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

arXiv: https://arxiv.org/abs/2512.01878 · HTML: https://mlsanity.com/paper/2512.01878/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 8 of 8)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Curiosity-driven Exploration by Self-supervised Prediction](https://mlsanity.com/paper/1705.05363/) (2017)
- [G-Retriever: Retrieval-Augmented Generation for Textual Graph Understanding and Question Answering](https://mlsanity.com/paper/2402.07630/) (2024)
- [Plan-on-Graph: Self-Correcting Adaptive Planning of Large Language Model on Knowledge Graphs](https://mlsanity.com/paper/2410.23875/) (2024)
- [On the Relationship Between Active Inference and Control as Inference](https://mlsanity.com/paper/2006.12964/) (2020)
- [A Prompt-Based Knowledge Graph Foundation Model for Universal In-Context Reasoning](https://mlsanity.com/paper/2410.12288/) (2024)
- [Natural Language Syntax Complies with the Free-Energy Principle](https://mlsanity.com/paper/2210.15098/) (2022)

## 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.