Repository logo

Infoscience

  • English
  • French
Log In
Logo EPFL, École polytechnique fédérale de Lausanne

Infoscience

  • English
  • French
Log In
  1. Home
  2. Academic and Research Output
  3. Conferences, Workshops, Symposiums, and Seminars
  4. How Gradient Descent Balances Features: A Dynamical Analysis For Two-Layer Neural Networks
 
conference paper not in proceedings

How Gradient Descent Balances Features: A Dynamical Analysis For Two-Layer Neural Networks

Zhu, Zhenyu  
•
Liu, Fanghui  
•
Cevher, Volkan  orcid-logo
April 2025
The Thirteenth International Conference on Learning Representations

This paper investigates the fundamental regression task of learning k neurons (a.k.a. teachers) from Gaussian input, using two-layer ReLU neural networks with width m (a.k.a. students) and m, k = O(1), trained via gradient descent under proper initialization and a small step-size. Our analysis follows a threephase structure: alignment after weak recovery, tangential growth, and local convergence, providing deeper insights into the learning dynamics of gradient descent (GD). We prove the global convergence at the rate of O(T −3) for the zero loss of excess risk. Additionally, our results show that GD automatically groups and balances student neurons, revealing an implicit bias toward achieving the minimum "balanced" ℓ 2-norm in the solution. Our work extends beyond previous studies in exact-parameterization setting (m = k = 1, (Yehudai and Ohad, 2020)) and single-neuron setting (m ≥ k = 1, (Xu and Du, 2023)). The key technical challenge lies in handling the interactions between multiple teachers and students during training, which we address by refining the alignment analysis in Phase 1 and introducing a new dynamic system analysis for tangential components in Phase 2. Our results pave the way for further research on optimizing neural network training dynamics and understanding implicit biases in more complex architectures.

  • Files
  • Details
  • Metrics
Type
conference paper not in proceedings
Author(s)
Zhu, Zhenyu  
•
Liu, Fanghui  
•
Cevher, Volkan  orcid-logo
Date Issued

2025-04

Subjects

ML-AI

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LIONS  
Event nameEvent acronymEvent placeEvent date
The Thirteenth International Conference on Learning Representations

ICLR

Singapore

2025-04-24-2025-04-28

Available on Infoscience
May 5, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/249794
Logo EPFL, École polytechnique fédérale de Lausanne
  • Contact
  • infoscience@epfl.ch

  • Follow us on Facebook
  • Follow us on Instagram
  • Follow us on LinkedIn
  • Follow us on X
  • Follow us on Youtube
AccessibilityLegal noticePrivacy policyCookie settingsEnd User AgreementGet helpFeedback

Infoscience is a service managed and provided by the Library and IT Services of EPFL. © EPFL, tous droits réservés