AI & KNOWLEDGE GRAPHS
Graph Distance as Surprise: Free Energy Minimization in Knowledge Graph Reasoning
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) [1] 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 [2].
Authors: Gaganpreet Jhajj, Fuhua Lin
Executive Impact: Bridging Neuroscience with AI Reasoning
This paper introduces a novel framework connecting the Free Energy Principle (FEP) from neuroscience to Knowledge Graph (KG) reasoning. It proposes minimizing "surprise" in KGs, defining surprise inversely with shortest-path distance between entities. This approach treats the KG as an agent's generative model, where shorter paths imply lower surprise and higher plausibility. The work bridges FEP with practical AI systems, offering theoretical foundations for graph neural networks and model-based reinforcement learning by leveraging graph distance for surprise calculation, thereby guiding reasoning and entity grounding in complex AI agents.
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Theoretical Principles
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Practical Implications
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Novel KG-FEP Link
Deep Analysis & Enterprise Applications
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FEP: Surprise Minimization in AI Agents
The Free Energy Principle (FEP) posits that biological systems minimize surprise by maintaining accurate world models. In this work, the Knowledge Graph (KG) serves as the agent's generative model. The core idea is that entities with high probability under the generative model yield low surprise. For KGs, this translates to entities at shorter graph distances being less surprising, indicating higher plausibility.
Formalizing Surprise via Shortest-Path Distance
We formalize geometric surprise, Sgeo(e|C), using the shortest directed path length from a context 'C' to an entity 'e' in the KG. Shorter paths mean lower surprise. Disconnected entities are assigned a high penalty (α) to ensure they are always more surprising. This method directly connects to the FEP by proxying the negative log-probability of an observation.
min dg(c, e)
Geometric Surprise (Sgeo) Formula
Connecting Syntax to KG Semantics
Syntactic Trees (Murphy et al.)
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Graph Depth + Algorithmic Complexity (AK)
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Knowledge Graphs (This Work)
The framework extends surprise minimization from syntactic tree structures to arbitrary directed graphs with cycles. Using shortest-path distance for geometric surprise and Lempel-Ziv compression for algorithmic complexity, it effectively handles complex KG structures as shown in the Canadian Prime Minister example.
Theoretical Justification for Shortest-Path Distance
- Proper Generalization: Recovers Murphy's tree depth for tree structures.
- Least-Action: Aligns with active inference by minimizing cumulative cost via shortest paths.
- Computational Grounding: Directly relates to GNN message passing depth and BFS for efficient computation, handling cycles naturally.
Practical Implications Across AI Domains
- Entity Grounding: LLM-KG systems can rank candidate entity groundings by computing Sgeo, preferring groundings with lower free energy.
- KG Embeddings: Embedding methods can be developed to preserve distance-based surprise structure, enhancing semantic representation.
- GNN Architecture: Guides the selection of message-passing depth in Graph Neural Networks, balancing computational cost with the required "surprise horizon."
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Implementation Roadmap
A phased approach to integrating Graph Distance as Surprise into your enterprise AI strategy.
Phase 1: Discovery & Planning
In-depth analysis of existing KG structures, data sources, and reasoning requirements. Define specific use cases for surprise minimization and active inference integration. Establish performance benchmarks and success metrics.
Phase 2: Model Integration & Prototyping
Develop and integrate graph distance-based surprise modules with your existing AI agents or GNNs. Conduct pilot programs on a subset of your KG data to validate the FEP-driven reasoning and optimize surprise calculation parameters.
Phase 3: Scalable Deployment & Optimization
Full-scale deployment of the FEP-augmented KG reasoning system across your enterprise. Monitor performance, refine models, and continuously optimize for efficiency and accuracy. Train your teams on new AI reasoning capabilities.
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