Advanced · Research

Procedural Graphs

Visual diagram · Math · (in preparation) · Worked example · 3 difficulty levels.

TL;DR. Self-evolving execution structures that organize what-to-do knowledge into (procedure, relation, procedure) triplets, guiding an agent's next action at each step.

Technical Definition

Self-evolving execution structures that organize what-to-do knowledge into (procedure, relation, procedure) triplets, guiding an agent's next action at each step.

How it works

Introduced in a September 2026 paper (arXiv:2609.09153), a procedural graph does for procedures what a knowledge graph does for facts. As agent trajectories lengthen, agents lose track of objectives, invoke tools out of order, and repeat unproductive actions; a procedural graph localizes the agent's active node at each decision step and translates the surrounding subgraph into situational guidance that biases the next action without dictating it. The graph is self-evolving: an LLM refiner contrasts failed trajectories with successful ones and edits the topology, committing edits that improve held-out validation performance. Starting from a minimal skeleton, the loop builds graphs that match or surpass hand-designed ones — and can repair a flawed expert prior.

Visual Explanation (flowchart)

Active node → surrounding subgraph → guidance model → next action → outcome → refiner edits graph

Related Concepts

• Graph Engineering — Organizing multiple agents, work structures, and runtime states as one coordinated system — the layer above the individual agent harness.
• Agent Memory — Information an agent retains beyond the current context window — episodic history, learned facts, preferences, and task state.
• Knowledge Graph — A structured representation of knowledge as a network of entities and their relationships.