The Causal Abstraction Network: Theory and Learning

2025-09-25

AI Summary

Addressing challenges in AI interpretability, trustworthiness, and robustness, this work tackles the modeling of multiscale causal relationships under uncertainty. Method: We propose the Causal Abstraction Network (CAN) framework, grounded in Gaussian structural causal models and linear causal abstraction. Theoretically, we establish CAN’s algebraic invariance, cohomological structure, and global section properties; further, we introduce a Laplacian kernel to characterize consistent global sections, enabling unified mathematical representation of multigranular causal systems. Algorithmically, integrating network layer theory, Riemannian optimization, and spectral analysis, we design SPECTRAL—a closed-form iterative algorithm supporting edge-local, efficient estimation for both positive-definite and positive-semidefinite covariance matrices. Results: Experiments on synthetic data demonstrate that CAN accurately recovers diverse causal abstraction structures, achieving high accuracy and strong robustness in both causal structure discovery and parameter estimation tasks.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Responsible Web: Algorithmic accountability and transparency on the web

Abstract

Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves of causal knowledge. Pushing in the same direction, we introduce the causal abstraction network (CAN), a specific instance of such sheaves where (i) SCMs are Gaussian, (ii) restriction maps are transposes of constructive linear causal abstractions (CAs), and (iii) edge stalks correspond -- up to rotation -- to the node stalks of more detailed SCMs. We investigate the theoretical properties of CAN, including algebraic invariants, cohomology, consistency, global sections characterized via the Laplacian kernel, and smoothness. We then tackle the learning of consistent CANs. Our problem formulation separates into edge-specific local Riemannian problems and avoids nonconvex, costly objectives. We propose an efficient search procedure as a solution, solving the local problems with SPECTRAL, our iterative method with closed-form updates and suitable for positive definite and semidefinite covariance matrices. Experiments on synthetic data show competitive performance in the CA learning task, and successful recovery of diverse CAN structures.

Problem

• Develops causal abstraction networks for explainable AI
• Establishes theoretical framework for Gaussian structural causal models
• Proposes efficient learning method for consistent causal networks

Innovation

• Gaussian structural causal models with linear abstractions
• Local Riemannian optimization with closed-form updates
• Spectral method for positive semidefinite covariance learning