What is Backpropagation through time (BPTT)
by Stephen M. Walker II, CoFounder / CEO
What is Backpropagation through time (BPTT)?
Backpropagation through time (BPTT) is a method for training recurrent neural networks (RNNs), which are designed to process sequences of data by maintaining a 'memory' of previous inputs through internal states. BPTT extends the concept of backpropagation used in feedforward networks to RNNs by taking into account the temporal sequence of data.
Here's how BPTT works:

Unfolding in Time — The RNN is "unrolled" across time steps, creating a chain of copies of the network, each representing the network at a specific time step with shared parameters.

Forward Pass — During the forward pass, inputs are fed into the network sequentially, and the hidden states and outputs are computed for each time step.

Backward Pass — The network's output is compared to the desired output, and the error is calculated. This error is then propagated backward through the unrolled network, from the final time step to the first, to compute the gradients of the error with respect to the network's weights.

Gradient Calculation — The gradients are calculated using the chain rule of calculus, taking into account the influence of each weight on the error at every time step.

Weight Update — The weights are updated to minimize the error, typically using gradient descent or a variant thereof.
BPTT has several advantages, such as being significantly faster for training RNNs compared to generalpurpose optimization algorithms. However, it also has drawbacks, including the difficulty with local optima and the potential for vanishing or exploding gradients, which can make training unstable.
To mitigate these issues, variations like Truncated BPTT (TBPTT) are used, where the error is only propagated back for a fixed number of time steps, reducing computational complexity and helping to prevent gradient problems.
How does backpropagation through time differ from traditional backpropagation?
Backpropagation through time (BPTT) differs from traditional backpropagation in that it is specifically designed to train recurrent neural networks (RNNs) which handle sequential data and have internal state memory. Traditional backpropagation is used for static problems with fixed inputs and outputs, such as classifying images, where the input and output do not change over time.
In BPTT, the RNN is conceptually "unrolled" across time steps, creating a chain of copies of the network, each representing the network at a specific time step with shared parameters. This unrolling is necessary because the output at each time step in an RNN depends not only on the current input but also on the previous hidden state, which acts as a form of memory.
During the forward pass in BPTT, inputs are fed into the network sequentially, and the hidden states and outputs are computed for each time step. In the backward pass, the error is propagated backward through the unrolled network, from the final time step to the first, to compute the gradients of the error with respect to the network's weights. The gradients are calculated using the chain rule of calculus, considering the influence of each weight on the error at every time step.
In contrast, traditional backpropagation involves a single forward and backward pass through the network layers without the need to consider temporal dependencies. The weights in traditional neural networks are not shared across different parts of the network as they are in RNNs during BPTT.
BPTT can be computationally intensive and may suffer from issues such as vanishing or exploding gradients due to the long sequences involved. To address these issues, truncated BPTT (TBPTT) is often used, where the error is only propagated back for a fixed number of time steps.
What is Truncated BPTT?
Truncated Backpropagation Through Time (TBPTT) is a modification of the Backpropagation Through Time (BPTT) training algorithm for recurrent neural networks (RNNs). The main purpose of TBPTT is to keep the computational benefits of BPTT while reducing the need for a complete backtrack through the entire data sequence at every step.
In standard BPTT, the network is unrolled for the entire sequence, and the error is propagated back through all these steps. This can be computationally expensive and memoryintensive, especially for long sequences. It can also lead to problems such as vanishing or exploding gradients.
TBPTT addresses these issues by limiting the number of timesteps used in the backward pass, effectively truncating the sequence. It does this by chopping the initial sequence into evenly sized subsequences. The gradient flows are truncated between these contiguous subsequences, but the recurrent hidden state of the network is maintained.
The TBPTT algorithm has two parameters: k1 and k2. It processes the sequence one timestep at a time, and every k1 timesteps, it runs BPTT for k2 timesteps. This approach can make a parameter update cheaper if k2 is small, and the hidden states, having been exposed to many timesteps, may contain useful information.
However, there are some tradeoffs. Truncation can bias gradients, removing any theoretical convergence guarantee. Intuitively, TBPTT may have difficulty learning dependencies that span beyond the range of truncation. Despite these limitations, TBPTT is widely used due to its computational efficiency and practicality for training RNNs on long sequences.
Understanding Backpropagation Through Time (BPTT)
Backpropagation through time (BPTT) is a specialized training algorithm for recurrent neural networks (RNNs) that addresses the unique challenge of temporal dependencies in sequential data. By extending the backpropagation algorithm used in feedforward networks, BPTT effectively trains RNNs by considering both the current input and its relationship with previous inputs.
BPTT operates by unfolding the RNN across time steps, allowing the error from predictions to be propagated backward through the network, updating weights to minimize prediction errors. This backward flow of error is crucial for tasks where sequence and timing, such as in speech recognition or language translation, play a critical role.
Despite its strengths, BPTT has limitations. The algorithm's computational demands can escalate with longer sequences, making it challenging to train on extended data. Additionally, BPTT's sensitivity to noise can complicate the training process, and its implementation can be intricate, posing difficulties in debugging and error tracking.
Nevertheless, when applied effectively, BPTT enhances AI models by improving their ability to handle sequential prediction tasks, such as nextword prediction in language processing. By training on extensive text corpora, BPTT refines the neural network's predictive accuracy, contributing to advancements in fields like machine translation.