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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Einführung in die Volkswirtschaftslehreks, brain networks, molecule networks, etc. See some examples in Fig. 8.1. In fact, the complex interaction in real systems can be described by different forms of graphs, so that graphs can be a ubiquitous tool for representing complex systems.

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Paul Engelkamp,Friedrich L. Sell 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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ally 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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https://doi.org/10.1007/978-3-642-50938-4ective of classic machine learning. In particular, the number of trainable parameters in deep neural networks is often greater than the training data set, this situation being notorious for overfitting from the point of view of classical statistical learning theory. However, empirical results have s

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Verteilungen auf der reellen Achse,revolution”. 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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Biological Neural Networksf neurons and connections in a network may be significantly high. One of the amazing aspects of biological neural networks is that when the neurons are connected to each other, higher-level intelligence, which cannot be observed from a single neuron, emerges.

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Artificial Neural Networks and Backpropagation have been made to model all aspects of the biological neuron using a mathematical model, all of them may not be necessary: rather, there are some key aspects that should not be neglected when modeling a neuron. This includes the weight adaptation and the nonlinearity.

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Convolutional Neural Networksptrons, which we discussed in the previous chapter, usually require fully connected networks, where each neuron in one layer is connected to all neurons in the next layer. Unfortunately, this type of connections inescapably increases the number of weights.

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Graph Neural Networksks, brain networks, molecule networks, etc. See some examples in Fig. 8.1. In fact, the complex interaction in real systems can be described by different forms of graphs, so that graphs can be a ubiquitous tool for representing complex systems.