# Polymath: A Self-Optimizing Agent with Dynamic Hierarchical Workflow

arXiv: https://arxiv.org/abs/2508.02959 · HTML: https://mlsanity.com/paper/2508.02959/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 30 of its 51 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [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)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [SWE-agent: Agent-Computer Interfaces Enable Automated Software Engineering](https://mlsanity.com/paper/2405.15793/) (2024)
- [OpenHands: An Open Platform for AI Software Developers as Generalist Agents](https://mlsanity.com/paper/2407.16741/) (2024)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [A Survey on the Memory Mechanism of Large Language Model based Agents](https://mlsanity.com/paper/2404.13501/) (2024)
- [Promptbreeder: Self-Referential Self-Improvement Via Prompt Evolution](https://mlsanity.com/paper/2309.16797/) (2023)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Automated Design of Agentic Systems](https://mlsanity.com/paper/2408.08435/) (2024)
- [Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration](https://mlsanity.com/paper/2307.05300/) (2023)
- [Data Interpreter: An LLM Agent For Data Science](https://mlsanity.com/paper/2402.18679/) (2024)
- [Symbolic Learning Enables Self-Evolving Agents](https://mlsanity.com/paper/2406.18532/) (2024)
- [VerilogCoder: Autonomous Verilog Coding Agents with Graph-based Planning and Abstract Syntax Tree (AST)-based Waveform Tracing Tool](https://mlsanity.com/paper/2408.08927/) (2024)
- [AnalogCoder: Analog Circuit Design via Training-Free Code Generation](https://mlsanity.com/paper/2405.14918/) (2024)
- [AutoFlow: Automated Workflow Generation for Large Language Model Agents](https://mlsanity.com/paper/2407.12821/) (2024)
- [Archon: An Architecture Search Framework for Inference-Time Techniques](https://mlsanity.com/paper/2409.15254/) (2024)
- [EvoFlow: Evolving Diverse Agentic Workflows On The Fly](https://mlsanity.com/paper/2502.07373/) (2025)
- [UniParser: A Unified Log Parser for Heterogeneous Log Data](https://mlsanity.com/paper/2202.06569/) (2022)
- [SEW: Self-Evolving Agentic Workflows for Automated Code Generation](https://mlsanity.com/paper/2505.18646/) (2025)
- [DRC-Coder: Automated DRC Checker Code Generation Using LLM Autonomous Agent](https://mlsanity.com/paper/2412.05311/) (2024)
- [Timing Analysis Agent: Autonomous Multi-Corner Multi-Mode (MCMM) Timing Debugging with Timing Debug Relation Graph](https://mlsanity.com/paper/2504.11502/) (2025)

## Built on by (most cited first, 2 of 2)

- [Self-Evolving LLMs via Continual Instruction Tuning](https://mlsanity.com/paper/2509.18133/) (2025)
- [CB-Orchestrator: Adaptive Workflow Optimization for LLM Agents via Contextual Bandits](https://mlsanity.com/paper/2610.13064/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel at solving complex tasks by executing agentic workflows composed of detailed instructions and structured operations. Yet, building general-purpose agents by manually embedding foundation models into agentic systems such as Chain-of-Thought, Self-Reflection, and ReACT through text interfaces limits scalability and efficiency. Recently, many researchers have sought to automate the generation and optimization of these workflows through code-based representations. However, existing methods often rely on labeled datasets to train and optimize workflows, making them ineffective and inflexible for solving real-world, dynamic problems where labeled data is unavailable. To address this challenge, we introduce Polymath, a self-optimizing agent with dynamic hierarchical workflow that leverages the flexibility of task flow graphs and the expressiveness of code-represented workflows to solve a wide range of real-world, dynamic problems. The proposed optimization methodology integrates multi-grid-inspired graph optimization with a self-reflection-guided evolutionary algorithm to refine workflows without labeled data. Experimental results on six benchmark datasets across coding, math, and multi-turn QA tasks show that Polymath achieves 8.1% average improvement over state-of-the-art baselines.