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Related Experiment Videos

Deterministic design for neural network learning: an approach based on discrepancy.

Cristiano Cervellera1, Marco Muselli

  • 1Istituto di Studi sui Sistemi Intelligenti per l'Automazione, Consiglio Nazionale delle Ricerche, 16149 Genova, Italy.

IEEE Transactions on Neural Networks
|September 24, 2004
PubMed
Summary

This study explores deterministic learning for function reconstruction. Using low-discrepancy sequences improves learning rates and ensures consistency, even with some output noise.

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Area of Science:

  • Machine Learning
  • Numerical Analysis
  • Computational Mathematics

Background:

  • Function reconstruction from samples is a core machine learning challenge.
  • Traditional methods often assume fixed training data points.
  • Empirical risk minimization (ERM) is a key principle in learning theory.

Purpose of the Study:

  • To analyze the consistency of empirical risk minimization (ERM) in deterministic learning settings.
  • To investigate function reconstruction when input sample positions are learned.
  • To establish conditions for reliable learning with deterministic algorithms.

Main Methods:

  • Analysis of the empirical risk minimization (ERM) principle under deterministic learning.
  • Application of number-theoretic results on discrepancy and variation.

Related Experiment Videos

  • Utilizing low-discrepancy sequences for sample generation.
  • Extension of the analysis to include noisy output data.

    • Main Results:

    • A sufficient condition for ERM consistency is established for noise-free deterministic learning.
    • Low-discrepancy sequences yield a learning rate of O(1/L), where L is the training set size.
    • Deterministic learning properties are maintained in the presence of moderate output noise.

    Conclusions:

    • Deterministic learning offers a consistent approach to function reconstruction.
    • Low-discrepancy sequences enhance learning efficiency and reliability.
    • The method shows promise for both noise-free and noisy data scenarios.