How Complexity Contributes to Learning Opacity in Machine Learning

2026-06-23

AI Summary

This study addresses the opacity of neural network training by investigating its underlying dynamical complexity, which remains poorly understood. For the first time, the work adopts a complex dynamical systems perspective, integrating concepts from complex systems theory, neural network dynamics, and gradient-based optimization feedback mechanisms to systematically analyze training trajectories. The research identifies three fundamental sources of complexity: sensitivity to weight initialization, structural properties of gradient feedback, and dependence on training data. It demonstrates that these factors collectively induce an irreducible form of opacity in the learning process, thereby establishing a novel theoretical foundation for understanding the intrinsic limitations of explainability in deep learning.

Abstract

Machine learning (ML) algorithms are known to be opaque. We do not know the reasons for their predictions. The learning process leading to the prediction function is also opaque. We do not fully understand the time evolution of the weight values of neural nets (NN) and related dynamical phenomena. While prediction opacity is widely studied, learning opacity remains largely underexplored. This article studies learning opacity trough the lens of complex dynamical systems. We argue that NN learning is essentially a complex system and that learning opacity is due to dynamical complexity and the epistemological challenges that arise from it. We identify three key properties of training complexity -- sensitivity to weight initialization, feedback in gradient based optimization, and sensitivity to the training data -- and show how each contributes to learning opacity. As these properties are fundamental to the learning process damping or eliminating them would fundamentally alter how ML systems learn. Some sources of opacity in ML may hence be irreducible.

Problem

• learning opacity
• machine learning
• complex dynamical systems
• neural networks
• training complexity

Innovation

• learning opacity
• complex dynamical systems
• neural network training
• irreducible opacity
• gradient-based optimization