Titlebook: Geometry of Deep Learning; A Signal Processing Jong Chul Ye Textbook 2022 The Editor(s) (if applicable) and The Author(s), under exclusive

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Geometry of Deep Neural Networks 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 approach

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Deep Learning Optimizationally gradient-based local update schemes. However, the biggest obstacle recognized by the entire community is that the loss surfaces of deep neural networks are extremely non-convex and not even smooth. This non-convexity and non-smoothness make the optimization unaffordable to analyze, and the main

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Summary and Outlookrevolution”. Despite the great successes of deep learning in various areas, there is a tremendous lack of rigorous mathematical foundations which enable us to understand why deep learning methods perform well.

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tworks are extremely non-convex and not even smooth. This non-convexity and non-smoothness make the optimization unaffordable to analyze, and the main concern was whether popular gradient-based approaches might fall into local minimizers.

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