Mathematical notation for neural network

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there are so many "styles" to express neural net in mathematical notation, for example Michael Nielson defines $w_{jk}$ as weight from $k$-th neuron to $j$-th, Andrew Ng defines it otherwise, some people treat bias term as neuron with fixed weight equal to $1$,it is not big deal I guess, but when I derive equation from different notation style it makes different equation (however the both equations has the same meaning), and suppose that I want to write bachelor thesis or something, what is the most common mathematical notation style to express neural net ? is there any standard to write to represent neural net in mathematical notation...thank you

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One of the standard text books about neural networks is

Tom Mitchel. Machine Learning, 1997 (Mcgraw-Hill Education Ltd; ISBN-13 978-0071154673)

As it is so well-known, many lectures / papers use the same notation.

I don't think it matters too much which notation you use, as long as you explain it and as long as you are consistent. I think your notation should either be the same as one book / paper you rely on or be of advantage for whatever you want to do / show.