Gradient clipping is a technique used in deep learning to prevent the gradients from becoming too large or too small during the training process. This technique is particularly useful for avoiding the exploding gradient problem, which can lead to numerical instability, or the vanishing gradient problem, which can prevent convergence.

During backpropagation, the gradients are computed and used to update the weights of the neural network. However, if the gradients are too large, they can cause the weights to update too much, leading to instability. Similarly, if the gradients are too small, they may not be able to cause significant changes in the weights, leading to slow convergence or stagnation.

Gradient clipping addresses these issues by limiting the size of the gradients. Specifically, the gradients are clipped to a maximum or minimum value, depending on whether they exceed a certain threshold. This threshold is typically set to a value between 1 and 5, but it can vary depending on the specific problem and network architecture.

The gradient clipping operation can be mathematically represented as:

where $g$ is the gradient and $\text{threshold}$ is the maximum allowed value.

Gradient clipping has several benefits, including:

• Improved stability: By preventing the gradients from becoming too large, gradient clipping can improve the numerical stability of the training process.

• Faster convergence: By preventing the gradients from becoming too small, gradient clipping can help the network converge faster.

• Better generalization: By preventing the gradients from overfitting to the training data, gradient clipping can improve the generalization performance of the network.

While gradient clipping can be effective, it also has some drawbacks, including:

• Increased complexity: Gradient clipping adds additional complexity to the training process, which can make it more difficult to implement and tune.

• Loss of information: By limiting the size of the gradients, gradient clipping may result in a loss of information, which can negatively impact the performance of the network.

• Vanishing Gradient Problem
• Exploding Gradient Problem
• Batch Normalization

• Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning (Vol. 1). MIT Press.