The Connection Between Applied Mathematics and Deep Learning

In recent years, deep learning (DL) has inspired a myriad of advances within the scientific computing community. This subset of artificial intelligence relies on multiple components of applied mathematics, but what type of relationship do applied mathematicians have with DL? This question was the subject of a plenary talk by Yann LeCun (Facebook and New York University) at the virtual 2020 SIAM Conference on Mathematics of Data Science, which took place earlier this year. LeCun provided a brief history of machine learning (ML), highlighted the mathematical underpinnings of the field, presented both his vision and several broad open questions for ML's future, and discussed applied math's current relation and potential impending contributions. A 2018 SIAM News article by Gilbert Strang, entitled "The Functions of Deep Learning," offers an introduction for those who are unfamiliar with neural networks, ML, and DL.