The Relativity of Causal Knowledge

2025-03-13

AI Summary

Pure predictive models fail to capture the subjective and networked nature of causal knowledge in AI. Method: We propose the principle of “relative causal knowledge,” modeling structural causal models (SCMs) as dynamic, perspective-dependent representations embedded in relational networks. Integrating category theory (functor categories), sheaf theory (network sheaves/cosheaves), convex analysis, and intervention probability measures, we construct a convex probability measure encoding framework for SCMs. We formally define cross-network transfer mechanisms for causal knowledge across heterogeneous agents, ensuring intervention consistency and compatibility with agent-specific perspectives. Contribution/Results: This work establishes the first rigorous mathematical definition of relative causal knowledge, enabling verifiable and transmissible causal representations. It bridges foundational theories—category theory, sheaf theory, and convex probabilistic reasoning—to advance causal inference beyond static, agent-agnostic models toward collaborative, context-sensitive reasoning.

Technology Category

• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality
• Machine Learning: Causal Learning

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Social Networks and Social Media: Computational social science

Abstract

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

Problem

• Addressing limits of predictive AI with causal reasoning
• Introducing relativity in structural causal models (SCMs)
• Enabling transfer of causal knowledge across networks

Innovation

• Structural causal models arranged via category theory
• Convex spaces encode non-intervened causal models
• Sheaf theory constructs network for causal knowledge transfer