Procedural Graphs: Self-Evolving Execution Structures for LLM Agents

Procedural Graphs store procedural knowledge as (procedure, relation, procedure) triplets and self-evolve via an LLM refiner, guiding LLM agent tool use and planning and outperforming memory-based baselines across datasets, task types, and LLMs.

The Procedural Graph framework organizes procedural knowledge into (procedure, relation, procedure) triplets, analogous to knowledge graphs, to guide LLM agent actions in tool use and planning, addressing drift such as lost objectives, out-of-order tool calls, and repeated unproductive steps. At each decision step the framework localizes the agent's active node, and a guidance model translates the surrounding subgraph into step-level situational guidance that biases the solver's next action. An LLM refiner contrasts failed with successful trajectories and edits the graph's topology and attributes, retaining rejected edits to discourage repetition. Starting from a minimal skeleton, the self-evolving loop builds graphs that match or surpass hand-designed ones and can repair flawed expert priors without manual engineering, delivering consistent gains over memory-based baselines across multiple datasets, task types, and LLMs. Both reports describe the same work and agree on the mechanism and results; neither provides quantitative benchmark figures.

• Stores procedural knowledge as (procedure, relation, procedure) triplets, analogous to knowledge graphs, to guide LLM agent tool use and planning.
• Targets agent drift: lost objectives, out-of-order tool calls, and repeated unproductive steps.
• At each decision step the framework localizes the agent's active node; a guidance model converts the surrounding subgraph into step-level guidance that biases the solver's next action.
• An LLM refiner contrasts failed with successful trajectories and edits the graph's topology and attributes; rejected edits are retained to discourage repetition.
• Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones and can repair flawed expert priors without manual engineering.
• Outperforms memory-based baselines consistently across multiple datasets, task types, and LLMs.
• Appeared on Hugging Face daily papers (2026-09-07) and arXiv cs.AI/cs.LG/cs.CL (2026-09-08); no quantitative figures, CVE ids, or version numbers were provided in either report.