A Class of Intrinsic Schemes for Orthogonal Integration
SIAM Journal on Numerical Analysis
Quasi-Geodesic Neural Learning Algorithms Over the Orthogonal Group: A Tutorial
The Journal of Machine Learning Research
A Theory for Learning by Weight Flow on Stiefel-Grassman Manifold
Neural Computation
Trust-Region Methods on Riemannian Manifolds
Foundations of Computational Mathematics
Optimization algorithms exploiting unitary constraints
IEEE Transactions on Signal Processing
Equivariant adaptive source separation
IEEE Transactions on Signal Processing
Learning by natural gradient on noncompact matrix-type pseudo-Riemannian manifolds
IEEE Transactions on Neural Networks
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The present manuscript treats the problem of adapting a neural signal processing system whose parameters belong to a curved manifold, which is assumed to possess the structure of a Lie group. Neural system parameter adapting is effected by optimizing a system performance criterion. Riemannian-gradient-based optimization is suggested, which cannot be performed by standard additive stepping because of the curved nature of the parameter space. Retraction-based stepping is discussed, instead, along with a companion stepsize-schedule selection procedure. A case-study of learning by optimization of a non-quadratic criterion is discussed in detail.