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PhD Position in Mathematics: Geometric Deep Learning at Umeå University
2 months ago
The Department of Mathematics and Mathematical Statistics at Umeå University is seeking a PhD candidate to contribute to the WASP AI program, focusing on geometric deep learning. This four-year position will involve research and third-cycle courses, with the last day to apply being 10 June 2024.
This recruitment is part of a larger expansion of the research group at the department, investigating mathematical foundations of artificial intelligence. The group covers a diverse range of topics in modern machine learning research, including geometric deep learning, non-convex optimization problems, and federated learning.
Project Overview- Deep learning has achieved significant success on complex problems, but the fundamental mathematical understanding of deep learning models remains incomplete. This project aims to address this gap by exploring the mathematical foundations of deep learning, including differential geometry, numerical analysis, and dynamical systems.
- Neural ordinary differential equations (NODEs) represent a recent advance in geometric deep learning, incorporating symmetries and non-Euclidean structures using geometrical principles. NODEs describe the dynamics of information propagating through neural networks in the limit of infinite depth using ordinary differential equations (ODEs) on manifolds.
- The dynamical systems in NODE models are constrained by the intrinsic nature of the dimension of a manifold, fixing the dimension of their state vector. This limitation precludes the use of certain architectural elements, like the encoder-decoder structure used in autoencoders and sequence-to-sequence prediction.
- To remedy these limitations, the project aims to extend NODEs from manifolds to M-polyfolds, a generalization of manifolds where the number of local coordinates is allowed to vary smoothly. This requires the development of a comprehensive geometric framework for flows and integral curves on M-Polyfolds and a theory of group actions compatible with the M-polyfold structure.
The project is part of the AI-Math track within the Wallenberg AI, Autonomous Systems and Software Program (WASP). The PhD student will participate in the WASP graduate school.
For further information and instructions on how to apply, please see the provided link.