automatic differentiation
Automatic Differentiation in Recurrent Neural Networks (RNNs)
In the context of Recurrent Neural Networks (RNNs), automatic differentiation (autodiff) refers to a computational technique that automatically calculates derivatives (gradients) of functions expressed as computer programs—particularly the loss function with respect to the model’s parameters.
Why It Matters in RNNs
RNNs process sequential data by maintaining a hidden state that updates at each time step. To train an RNN, you must compute the gradient of the loss function over all time steps in the sequence using backpropagation through time (BPTT).
This involves:
- Unrolling the RNN across time
- Computing how changes in weights affect the loss over all time steps
- Accumulating gradients with respect to shared parameters
Manually deriving these gradients is tedious and error-prone, especially for long sequences—this is where autodiff is essential.
How Automatic Differentiation Works
- The RNN’s forward pass is recorded as a computational graph.
- The autodiff engine traces this graph during execution (e.g., PyTorch, TensorFlow).
- During the backward pass, it applies the chain rule to compute gradients automatically.
Benefits in RNNs
- Efficiency: Eliminates manual gradient derivation.
- Accuracy: Reduces human error.
- Flexibility: Supports loops and shared parameters across time steps.
Example (PyTorch)
loss = criterion(output, target)
loss.backward() # Automatic differentiation happens here
optimizer.step()
Calling loss.backward() triggers automatic differentiation, computing gradients for all parameters, including those reused across the time steps in an RNN.
Summary
Automatic differentiation in RNNs is essential for training. It enables the computation of gradients across
time-unrolled sequences automatically and efficiently, supporting gradient-based optimization methods
like SGD or Adam without the need for manual derivation.