# Neural Network - Can Hidden Layer Nodes be omitted from output equation

I was considering a feedforward neural network, where the output can be written as:

$$y_o = \sigma(z_h)$$,

where $$z_h$$ is the logit from the hidden layer, say, $$w^T_{h}. x_h$$, where the $$h$$ subscript denotes the hidden layer.

My question is since the hidden layer inputs $$x_h$$ are just the outputs from the input layer, can one just not write this as:

$$y_o = \sigma(z_h) = \sigma(w^T_{h} . x_h) = \sigma(w^T_{h} y_i) = \sigma(w^T_{h} \sigma(w^T_{i} x_{i}))$$, where this last equality explicitly shows the composition of functions (i denotes the input layer), and you don't have any $$x_h$$ terms in there?

Thanks.

• Hi. Thanks for your answer. No, I didn't want to omit the hidden layer nodes, as the $w_h^T$ term is still present in the last equality. Dec 25, 2019 at 5:48
• Ah, I slightly misinterpreted what you were asking. The first sentence still holds though, you are correct in expanding it s.t. $x_h$ is replaced by $\sigma(w_i^Tx_i)$. Dec 25, 2019 at 5:52