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Geometry of Deep Neural Networks

Part of the Mathematics in Industry book series (MATHINDUSTRY,volume 37)

Abstract

In this chapter, which is mathematically intensive, we will try to answer perhaps the most important questions of machine learning: what does the deep neural network learn? How does a deep neural network, especially a CNN, accomplish these goals? The full answer to these basic questions is still a long way off. Here are some of the insights we’ve obtained while traveling towards that destination. In particular, we explain why the classic approaches to machine learning such as single-layer perceptron or kernel machines are not enough to achieve the goal and why a modern CNN turns out to be a promising tool.

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Ye, J.C. (2022). Geometry of Deep Neural Networks. In: Geometry of Deep Learning. Mathematics in Industry, vol 37. Springer, Singapore. https://doi.org/10.1007/978-981-16-6046-7_10

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