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Related Experiment Video

Updated: Apr 30, 2026

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

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Convergence analyses on on-line weight noise injection-based training algorithms for MLPs.

John Sum, Chi-Sing Leung, Kevin Ho

    IEEE Transactions on Neural Networks and Learning Systems
    |May 9, 2014
    PubMed
    Summary

    This study analyzes weight noise injection for training neural networks. We prove that under specific learning rate conditions, these algorithms reliably converge to optimal solutions.

    Related Experiment Videos

    Last Updated: Apr 30, 2026

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    1.7K

    Area of Science:

    • Machine Learning
    • Artificial Intelligence
    • Optimization Algorithms

    Background:

    • Weight noise injection is a long-standing technique in neural network training.
    • Its convergence properties, however, remain largely unexamined.
    • Understanding convergence is crucial for reliable model training.

    Purpose of the Study:

    • To investigate the convergence behavior of two weight noise injection algorithms.
    • Specifically, multiplicative and additive weight noise injection with weight decay.
    • Analysis is performed on multilayer perceptrons with linear or sigmoid output nodes.

    Main Methods:

    • Mathematical analysis of algorithm convergence under specific conditions.
    • Derivation of theoretical guarantees for weight noise injection algorithms.
    • Focus on the objective function V(w), weight vector w(t), weight decay α, and step size μ(t).

    Main Results:

    • Demonstrated that under decaying step sizes (μ(t)→ 0), the expected squared norm of weights remains bounded and converges.
    • Established conditions (μ(t)→ 0, Σtμ(t)=∞, Σtμ(t)² < ∞) for probabilistic convergence.
    • Showed convergence to a point where the gradient of the objective function is zero (∇wV(w)=0).

    Conclusions:

    • Weight noise injection algorithms, when combined with weight decay and appropriate step size schedules, are theoretically proven to converge.
    • These findings provide a theoretical foundation for using weight noise injection in deep learning.
    • The study offers insights into the optimization dynamics of noisy training methods.