How the backpropagation algorithm works

Chapter 2 of my free online book about “Neural Networks and Deep Learning” is now available. The chapter is an in-depth explanation of the backpropagation algorithm. Backpropagation is the workhorse of learning in neural networks, and a key component in modern deep learning systems. Enjoy!


  1. This is a damn good treatment of backprop, Appreciate the amount of work you are putting into this. Also this is unbelievably clear writing and keep those diagrams and plots coming..

  2. Thanks! Yes, I’ll keep the diagrams and plots coming. There will also be some animations in the next chapter (very nice for showing how networks change over time).

  3. Hi, I liked chapter 1 very much. Like Thimothy i find that you are extremely good at explaining how NN works. Can’t wait to begin reading chapter 2!!!

  4. Hi, Michael

    I am a Chinese graduate student and this book is really good. Can not wait for the following chapters~;)

    I would like to translate this book into Chinese and share your great ideas with my friends.

    Any ideas?

  5. Glad you’re enjoying it! As regards a translation, please look at the licensing information in the footer of the book’s webpages. Briefly, the license allows translation provided you’re not making money from it, i.e., it’s not a commercial translation. If you have a commercial use in mind, please email me and we can talk about it.

  6. Currently I don’t have any commercial use in mind. After finished, I will send you the translated version and provide proper attribution.

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