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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.

Octavian Ganea is a postdoctoral researcher at CSAIL MIT in the group of Prof. T. Jaakkola and Prof. R. Barzilay. He obtained his PhD from the Data Analytics Lab at ETH Zurich under the supervision of prof. Thomas Hofmann. His research interests lie around representation learning for text, graphs or images through statistical and geometric models such as leveraging non-Euclidean geometries and tractable Riemannian manifolds in graph representation learning. Octavian has explored finding and learning latent hierarchical structures in data via the inductive bias of hyperbolic geometry, as well as combining optimal transport and graph neural networks for better graph models. He is also currently investigating problems related to computational chemistry such as drug discovery.

Octavian Ganea is a postdoctoral researcher at CSAIL MIT in the group of Prof. T. Jaakkola and Prof. R. Barzilay. He obtained his PhD from the Data Analytics Lab at ETH Zurich under the supervision of prof. Thomas Hofmann. His research interests lie around representation learning for text, graphs or images through statistical and geometric models such as leveraging non-Euclidean geometries and tractable Riemannian manifolds in graph representation learning. Octavian has explored finding and learning latent hierarchical structures in data via the inductive bias of hyperbolic geometry, as well as combining optimal transport and graph neural networks for better graph models. He is also currently investigating problems related to computational chemistry such as drug discovery.