I am struggling to write a simple proof for the following statement:
The neuron's inputs are proportional to the probability of the respective feature in the input layer
In particular, I am not sure what $y'$ means here and how we get to an expression of $p(\mathbb{y}|x)$ that depends on $p(\mathbb{x}|y)/p(\mathbb{x}|y')$. Also not 100% sure what $n$ means.
source: https://arxiv.org/pdf/1503.02406.pdf
EDIT 1 I found this question to be a duplicate of this older question. There, the author of the referenced paper points the reader in the right direction.
EDIT 2 In light of the answer provided, I feel that the only missing piece of the puzzle is equation (2) - below.