Gradient Clipping

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Gradient Clipping

What is Gradient Clipping?

Gradient Clipping handles one of the most difficult challenges in Backpropagation for Neural Networks: computing gradients. To converge our cost function, we calculate gradients of all weights and biases in a backward pass. The success of Artificial Neural Networks in any domain is due to these gradients and how they are calculated.

However, every excellent thing comes with a stipulation. Gradients tend to encapsulate the data's content, which can include long-range dependencies in huge text or multidimensional data. 

As a result, things can quickly go wrong while processing complex data, and you'll blow your next million-dollar model in the process. Gradient clipping reduces the amplitude of the gradient and improves the behavior of stochastic gradient descent (SGD) near cliffs:

  • In recurrent networks, high cliffs are typical in the area where the recurrent network behaves roughly linearly. 
  • SGD without gradient clipping exceeds the landscape minimum, whereas SGD with gradient clipping falls below it. 

Source: towardsdatascience

What is exploding gradient problem in deep neural networks?

In artificial intelligence, the exploding gradient problem arises while using gradient-based learning methods and backpropagation to train neural networks. An artificial neural network also referred to as a neural network or a neural net, is an AI learning algorithm that allows a network of functions to save/store and translate data input into a specific output as per the training. This type of algorithm aims to clone the way neurons in the human brain function. 

Exploding gradient occurs as a result of the accumulation of large error gradients,  which impact the neural network model weights and re-updating the same during the training process. As gradients are used to moderate the network weights during training, this process works well when the moderations are small and controlled.

So, when the magnitude or weight of these gradients adds up, the network might go unstable impacting the overall functionality of the neural network and poor prediction results. These exploding gradients influence the performance of the neural network and create hindrances in completing the learning of artificial neural networks. 

Therefore, network engineers use gradient clipping and weight regularization to repair or control the exploding gradients. 

How does gradient clipping work?

As discussed above, gradient clipping is a technique that handles or avoids exploding gradients. 

Gradient clipping will ‘clip’ the gradients or cap them to a Threshold value to prevent the gradients from getting too large.

The basic principle of gradient clipping is to rescale the size and value of the gradient, bringing it down to the appropriate scale. 

If the gradient gets too large, we rescale it to keep it appropriate. More precisely, if ‖g‖ ≥ c, then

gc · g/‖g

where c is a hyperparameter, g is the gradient, and ‖g‖ is the norm of g. Since g/‖g‖ is a unit vector, after rescaling the new g will have norm c. Note that if ‖g‖ < c, then we don’t need to do anything.

Gradient clipping ensures the gradient vector g has norm at most c

The clipping method helps gradients to have a reasonable functionality and be consistent in the data training process.  

How to identify and catch Exploding Gradients?

There are a few subtle ways to determine whether your model is suffering from the problem of exploding gradients;

  • The model is not training much on the training data, affecting the functionality of the network. 
  • The model losses out training data on update due to the model's instability.
  • The weights’ values can also grow to the point where they overflow, resulting in NaN values. 
  • Gradient weights grow exponentially and become very large when training the gradients.
  • The derivatives are constantly changing the value to due overflow of data training. 

How to avoid exploding gradients with gradient clipping? 

Error derivative is the key factor to consider while working on the gradient problem. If we change or moderate the error derivative before it starts to impact the network, we need to put it back into the network learning process and update the weights of that gradient to avoid exploding. Preemptively rescaling or re-updating the error derivative helps the gradient weight to rescale and reduces an overflow or underflow on the neural network. 

Network engineers force or imbibe gradient values to a specific minimum or maximum value if they exceed an expected range and this process is called Gradient Clipping. 

Gradient Clipping is used to clip or ground the gradients all over the neural network by configuring their data processing and intake values. 

What do Clipnorm and Clipvalue mean in gradient clipping?

Clipnorm

Gradient norm refers to modifying or altering the derivatives of the loss function to have a specified vector when the gradient vector’s L2 vector norm (sum of squared values) exceeds a threshold value or standard weight. 

For example, we may set a norm of 2.0, which means that if the vector norm for a gradient exceeds 2.0, the vector values would be altered so that the vector norm equals 2.0 to avoid the exploding gradient problem. 

If we clip the gradient with the norm, the following algorithm is used:

g ← ∂C/∂W

if ‖g‖ ≥ threshold then

g ← threshold * g/‖g‖

 

Clipvalue

Gradient value clipping is about clipping the derivatives of the loss function to a specific value or place on the neural network. 

If a gradient value is less than or greater than a negative or positive threshold, the clip value changes the value to avoid the threshold. For instance, we may define a norm of 1.0, which means that if a gradient value is less than -1.0, it is set to -1.0, and if it is greater than 1.0, it is set to 1.0.

If we clip the gradient with the value, the following algorithm is used:

g ← ∂C/∂W

if ‖g‖ ≥ max_threshold or ‖g‖ ≤ min_threshold then

g ← threshold (accordingly)

What are the different frameworks for gradient clipping in deep learning?

We know why Exploding Gradients occur and how Gradient Clipping can resolve it. There are two different methods that we can use for Clipping to our deep neural network. 

Following are the major frameworks for implementing both the Gradient Clipping algorithms in  Machine Learning. 

  • Data loading
  • TensorFlow
  • Keras
  • PyTorch
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