Large language models (LLMs) used as agents often lose track of objectives over long tasks, repeating actions or using tools incorrectly. To address this, researchers from Google, Georgia Tech, and Peking University introduce the Procedural Graph—a structured memory that stores procedural knowledge as (procedure, relation, procedure) triplets, similar to how knowledge graphs store facts. At each step, the agent's active node localizes relevant subgraph information, which a guidance model converts into situational advice that biases but does not dictate the next action.

The graph self-evolves: an LLM refiner compares failed and successful trajectories, editing graph topology and attributes, and only commits changes that improve held-out validation performance. Rejected edits are kept to avoid repeating mistakes. Starting from a minimal skeleton, this method builds graphs that match or exceed hand-designed ones, and it can repair flawed expert priors.

Across multiple datasets, task types, and backbone LLMs, the Procedural Graph consistently outperforms memory-based baselines, with self-evolution adding further gains without manual engineering.