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Interest has been rising lately towards methods representing data in non-Euclidean spaces, e.g. hyperbolic or spherical, that provide specific inductive biases useful for certain real-world data properties, e.g. scale-free, hierarchical or cyclical. However, most of the popular embedding and deep learning methods are Euclidean by design, e.g. use associated vector space operations. In this talk I will discuss mathematically grounded generalizations of basic deep learning operations to constant curvature spaces, as well as proposing hierarchical hyperbolic embeddings, hyperbolic neural networks and constant curvature graph convolutional networks, with different applications. This talk will also have an introductory part into concepts of Riemannian manifolds (e.g. curvature) and hyperbolic geometry.
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