Deep neural networks on Riemannian manifolds are evolving due to their ability to apply successful DNN structures on spherical and hyperbolic geometries to complex tasks.
The algebraic structures inherent in gyrogroups and gyrovector spaces enable more effective adaptations of neural networks, fostering innovations in machine learning applications.
This work extends the theory of gyrogroups to matrix manifolds, allowing for analogous implementations of multinomial logistic regression in neural networks, enhancing their capability.
By establishing fully-connected and convolutional layers for SPD networks, we bridge the gap between traditional DNNs and advanced geometrical techniques, improving model performance.
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