Second, visual signals usually havehigh information densities, which may contain distractions and redundancies for policylearning.

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, mostly because of the absence of corresponding hyperbolic neural networklayers.

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean multinomial logistic regression (MLR) into Riemannian manifolds. However, existing approaches suffer from limited applicability due to their strong reliance on specific geometric properties. This paper proposes a framework for designing Riemannian MLR over general geometries, referred to as RMLR. Our framework only requires minimal geometric properties, thus exhibiting broad applicability and enabling its use with a wide range of geometries.

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties.

Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning.

This work was done when Tao Y u was an intern at Microsoft Research Asia.