Saved in:
Bibliographic Details
Main Authors: Zhou, Zhanpeng, Yang, Yongyi, Sugiyama, Mahito, Yan, Junchi
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2505.13900
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908371393708032
author Zhou, Zhanpeng
Yang, Yongyi
Sugiyama, Mahito
Yan, Junchi
author_facet Zhou, Zhanpeng
Yang, Yongyi
Sugiyama, Mahito
Yan, Junchi
contents Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this transition is still incomplete. In this paper, we introduce an interval-wise perspective that compares network states across a time window, revealing two new phenomena that illuminate the two-phase nature of deep learning. i) \textbf{The Chaos Effect.} By injecting an imperceptibly small parameter perturbation at various stages, we show that the response of the network to the perturbation exhibits a transition from chaotic to stable, suggesting there is an early critical period where the network is highly sensitive to initial conditions; ii) \textbf{The Cone Effect.} Tracking the evolution of the empirical Neural Tangent Kernel (eNTK), we find that after this transition point the model's functional trajectory is confined to a narrow cone-shaped subset: while the kernel continues to change, it gets trapped into a tight angular region. Together, these effects provide a structural, dynamical view of how deep networks transition from sensitive exploration to stable refinement during training.
format Preprint
id arxiv_https___arxiv_org_abs_2505_13900
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle New Evidence of the Two-Phase Learning Dynamics of Neural Networks
Zhou, Zhanpeng
Yang, Yongyi
Sugiyama, Mahito
Yan, Junchi
Machine Learning
Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this transition is still incomplete. In this paper, we introduce an interval-wise perspective that compares network states across a time window, revealing two new phenomena that illuminate the two-phase nature of deep learning. i) \textbf{The Chaos Effect.} By injecting an imperceptibly small parameter perturbation at various stages, we show that the response of the network to the perturbation exhibits a transition from chaotic to stable, suggesting there is an early critical period where the network is highly sensitive to initial conditions; ii) \textbf{The Cone Effect.} Tracking the evolution of the empirical Neural Tangent Kernel (eNTK), we find that after this transition point the model's functional trajectory is confined to a narrow cone-shaped subset: while the kernel continues to change, it gets trapped into a tight angular region. Together, these effects provide a structural, dynamical view of how deep networks transition from sensitive exploration to stable refinement during training.
title New Evidence of the Two-Phase Learning Dynamics of Neural Networks
topic Machine Learning
url https://arxiv.org/abs/2505.13900