Graph Distance as Surprise: Free Energy Minimization in Knowledge Graph Reasoning

TL;DR

This paper introduces a novel approach to knowledge graph reasoning by applying the Free Energy Principle, using graph distance as a measure of surprise to guide inference and decision-making.

Contribution

It formalizes surprise based on shortest-path graph distance within the Free Energy framework, connecting neuroscience principles to knowledge graph systems.

Findings

Graph distance correlates with surprise levels in KG reasoning.

Distance-based surprise can enhance message passing in graph neural networks.

The framework links KG reasoning to neuroscience-inspired free energy minimization.

Abstract

In this work, we propose that reasoning in knowledge graph (KG) networks can be guided by surprise minimization. Entities that are close in graph distance will have lower surprise than those farther apart. This connects the Free Energy Principle (FEP) from neuroscience to KG systems, where the KG serves as the agent's generative model. We formalize surprise using the shortest-path distance in directed graphs and provide a framework for KG-based agents. Graph distance appears in graph neural networks as message passing depth and in model-based reinforcement learning as world model trajectories. This work-in-progress study explores whether distance-based surprise can extend recent work showing that syntax minimizes surprise and free energy via tree structures.