Recurrent neural nets. Vanishing gradient problem, naively, RNNs don't give you long term memory.. so you have Long short-term memory networks
Recurrent neural networks -- Schmidhuber
Recurrent Neural Network Writes Music and Shakespeare Novels - Two Minute Papers
Proposed to solve the vanishing gradients problem
http://colah.github.io/posts/2015-08-Understanding-LSTMs/
See also Neural networks with memory, Deep learning
A variation of the Long short-term memory network
Nice curated list of RNNs: https://github.com/kjw0612/awesome-rnn
Higher Order Recurrent Neural Networks . We propose to use more memory units to keep track of more preceding states in recurrent neural networks (RNNs), which are all recurrently fed to the hidden layers as feedback through different weighted path