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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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    $\begingroup$ Read some papers in your intended field, and see what notation they use. You are right to be concerned. The history of mathematics is full of advances which went unnoticed for years because the discoverer used an unfamiliar notation. $\endgroup$ – Martin Kochanski Jul 12 '16 at 7:15
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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.

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