Simula@BI: On computational barriers in inverse problems

Simula@BI invites Phd Candidate Luca Gazdag to talk about the difficulty of computing stable and accurate neural networks.

Deep learning (DL) has had unprecedented success and is now rapidly entering scientific computing. However, DL suffers from a universal phenomenon: Instability, despite universal approximation results that often guarantee the existence of stable and accurate neural networks (NNs).

They show the following paradox: There are infinitely many inverse problems where one can prove the existence of optimal NNs for solving the problem, but any algorithm will fail to compute these NNs to an accuracy below a certain approximation threshold. These results suggest a classification theory describing conditions under which (stable) NNs with a given accuracy can be trained. This is joint work with Anders C. Hansen.

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