The term hidden nodes refers to the cells of inner layers of artificial networks are not exposed for connectivity outside of their connectivity within the network. Their values can be read and visualized, but the network function is not dependent upon such tapping of signals internal to the network. Neither are the input of inner layers and their hidden cells connected to network inputs nor are the outputs of inner layers and their hidden cells connected to network outputs.
The purpose of inner layers is related to network flexibility and thus accuracy of the functional approximation that may be achieved. An activation function by itself rarely approximates the desired mapping between input values and output values that is optimally achieved by training.
Attenuated substitution of one parallel activation function into another leads to greater functional flexibility. Attenuation is achieved by multiplying the vector of layer activation function outputs by a matrix of parameters and feeding the resulting product vector into the next layer's activation function units. In combination with a convergence strategy like gradient descent and a corrective distribution strategy like back-propagation to update the parameters, the flexibility in functionality can be directed to achieve higher resulting accuracy by the end of training.
There are no action layers or action cells. The cells in an artificial network do not perform actions other than the evaluation of their activation function (and gating in the case of gated units). The output of the network may lead to actions if the network is a component in a controller, in which case the output of the network is connected to other system components so that action is controlled.