Machine learning in spectral domain.

Area of Science:

• Machine Learning
• Computational Science
• Linear Algebra

Background:

• Deep neural networks (DNNs) are typically trained by adjusting link weights in the node space.
• Optimization protocols in node space are standard for DNN training.

Purpose of the Study:

• To propose a novel deep learning training method anchored in reciprocal space.
• To explore modifying eigenvalues and eigenvectors of transfer operators for learning.

Main Methods:

• The proposed method operates in the spectral domain, adjusting eigenvalues and eigenvectors.
• The approach is adaptable for linear or non-linear classifiers.
• A nested indentation of eigenvectors is used to recover feed-forward architectures.

Main Results:

• Adjusting eigenvalues with frozen eigenvectors surpasses standard methods with equivalent parameters.
• The spectral learning approach demonstrates superior performance.
• The method is ductile and can be tailored for specific classification tasks.

Conclusions:

• Spectral domain training offers a powerful alternative to traditional node-space DNN training.
• The method's flexibility allows for diverse applications, including reservoir computing.
• This approach advances deep learning by leveraging principles from linear algebra and spectral analysis.