Neural Networks and Deep Learning

What this book is about

On the exercises and problems

Using neural nets to recognize handwritten digits

• Perceptrons
• Sigmoid neurons
• The architecture of neural networks
• A simple network to classify handwritten digits
• Learning with gradient descent
• Implementing our network to classify digits
• Toward deep learning

How the backpropagation algorithm works

• Warm up: a fast matrix-based approach to computing the output from a neural network
• The two assumptions we need about the cost function
• The Hadamard product, $s \odot t$
• The four fundamental equations behind backpropagation
• Proof of the four fundamental equations (optional)
• The backpropagation algorithm
• The code for backpropagation
• In what sense is backpropagation a fast algorithm?
• Backpropagation: the big picture

Improving the way neural networks learn

• The cross-entropy cost function
• Overfitting and regularization
• Weight initialization
• Handwriting recognition revisited: the code
• How to choose a neural network's hyper-parameters?
• Other techniques

A visual proof that neural nets can compute any function

• Two caveats
• Universality with one input and one output
• Many input variables
• Extension beyond sigmoid neurons
• Fixing up the step functions
• Conclusion

Why are deep neural networks hard to train?

• The vanishing gradient problem
• What's causing the vanishing gradient problem? Unstable gradients in deep neural nets
• Unstable gradients in more complex networks
• Other obstacles to deep learning

Deep learning

• Introducing convolutional networks
• Convolutional neural networks in practice
• The code for our convolutional networks
• Recent progress in image recognition
• Other approaches to deep neural nets
• On the future of neural networks

Appendix: Is there a simple algorithm for intelligence?

Acknowledgements

Frequently Asked Questions

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If you benefit from the book, please make a small donation. I suggest $5, but you can choose the amount.

Alternately, you can make a donation by sending me Bitcoin, at address 1Kd6tXH5SDAmiFb49J9hknG5pqj7KStSAx

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Sponsors

Deep Learning Workstations, Servers, and Laptops

Thanks to all the supporters who made the book possible, with especial thanks to Pavel Dudrenov. Thanks also to all the contributors to the Bugfinder Hall of Fame.

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Resources

Michael Nielsen on Twitter

Book FAQ

Code repository

Michael Nielsen's project announcement mailing list

Deep Learning, book by Ian Goodfellow, Yoshua Bengio, and Aaron Courville

cognitivemedium.com

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By Michael Nielsen / Dec 2019

It's not uncommon for technical books to include an admonition from the author that readers must do the exercises and problems. I always feel a little peculiar when I read such warnings. Will something bad happen to me if I don't do the exercises and problems? Of course not. I'll gain some time, but at the expense of depth of understanding. Sometimes that's worth it. Sometimes it's not.

So what's worth doing in this book? My advice is that you really should attempt most of the exercises, and you should aim not to do most of the problems.

You should do most of the exercises because they're basic checks that you've understood the material. If you can't solve an exercise relatively easily, you've probably missed something fundamental. Of course, if you do get stuck on an occasional exercise, just move on - chances are it's just a small misunderstanding on your part, or maybe I've worded something poorly. But if most exercises are a struggle, then you probably need to reread some earlier material.

The problems are another matter. They're more difficult than the exercises, and you'll likely struggle to solve some problems. That's annoying, but, of course, patience in the face of such frustration is the only way to truly understand and internalize a subject.

With that said, I don't recommend working through all the problems. What's even better is to find your own project. Maybe you want to use neural nets to classify your music collection. Or to predict stock prices. Or whatever. But find a project you care about. Then you can ignore the problems in the book, or use them simply as inspiration for work on your own project. Struggling with a project you care about will teach you far more than working through any number of set problems. Emotional commitment is a key to achieving mastery.

Of course, you may not have such a project in mind, at least up front. That's fine. Work through those problems you feel motivated to work on. And use the material in the book to help you search for ideas for creative personal projects.