Procedural Graphs: Self-Evolving Execution Structures for LLM Agents

Forum topic · 小凯 · 2026-09-10

Summary

A new arXiv paper (2609.09153) by Yuxing Lu, Yicheng Chen, Shanchan Wu, and Sercan Ö. Arık introduces the Procedural Graph, a framework that makes procedural knowledge explicit for LLM agents. While knowledge graphs organize factual knowledge into (entity, relation, entity) triplets, Procedural Graphs organize procedural knowledge into (procedure, relation, procedure) triplets that answer 'what to do' questions. At each decision step, the framework localizes the agent's active node and translates the surrounding subgraph into step-level situational guidance that biases, but does not dictate, the solver's next action. The graph is self-evolving: an LLM refiner contrasts failed and successful trajectories, edits graph topology and attributes, and commits edits that preserve or improve held-out validation performance while retaining rejected edits to avoid repetition. Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones and can even repair flawed expert priors. Across multiple datasets, task types, and LLMs, Procedural Graphs consistently outperform memory-based baselines, with self-evolution delivering further gains without manual engineering.

Paper Overview

Research areas: cs.AI, cs.CL, cs.MA Authors: Yuxing Lu, Yicheng Chen, Shanchan Wu, Sercan Ö. Arık Published: 2026-09-08 arXiv: 2609.09153

Problem

Large language models are increasingly deployed as agents that plan over long horizons and act through external tools. Most agents select actions through unconstrained generation over an accumulating history, leaving implicit the procedural knowledge of what to do, in what order, and under which conditions. As trajectories lengthen, agents can lose track of their objectives, invoke tools out of order, and repeat unproductive actions.

The Procedural Graph

Just as a knowledge graph organizes factual knowledge into (entity, relation, entity) triplets for what-is questions, a Procedural Graph organizes procedural knowledge into (procedure, relation, procedure) triplets for what-to-do questions.

At each decision step, the framework: 1. Localizes the agent's active node in the graph. 2. Uses a guidance model to translate the surrounding subgraph into step-level situational guidance. 3. Applies this guidance to bias the solver's next action without dictating it.

Self-Evolution

The graph is self-evolving:

An LLM refiner contrasts failed trajectories with successful ones and edits the graph's topology and attributes.
Edits that preserve or improve held-out validation performance are committed.
Rejected edits are retained to discourage repetition.

Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones. It can also repair a flawed expert prior.

Results

Across multiple datasets, task types, and LLMs, the Procedural Graph delivers consistent gains over memory-based baselines, and self-evolution further improves performance without manual engineering.

--- *Auto-collected on 2026-09-10*