Consider an MLP with one hidden layer. Mathematically, denoting the input as $x$, the output, say, $y$ is calculated by $$ y = \sigma(W_2a_2 + b_2) $$ where $$ a_2 = \sigma(z_2), \qquad z_2 = W_1x+b_1. $$ What confuses me is which one is called activation, for example, in the second layer? Is the activated signal $a_2$ called the activation of 2-nd layer? Or is $z_2$, the signal before activated, called so?
A 'layer' does not have an activation. Each individual neuron has an activation.
The state of a neuron is it's bias + all incoming connections (weight * activation from source neuron). So that's $z_2$.
The activation is the state of a neuron passed through an activation function. So that's $a_2$. As $\sigma()$ is the activation function.
The answer below seems contradictory, however (logically) it makes sense to call the activation of a neuron the value that is received from the activation function. References to support my claim:
As you see, the value neuron y is getting from x1 is called the 'activation of neuron1', meaning its output - thus the value received after the activation function. [Source]
I've seen people calling both activation, but the input of the activation function ($z_2$) seems more formal.
For example in Pattern Recognition and Machine Learning (the following $a_j$ and $z_j$ are not the same as in the question)