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Learning Algorithm for Boltzmann Machines With Additive Weight and Bias Noise.

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    Noise in Boltzmann machines (BMs) elevates temperature but maintains a Boltzmann distribution. The derived learning algorithm for noisy BMs is identical to that for noise-free BMs, enabling online learning for analog circuits.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Computational Neuroscience

    Background:

    • Boltzmann machines (BMs) are probabilistic models used in machine learning.
    • Understanding the impact of noise is crucial for robust model training, especially in analog implementations.
    • Standard BMs typically use binary {-1, 1} or {0, 1} unit outputs.

    Purpose of the Study:

    • To analyze the effect of additive weight and bias noise on Boltzmann machines with {-1, 1} unit outputs.
    • To derive a learning algorithm for noisy Boltzmann machines.
    • To compare this learning algorithm with that of noise-free Boltzmann machines.

    Main Methods:

    • Analytical derivation of the state distribution under additive noise.
    • Development of a gradient ascent learning algorithm for noisy BMs.
    • Comparative analysis of learning procedures for noisy and noise-free BMs.

    Main Results:

    • Additive noise results in an elevated temperature factor within the Boltzmann distribution.
    • The derived learning algorithm for noisy BMs is mathematically identical to the standard algorithm for noise-free BMs.
    • The learning procedure remains effective even with unknown noise variances.

    Conclusions:

    • The learning algorithm for noise-free Boltzmann machines is suitable for online implementation in analog circuit-based BMs.
    • The robustness of the learning algorithm to unknown noise variances is demonstrated.
    • This finding simplifies the training of analog Boltzmann machines in the presence of inherent noise.