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BackPropagation Through Time

BackPropagation Through Time Jiang Guo Abstract This report provides detailed description and necessary derivations for the BackPropagation Through Time (BPTT) algorithm. BPTT is often used to learn recurrent neural networks (RNN). Contrary to feed-forward neural networks, the RNN is characterized by the ability of encoding longer past information, thus very suitable for sequential models. The BPTT extends the ordinary BP algorithm to suit the recurrent neural architecture. 1 Basic Definitions For a two-layer feed-forward neural network, we notate the input layer as x indexed by variable i, the hidden layer as s indexed by variable j, and the output layer as y indexed by variable k. The weight matrix that map the input vector to the hidden layer is V, while the hidden layer is propagated Through the weight matrix W, to the output layer.

The unfolded recurrent neural network can be seen as a deep neural network, except that the recurrent weights are tied. Consequently, in BPTT training, the weight changes at each recurrent layer should be added up to one big change, in order to keep the recurrent weights consistent. A similar algorithm is the

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