# How do hidden layer of a trained network look like?

Suppose I have a deep feed-forward neural network with sigmoid activation $$\sigma$$ already trained on a dataset $$S$$. Let's consider a training point $$x_i \in S$$. I want to analyze the entries of a hidden layer $$h_{i,l}$$, where

$$h_{i,l} = \sigma(W_l ( \sigma (W_{l-1} \sigma( \dots \sigma ( W_1 \cdot x_i))\dots).$$

My intuition would be that, since gradient descend has passed many times on the point $$x_i$$ updating the weights at every iteration, the entries of every hidden layer computed on $$x_i$$ would be either very close to zero or very close to one (thanks to the effect of the sigmoid activation).

Is this true? Is there a theoretical result in the literature which shows anything similar to this? Is there an empirical result which shows that?