Recurrent neural network
Also: RNN
An RNN applies the same weights at every time step, combining the current input with the previous hidden state. This handles sequences of any length, but training by backpropagation through time suffers from vanishing or exploding gradients over long spans.
hₜ = tanh(W_h hₜ₋₁ + W_x xₜ + b)
Example
A character-level RNN reading "hello" updates its hidden state five times with the same weight matrices; the state after "hell" is what lets it predict "o".