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I am asking for a book (or any other online resource) where we can solve exercises related to neural networks, similar to the books or online resources dedicated to mathematics where we can solve mathematical exercises.

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The book Grokking Deep Learning, by Andrew Trask (a PhD student at Oxford University and a research scientist at DeepMind), a wonderful, clean, and plain-English discussion of the basic mechanics that go on under the hood of neural networks - from data flow to updating of weights. It is written without a slant on normally-wonky math, the concepts are presented and then advanced at a digestible pace for anyone.

Here are a few more possibly useful resources.

  1. Neural Networks: Playground Exercises

  2. Getting Started With Deep Learning: Convolutional Neural Networks

  3. Deep learning focuses on practical aspects of deep learning

  4. First lab assignment in Deep learning

  5. Deeplearning stanford

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There are actually quite a few. Personally I would say these courses have high quality and strong focus on practice:

  • Standford computer vision cs231. Check the assignments materials on this page. This course has good explanation/exercises of how generally neural nets and backprop works.
  • Fastai course notebooks. You can listen to the lectures as well, but notebooks are quite self-containing
  • Practical reinforcement learning course, if you interested in NN application for RL
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One of the most famous books dedicated to neural networks is Neural Networks - A Systematic Introduction (1996) by Raul Rojas. Most chapters end with a series of exercises that test your understanding of the material. For example, in chapter 14 Stochastic Networks, one of the exercises is

Solve the eight queens problem using a Boltzmann machine. Define the network's weights by hand.

This should give you a sense of the type of exercise that you will find in this book.

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