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I've found this equation that explains the output of a neuron in a MLP network:

$y(n) = f(\mathbf{w}^T \mathbf{x}(n) + b)$

I can understand the general context, but since i have no background with mathematical notation, i don't understand what the $(n)$ parameter means (e.g. $y(n)$, $x(n)$). Is it sort of a temporal or sample index? I've seen this notation in other machine learning subjects, but didn't find an explanation.

Ben
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heresthebuzz
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1 Answers1

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n is the dimension of the vector x and also y, as you can see wT is a transpose of w with dimension (n,n), is the image z is y and a is x. and dont bother about l it indicates the index of layer.

enter image description here

Simone
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  • Is it mandatory to denote n? I mean, can i omit n and just write y or x? – heresthebuzz Oct 19 '20 at 21:10
  • I can't say for sure, but in the text i'm reading the author should've used $n$ as a temporal index because the dimensions of $y$ and $x$ are given in the text as follows: "[...] where $x \in \mathbb{R}^{K \times 1}$, [...]" – heresthebuzz Oct 19 '20 at 21:25
  • yes u can omit n, however that K means the length of x – Simone Oct 19 '20 at 22:35
  • Thank you very much. I will accept your answer as correct. – heresthebuzz Oct 19 '20 at 22:37
  • is there any info about n, absolutly x(n) cant be a scalar, x(n) needs to be a vector. However dont bother with it, try to understand the formula with the illustration. Happy learning – Simone Oct 19 '20 at 22:38
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    x is the input vector, but no information is given about (n). It could be a sample or temporal index. Since i'm writing a paper about this theme, i will just omit (n). – heresthebuzz Oct 19 '20 at 23:12