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    Adding fault/noise during neural network training is often misinterpreted. This study clarifies the learning objective and reveals that noise injection, particularly in Radial Basis Function networks, acts as a regularization technique by reducing network complexity.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Neural Networks

    Background:

    • Fault/noise injection during training has been used for decades to improve neural network (NN) tolerance and generalization.
    • This technique has seen renewed interest in deep learning to combat overfitting.
    • A common misconception exists regarding the objective function in fault/noise injection learning, often equated with the desired mean squared error (MSE) of the NN under the same fault/noise conditions.

    Purpose of the Study:

    • To clarify the misconception surrounding the objective function of fault/noise injection learning.
    • To investigate the actual regularization effect of adding node fault/noise during gradient descent training.
    • To analyze the impact of different fault/noise types on Multilayer Perceptrons (MLPs) and Radial Basis Function (RBF) networks.

    Main Methods:

    • Theoretical analysis of the learning objective for MLPs and RBF networks under various fault/noise injection scenarios (random node fault, additive node noise, multiplicative node noise).
    • Empirical validation of theoretical results using experimental evidence.
    • Investigation of the regularization effect of fault/noise injection, specifically focusing on RBF networks and comparing it to dropout regularization.

    Main Results:

    • For MLPs, the learning objective matches the desired measure only for random node faults; additive and multiplicative node noise lead to different objectives.
    • For RBF networks, the learning objective is identical to the desired measure across all three fault/noise conditions (random, additive, multiplicative).
    • Fault/noise injection during RBF network training effectively reduces network complexity, acting as a regularization method similar to dropout.

    Conclusions:

    • The objective function of fault/noise injection learning is not always equivalent to the desired measure of the NN with the same fault/noise, contrary to common belief.
    • Adding node fault/noise during gradient descent learning provides a regularization effect, particularly in RBF networks.
    • The regularization effect of additive or multiplicative node noise in RBF networks is equivalent to reducing network complexity, mirroring the effect of dropout regularization.