Recurrent Neural Network (RNN)

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A Recurrent Neural Network (RNN) is an multi hidden-layer neural network with neuron connections that are feedback connections (to form a directed cycle).





  1. A. Graves, M. Liwicki, S. Fernandez, R. Bertolami, H. Bunke, J. Schmidhuber. A Novel Connectionist System for Improved Unconstrained Handwriting Recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 31, no. 5, 2009.
  2. H. Sak and A. W. Senior and F. Beaufays. Long short-term memory recurrent neural network architectures for large scale acoustic modeling. Proc. Interspeech, pp338-342, Singapore, Sept. 201






rnn x0 y0 x1 y1 x2 y2 x3 y3 One cell... can be used over... and over... and over... x4 y4 again.



  • (Karpathy, 2015) ⇒ Andrej Karpathy. (2015). “The Unreasonable Effectiveness of Recurrent Neural Networks." May 21, 2015
    • QUOTE: ... What makes Recurrent Networks so special? A glaring limitation of Vanilla Neural Networks (and also Convolutional Networks) is that their API is too constrained: they accept a fixed-sized vector as input (e.g. an image) and produce a fixed-sized vector as output (e.g. probabilities of different classes). Not only that: These models perform this mapping using a fixed amount of computational steps (e.g. the number of layers in the model). The core reason that recurrent nets are more exciting is that they allow us to operate over sequences of vectors: Sequences in the input, the output, or in the most general case both. A few examples may make this more concrete:

      ...RNNs combine the input vector with their state vector with a fixed (but learned) function to produce a new state vector. This can in programming terms be interpreted as running a fixed program with certain inputs and some internal variables. Viewed this way, RNNs essentially describe programs. ...


  • (Olah, 2015) ⇒ Christopher Olah. (2015). “Understanding LSTM Networks.” GITHUB blog 2015-08-27
    • QUOTE: A recurrent neural network can be thought of as multiple copies of the same network, each passing a message to a successor. Consider what happens if we unroll the loop: This chain-like nature reveals that recurrent neural networks are intimately related to sequences and lists. They’re the natural architecture of neural network to use for such data.





  • (Grossberg,2013) ⇒ Stephen Grossberg (2013), Recurrent neural networks"Scholarpedia, 8(2):1888. doi:10.4249/scholarpedia.1888
    • QUOTE: A recurrent neural network (RNN) is any network whose neurons send feedback signals to each other. This concept includes a huge number of possibilities. A number of reviews already exist of some types of RNNs. These include [1], [2], [3], [4].

      Typically, these reviews consider RNNs that are artificial neural networks (aRNN) useful in technological applications. To complement these contributions, the present summary focuses on biological recurrent neural networks (bRNN) that are found in the brain. Since feedback is ubiquitous in the brain, this task, in full generality, could include most of the brain's dynamics. The current review divides bRNNS into those in which feedback signals occur in neurons within a single processing layer,  which occurs in networks for such diverse functional roles as storing spatial patterns in short-term memory, winner-take-all decision making, contrast enhancement and normalization, hill climbing, oscillations of multiple types (synchronous, traveling waves, chaotic), storing temporal sequences of events in working memory, and serial learning of lists; and those in which feedback signals occur between multiple processing layers, such as occurs when bottom-up adaptive filters activate learned recognition categories and top-down learned expectations focus attention on expected patterns of critical features and thereby modulate both types of learning.