Backpropagation through time (BPTT) is a technique of updating tuned
parameters within recurrent neural networks (RNNs). Several attempts at
creating such an algorithm have been made including: Nth Ordered Approximations
and Truncated-BPTT. These methods approximate the backpropagation gradients
under the assumption that the RNN only utilises short-term dependencies. This
is an acceptable assumption to make for the current state of artificial neural
networks. As RNNs become more advanced, a shift towards influence by long-term
dependencies is likely. Thus, a new method for backpropagation is required. We
propose using the 'discrete forward sensitivity equation' and a variant of it
for single and multiple interacting recurrent loops respectively. This solution
is exact and also allows the network's parameters to vary between each
subsequent step, however it does require the computation of a Jacobian.

本文介绍一种称为离散前向灵敏度方程和其变体的反向传播方法，该方法准确而且允许网络参数在每个后续步骤之间变化，但需要计算 Jacobian 矩阵，以适应现今人工神经网络的长期依赖关系的发展趋势。