Machine Learning as Iterated Belief Change a la Darwiche and Pearl

2026-05-05 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, extended

Summary

This article extends previous research on modeling binary Artificial Neural Network (ANN) training as belief change, specifically within the Alchourrón, Gärdenfors and Makinson (AGM) framework. It addresses limitations of prior work by demonstrating that Dalal's method for belief change naturally induces a gradual evolution of belief states. Crucially, the study shows that the training dynamics of binary ANNs can be more effectively modeled using robust AGM-style operations, namely lexicographic revision and moderate contraction, which align with the Darwiche-Pearl (DP) framework for iterated belief change. This approach offers a more principled foundation for understanding how ANNs modify their internal knowledge representations during learning, moving beyond the "amnesic" behavior of full-meet belief change. The work is situated at the intersection of neuro-symbolic AI, aiming to integrate formal logic and belief dynamics into machine learning systems.

Key takeaway

For AI scientists and research scientists developing explainable AI systems, this work provides a robust theoretical framework for understanding how neural networks learn. By modeling ANN training as Darwiche-Pearl compatible iterated belief change, you can gain deeper insights into the symbolic evolution of a network's knowledge. This approach offers a more nuanced alternative to traditional methods, enabling the development of more transparent and principled learning architectures.

Key insights

Binary ANN training can be formally modeled as iterated belief change using Darwiche-Pearl compliant operations.

Principles

• Belief change should be gradual, not abrupt.
• Full-meet belief change is often implausible and "amnesic."
• Lexicographic revision and moderate contraction offer robust belief change.

Method

Model binary ANN training as a sequence of belief set transitions using lexicographic revision and moderate contraction, which are DP-compatible and ensure gradual, robust knowledge updates.

In practice

• Represent ANN knowledge symbolically via propositional logic.
• Use Hamming distance to quantify belief set differences.
• Apply DP-compatible operators for principled knowledge updates.

Topics

• Binary Artificial Neural Networks
• Iterated Belief Change
• Darwiche-Pearl Framework
• AGM Belief Change
• Lexicographic Revision

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.