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Partial BFGS update and efficient step-length calculation for three-layer neural networks

K Saito1, R Nakano

  • 1NTT Communication Science Laboratories, Kyoto, Japan.

Neural Computation
|January 1, 1997
PubMed
Summary
This summary is machine-generated.

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This study introduces a novel second-order learning algorithm using a partial Broyden-Fletcher-Goldfarb-Shanno (BFGS) update. It efficiently solves large-scale problems by reducing memory requirements and improving convergence performance.

Area of Science:

  • Machine Learning
  • Optimization Algorithms
  • Numerical Analysis

Background:

  • Second-order learning algorithms, like quasi-Newton methods, face challenges with large-scale problems due to high memory demands (N^2) for Hessian approximations.
  • Efficient and accurate line searches are crucial for the performance of these algorithms, but are often computationally intensive.

Purpose of the Study:

  • To develop a novel second-order learning algorithm that addresses the memory and line search limitations of standard quasi-Newton methods.
  • To improve the efficiency and scalability of second-order optimization for large-scale machine learning tasks.

Main Methods:

  • A new algorithm is proposed utilizing a partial Broyden-Fletcher-Goldfarb-Shanno (BFGS) update, reducing memory requirements to 2Ns (where s << N).
  • An efficient line search is implemented by finding the minimal point of a second-order approximation of the objective function with respect to the step length.

Related Experiment Videos

Main Results:

  • The proposed algorithm demonstrated superior performance compared to major learning algorithms on parity and speech synthesis problems.
  • The partial BFGS update significantly reduced storage space without compromising convergence performance.
  • An efficient and accurate step-length calculation was found to be critical for the convergence of quasi-Newton algorithms.

Conclusions:

  • The developed algorithm offers a practical and efficient solution for large-scale second-order learning.
  • Partial BFGS updates and efficient line searches are key components for enhancing the scalability and performance of quasi-Newton methods.