Singular value decomposition learning on double Stiefel manifold

Area of Science:

• Computational neuroscience
• Machine learning
• Differential geometry

Background:

• Several Singular Value Decomposition (SVD)-based neural computation techniques exist in the literature.
• A unified theoretical framework for these methods is lacking.

Purpose of the Study:

• To present a unifying perspective on four SVD-neural-computation techniques.
• To investigate the theoretical behavior and properties of these algorithms.
• To establish connections between SVD-neural algorithms and geometric concepts.

Main Methods:

• Utilizing differential geometry to analyze neural algorithms.
• Framing SVD neural algorithms as Riemannian-gradient flows.
• Investigating behavior on the double Stiefel manifold.

Main Results:

• Demonstrating that four SVD neural algorithms emerge as Riemannian-gradient flows.
• Providing a unified view of these distinct computational techniques.
• Characterizing the geometric and dynamical properties of these flows.

Conclusions:

• The study offers a novel geometric interpretation of SVD-neural-computation techniques.
• This unification simplifies understanding and may inspire new algorithm development.
• Differential geometry provides powerful tools for analyzing neural computation models.