Publisher DOI: 10.1103/PhysRevE.111.054208
Title: Weight dynamics of learning networks
Language: English
Authors: Sharafi, Nahal 
Martin, Christoph 
Hallerberg, Sarah 
Keywords: Dynamical systems; Artificial neural networks; Chaos & nonlinear dynamics
Issue Date: 12-May-2025
Publisher: American Physical Society
Journal or Series Name: Physical review / publ. by The American Institute of Physics. E 
Volume: 111
Issue: 5
Startpage: 054208-1
Endpage: 054208-14
Abstract: 
Neural networks have become a widely adopted tool for tackling a variety of problems in machine learning and artificial intelligence. In this contribution, we use the mathematical framework of local stability analysis to gain a deeper understanding of the learning dynamics of feedforward neural networks. We derive equations for the tangent operator of the learning dynamics of three-layer networks learning regression tasks. The results are valid for an arbitrary number of nodes and arbitrary choices of activation functions. Applying the results to a network learning a regression task, we investigate numerically how stability indicators relate to the final training loss. Although the specific results vary with different choices of initial conditions and activation functions, we demonstrate that it is possible to predict the final training loss by monitoring finite-time Lyapunov exponents during the training process.
URI: https://hdl.handle.net/20.500.12738/17863
ISSN: 2470-0053
Review status: This version was peer reviewed (peer review)
Institute: Department Maschinenbau und Produktion 
Fakultät Technik und Informatik 
Type: Article
Additional note: article number: 054208
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