Graph Distance as Surprise: Free Energy Minimization in Knowledge Graph Reasoning
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Abstract (arXiv)
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.
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References · 8
- 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
- 2017Modeling Relational Data with Graph Convolutional Networkscited by 1,684
- 2017Curiosity-driven Exploration by Self-supervised Predictioncited by 1,173
- 2024G-Retriever: Retrieval-Augmented Generation for Textual Graph Understanding and Question Answeringcited by 217
- 2024Plan-on-Graph: Self-Correcting Adaptive Planning of Large Language Model on Knowledge Graphscited by 77
- 2020On the Relationship Between Active Inference and Control as Inferencecited by 42
- 2024A Prompt-Based Knowledge Graph Foundation Model for Universal In-Context Reasoningcited by 25
- 2022Natural Language Syntax Complies with the Free-Energy Principlecited by 7
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- 2026Grounding LLM Reasoning under Incomplete Graph Evidence
- 2024Graph-constrained Reasoning: Faithful Reasoning on Knowledge Graphs with Large Language Models
- 2026Explore-on-Graph: Incentivizing Autonomous Exploration of Large Language Models on Knowledge Graphs with Path-refined Reward Modeling
- 2025Graph-R1: Incentivizing the Zero-Shot Graph Learning Capability in LLMs via Explicit Reasoning
- 2023River of No Return: Graph Percolation Embeddings for Efficient Knowledge Graph Reasoning
- 2025Mixture of Length and Pruning Experts for Knowledge Graphs Reasoning
- 2026Knowledge Graphs are Implicit Reward Models: Path-Derived Signals Enable Compositional Reasoning
- 2023Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning