An Analysis Framework for Understanding Deep Neural Networks Based on Network Dynamics

2025-01-05

AI Summary

This paper addresses the fundamental challenges of interpretability and generalization mechanisms in deep neural networks (DNNs) by proposing a unified analytical framework grounded in neural dynamics. Methodologically, it introduces a novel integration of neuron-wise order-preserving versus non-order-preserving dynamical pattern classification with quantitative characterization of attraction basins in the sample-weight space—synthesizing order theory, information theory, and dynamical systems modeling. The framework provides the first unified explanation of diverse phenomena including “flat minima,” “grokking,” and the “double descent” curve, while enabling scalable analysis up to 100-layer networks. Its theoretical contribution lies in revealing cross-layer information optimization mechanisms in DNNs; practically, it informs principled selection of optimal depth and width. Empirical validation spans architectures up to 100 layers, establishing a rigorous foundation for understanding DNN generalization and guiding architecture design.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: Learning & Optimization for NLP
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Advancing artificial intelligence demands a deeper understanding of the mechanisms underlying deep learning. Here, we propose a straightforward analysis framework based on the dynamics of learning models. Neurons are categorized into two modes based on whether their transformation functions preserve order. This categorization reveals how deep neural networks (DNNs) maximize information extraction by rationally allocating the proportion of neurons in different modes across deep layers. We further introduce the attraction basins of the training samples in both the sample vector space and the weight vector space to characterize the generalization ability of DNNs. This framework allows us to identify optimal depth and width configurations, providing a unified explanation for fundamental DNN behaviors such as the"flat minima effect,""grokking,"and double descent phenomena. Our analysis extends to networks with depths up to 100 layers.

Problem

• Deep Neural Networks
• Optimal Configuration
• Phenomena Explanation

Innovation

• Deep Neural Networks
• Neuron Classification
• Performance Optimization