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During ‘Training’ of a Deep Learning Model, we backpropogate our Gradients through the Network’s layers.

During experimentation, once the gradient value grows extremely large, it causes an overflow (i.e. NaN) which is easily detectable at runtime or in a less extreme situation, the Model starts overshooting past our Minima; this issue is called the Gradient Explosion Problem.

This is when they get exponentially large from being multiplied by numbers larger than 1, consider the example:

Source: Hinton’s Coursera Lecture Videos.

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

In the above image, Gradient is clipped from Overshooting and our cost function follows the Dotted values rather than its original trajectory.

L2 Norm Clipping

There exist various ways to perform gradient clipping, but the a common one is to normalize the gradients of a parameter vector when its L2 norm exceeds a certain threshold:

new_gradients = gradients * threshold / l2_norm(gradients)

We can do this in Tensorflow using the Function

tf.clip_by_norm(t, clip_norm, axes=None, name=None)

This normalises t so that its L2-norm is less than or equal to clip_norm

This operation is typically used to clip gradients before applying them with an optimizer.

You can find me on twitter @bhutanisanyam1
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