BPTT

Backpropagation Through Time (BPTT) is a gradient-based learning algorithm used to train recurrent neural networks (RNNs) by unrolling the network in time and applying backpropagation to compute weight updates across multiple time steps.

During training, the RNN is unrolled for a sequence of length T, creating a feedforward network with T copies of each recurrent cell. The loss is computed at each time step, and gradients are propagated backward through the unrolled network using the chain rule. Weights are updated based on their cumulative influence over all time steps in the window.

Because BPTT backpropagates through many steps, it can require substantial memory and computation. It is also susceptible to vanishing and exploding gradients for long sequences, which can hamper learning.

To manage cost and memory, truncated BPTT limits the unrolling to a fixed window of recent time steps, trading long-range temporal credit assignment for efficiency. Real-time recurrent learning (RTRL) provides an online alternative with different complexity characteristics, but is rarely used in practice.

In modern practice, BPTT is commonly used with architectures such as long short-term memory (LSTM) and gated recurrent units (GRU), which mitigate gradient problems. It remains a standard procedure in training RNNs for sequential data tasks such as language modeling, speech recognition, and time-series prediction.