What is the name of this neural network architecture with layers that are also connected to non-neighbouring layers?

Consider a feedforward neural network. Suppose you have a layer of inputs, which is feedforward to a hidden layer, and feedforward both the input and hidden layers to an output layer. Is there a name for this architecture? A layer feeds forward around the layer after it?

• How are you combining the two layers - concatenating the two vectors to make one longer vector size num_imputs + num_hidden? Feb 3 '20 at 20:05

$$z$$ acts as a Gating Function, which controls how much information is to be transmitted from a previous layer in the network. An additional weight matrix is used to estimate the skip weights.