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Published on: February 15, 2017
Lie-group-type neural system learning by manifold retractions
1Dipartimento di Ingegneria Biomedica, Elettronica, e Telecomunicazioni (DIBET), Università Politecnica delle Marche, Via Brecce Bianche, I-60131 Ancona, Italy. s.fiori@univpm.it
Summary
This study introduces Riemannian-gradient optimization for neural signal processing systems with parameters on Lie group manifolds. It details retraction-based stepping and stepsize selection for effective adaptation.
Area of Science:
- Neuroscience
- Signal Processing
- Differential Geometry
Background:
- Neural signal processing systems often involve parameters residing in complex, curved spaces.
- Standard optimization methods fail on these curved manifolds, necessitating specialized approaches.
Purpose of the Study:
- To develop and present a novel optimization method for adapting neural signal processing systems with parameters on Lie group manifolds.
- To address the limitations of standard additive stepping in curved parameter spaces.
Main Methods:
- Utilizing Riemannian-gradient-based optimization tailored for curved manifolds.
- Implementing retraction-based stepping as an alternative to standard additive steps.
- Developing a companion procedure for selecting the stepsize schedule.
Main Results:
- Demonstrated the feasibility of Riemannian optimization for neural system adaptation on Lie groups.
- Successfully applied retraction-based stepping to navigate the curved parameter space.
- Validated the proposed methods through a detailed case study involving non-quadratic criterion optimization.
Conclusions:
- The proposed Riemannian-gradient optimization framework with retraction-based stepping is effective for neural signal processing systems with Lie group parameter structures.
- This approach offers a robust solution for parameter adaptation in complex, curved spaces, enhancing system performance.
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