Back propagation through time, simple explanation for a beginner

Question

I'm a totally new to machine learning, and I understand the concept of backpropagation and recurrent neural networks, but I can't seem to grasp the backpropagation through time. In Wikipedia pseudocode,

Back_Propagation_Through_Time(a, y)   // a[t] is the input at time t. y[t] is the output
Unfold the network to contain k instances of f
do until stopping criteria is met:
    x = the zero-magnitude vector;// x is the current context
    for t from 0 to n - 1         // t is time. n is the length of the training sequence
        Set the network inputs to x, a[t], a[t+1], ..., a[t+k-1]
        p = forward-propagate the inputs over the whole unfolded network
        e = y[t+k] - p;           // error = target - prediction
        Back-propagate the error, e, back across the whole unfolded network
        Update all the weights in the network
        Average the weights in each instance of f together, so that each f is identical
        x = f(x);                 // compute the context for the next time-step

So as I understand, we have the desired output at the current step, we forward pass the steps before, calculate the error between the previous step outputs and the current output.

How are we updating the weights?

Average the weights in each instance of f together, so that each f is identical

What's the meaning of this?

Can anyone describe what BPTT is in simple terms of give a simple reference for a beginner?

Answer 1

You unfold the RNN f for n time-steps into a plain DNN, where n is the length of your training feature-label sequence, and the DNN contains n instances of f. Then you could use the n-step feature-label sequence to train this DNN with standard BP. In the DNN, each instance of f contains a copy of the weights W. Each will be updated to a different new W_1 to W_n. Then the average of W_1 to W_n is the new weights of the original RNN f after trained by that n-step sequence. The whole procedure of training the RNN f is BPTT.