What are examples of good free books that cover the back-propagation used to train multilayer perceptrons? I've just started to learn about artificial neural networks, so I'm looking for books that cover the theoretical basics of back-propagation.

  • 1
    $\begingroup$ this is not a book, but if you want to try understand backprop calculation step-by-step, this blog is amazing: mattmazur.com/2015/03/17/a-step-by-step-backpropagation-example $\endgroup$
    – malioboro
    Commented Feb 26, 2021 at 3:08
  • $\begingroup$ @malioboro this blog falls into the same pitfall that most do - it doesn't cover the case of multiple hidden layers. While the task isn't actually that much more complicated, the notation used quickly falls apart because it becomes way too long to write out. This made learning back propagation initially for me extremely difficult, because it seems no one actually covered the case of multiple hidden layers. Until I found this: youtu.be/d14TUNcbn1k?t=354 $\endgroup$
    – Recessive
    Commented Feb 26, 2021 at 5:22
  • $\begingroup$ @Recessive Oh I see, multiple hidden layers means more than one hidden layer, that's true the notation will become complicated $\endgroup$
    – malioboro
    Commented Feb 26, 2021 at 9:28
  • $\begingroup$ @malioboro Thank you. I actually was looking for different sources as books, videos, papers, etc. but moderator nbro asked me to modify my post and to focus only on 1 source. $\endgroup$ Commented Feb 27, 2021 at 2:44
  • $\begingroup$ @Recessive Thanks $\endgroup$ Commented Feb 27, 2021 at 2:57

1 Answer 1


Deep Learning by Goodfellow et. al is a good book for anything related neural networks, and it's freely available online. Backpropagation is covered in Chapter 6.5.

  • $\begingroup$ Thanks. Can one go straight to Chapter 6.5. to read the 21 pages or is it required to read previous text? $\endgroup$ Commented Feb 27, 2021 at 3:03
  • $\begingroup$ @veronika Well I guess it really depends on your background. You can try reading it and see if you can follow the material. $\endgroup$
    – SpiderRico
    Commented Feb 27, 2021 at 13:40

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