/) (2024)
- [Language Agents as Optimizable Graphs](https://mlsanity.com/paper/2402.16823/) (2024)
- [Watch Every Step! LLM Agent Learning via Iterative Step-Level Process Refinement](https://mlsanity.com/paper/2406.11176/) (2024)
- [A Self-Improving Coding Agent](https://mlsanity.com/paper/2504.15228/) (2025)
- [Feedback Loops With Language Models Drive In-Context Reward Hacking](https://mlsanity.com/paper/2402.06627/) (2024)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [LLM2LLM: Boosting LLMs with Novel Iterative Data Enhancement](https://mlsanity.com/paper/2403.15042/) (2024)
- [Trace is the Next AutoDiff: Generative Optimization with Rich Feedback, Execution Traces, and LLMs](https://mlsanity.com/paper/2406.16218/) (2024)
- [StateFlow: Enhancing LLM Task-Solving through State-Driven Workflows](https://mlsanity.com/paper/2403.11322/) (2024)
- [HyperAgent: Generalist Software Engineering Agents to Solve Coding Tasks at Scale](https://mlsanity.com/paper/2409.16299/) (2024)
- [Prompt Engineering a Prompt Engineer](https://mlsanity.com/paper/2311.05661/) (2023)
- [Huxley-G"odel Machine: Human-Level Coding Agent Development by an Approximation of the Optimal Self-Improving Machine](https://mlsanity.com/paper/2510.21614/) (2025)
- [Evolving Code with A Large Language Model](https://mlsanity.com/paper/2401.07102/) (2024)
- [Group-Evolving Agents: Open-Ended Self-Improvement via Experience Sharing](https://mlsanity.com/paper/2602.04837/) (2026)
- [Recursive Harness Self-Improvement](https://mlsanity.com/paper/2607.15524/) (2026)
- [G"odel Agent: A Self-Referential Agent Framework for Recursive Self-Improvement](https://mlsanity.com/paper/2410.04444/) (2024)
- [AI Agentic Programming: A Survey of Techniques, Challenges, and Opportunities](https://mlsanity.com/paper/2508.11126/) (2025)
- [Understanding the Importance of Evolutionary Search in Automated Heuristic Design with Large Language Models](https://mlsanity.com/paper/2407.10873/) (2024)
- [MetaSkill-Evolve: Recursive Self-Improvement of LLM Agents via Two-Timescale Meta-Skill Evolution](https://mlsanity.com/paper/2607.05297/) (2026)
- [Learning to Reason via Mixture-of-Thought for Logical Reasoning](https://mlsanity.com/paper/2505.15817/) (2025)

## Abstract (arXiv)

Several recent advances in AI systems solve problems by providing a "scaffolding" program that structures multiple calls to language models (LMs) to generate better outputs. A scaffolding program is written in a programming language such as Python. In this work, we use a language-model-infused scaffolding program to improve itself. We start with a seed "improver" that improves an input program according to a given utility function by querying an LM several times and returning the best solution. We then run this seed improver to improve itself. Across a small set of downstream tasks, the resulting improved improver generates programs with significantly better performance than its seed improver. A variety of self-improvement strategies are proposed by the language model, including beam search, genetic algorithms, and simulated annealing. Since the language models themselves are not altered, this is not full recursive self-improvement. Nonetheless, it demonstrates that a modern language model, GPT-4 in our experiments, is capable of writing code that can call itself to improve itself. We consider concerns around the development of self-improving technologies and evaluate the frequency with which the generated code bypasses a sandbox.