Adaptive Gradient Clipping

Dynamically tackle Exploding Gradients!

Adaptive gradient clipping(AGC) is a technique used in deep learning to prevent the gradients from becoming too large during training. It dynamically adjusts the scaling of gradients based on their magnitude relative to the model’s parameters, leading to a more stable optimization process and improved convergence of models.

How it works ?

1. Gradient Calculation: During training, the model computes gradients for each parameter with respect to the loss function. These gradients indicate the direction and magnitude of the change needed to minimize the loss.
2. Norm Calculation: AGC calculates the norm (magnitude) of both the gradients and the parameters themselves. The norm of a vector is essentially its length in a mathematical sense. For the gradients, this norm represents the overall magnitude of the changes needed for the parameters to reduce the loss. Similarly, the parameter norm represents the overall magnitude of the parameters.
3. Clipping Condition: AGC compares the ratio of the gradient norm to the parameter norm with a predefined threshold. This ratio indicates how much a single gradient step will change the parameter relative to its current value. If this ratio exceeds the threshold, it suggests that the gradients are too large relative to the parameter values, which could lead to instability during optimization.
4. Gradient Scaling: If the ratio exceeds the threshold, AGC scales down the gradients to prevent them from becoming too large. This scaling factor is adaptive, meaning it changes based on the current gradient and parameter values. By scaling down the gradients, AGC ensures that the updates to the parameters remain within a reasonable range, preventing them from growing too large and causing instability in the optimization process.

How is it different from Traditional Gradient Clipping ?

• Dynamic Threshold: AGC does not rely on a fixed threshold. Instead, it computes a dynamic threshold based on the ratio of the gradient norm to the parameter norm.
• Adaptive Scaling: The scaling factor for each gradient is determined individually based on this ratio. Gradients with larger ratios (relative to their parameter norms) are scaled down more aggressively than those with smaller ratios.

Conclusion

In essence, the key insight behind AGC is that a small change in a small number can be more significant than the same change in a large number.

Therefore, adapting the clipping threshold relative to the magnitude of both gradients and parameters allows for more effective control over the optimization process, ensuring stability while allowing for efficient learning across different scales within the model.