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Banff-s new workshop on Continuum models and optimisation for deep neural networks brings together scientists to discuss the foundations of our digital revolution, and to investigate the reliability of their results. As often, mathematics is the fundamental tool to examine today-s challenges. Mathematics structures knowledge and identifies the strengths and limitations of deep learning algorithms. A better understanding of the maths behind deep learning helps us to develop more efficient algorithms and to put safety critical industrial areas such as autonomous driving on a firm ground.