Meaning of Weight Gradient in CNN

Question

I developed a CNN using MatConvNet and am able to visualize the weights of the 1st layer. It looked very similar to what is shown here (also attached below incase I am not specific enough) http://cs.stanford.edu/people/karpathy/convnetjs/demo/cifar10.html

My question is, what are the weight gradients ? I'm not sure what those are and am unable to generate those...

Answer 1

My answer here covers this question https://stackoverflow.com/a/68988426/10661506 Long story short, weight gradient of layer l is the gradient of the loss with respect to the weights of layer l.

If you have a correct implementation of backpropagation, you should have access to these gradients as they are needed to compute the weights update at every layer.

Answer 2

Weights in a NN

In a neural network, a series of linear functions represented as matrices are applied to features (usually with a nonlinear joint between them). These functions are determined by the values in the marices, referred to as weights.

You can visualize the weights of a normal neural network, but it usually means something slightly different to visualize the convolutional layers of a cnn. These layers are designed to learn a feature computation over the space.

When you visualize the weights, you're looking for patterns. A nice smooth filter may mean that the weights are well learned and "looking for something in particular". A noisy weight visualization may mean that you've undertrained your network, overfit it, need more regularization, or something else nefarious (a decent source for these claims).

From this decent review of weight visualizations, we can see patterns start to emerge from treating the weights as images:

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Weight Gradients

"Visualizing the gradient" means taking the gradient matrix and treating like an image [1], just like you took the weight matrix and treated it like an image before.

A gradient is just a derivative; for images, it's usually computed as a finite difference - grossly simplified, the X gradient subtracts pixels next to each other in a row, and the Y gradient subtracts pixels next to each other in a column.

For the common example of a filter that extracts edges, we may see a strong gradient in a particular direction. By visualizing the gradients (taking the matrix of finite differences and treating it like an image), you can get a more immediate idea of how your filter is operating on the input. There are a lot of cutting edge techniques (eg, eg) for interpreting these results, but making the image pop up is the easy part!

A similar technique involves visualizing the activations after a forward pass over the input. In this case, you're looking at how the input was changed by the weights; by visualizing the weights, you're looking at how you expect them to change the input.

Don't over-think it - the weights are interesting because they let us see how the function behaves, and the gradients of the weights are just another feature to help explain what's going on. There's nothing sacred about that feature: here are some cool clustering features (t-SNE) from the google paper that look at space separability.

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[1] It can be more complicated if you introduce weight sharing, but not that much