Welcome back to deep learning. Today we want to look a bit more into visualization techniques

and in particular the gradient based and optimization based procedures.

You wanted to know what the matrix is, didn't you?

Okay, so let's see what I've got for you. Let's talk first about the gradient based

visualizations and here the idea is that we want to figure out which input pixel is most

significant to a neuron and if we would change it what would cause a large variation in the

actual output of our neural network. Try to relax. So what we actually want to compute is the partial

derivative of the neuron under consideration, maybe an output neuron like for the class cat,

and then we want to compute the partial derivative with respect to the respective input and this is

essentially back propagation through the entire network and then we can visualize this gradient

as type of image which we have been doing here for this cat image and you can see that of course

this is a color gradient you see that this is a bit of a noisy image but you can see that what

is related to cat here is obviously also located in the area where the cat is actually located in

the image. So we will learn several different approaches to do this and the first one is

based here on reference number 20. For back propagation we actually need a loss what we

want to back propagate and we simply take a pseudo loss that is simply the activation of an

arbitrary neuron or layer and typically what you want to do is you want to take neurons in the

output layer because they can be associated to a class and what you can also do is instead of

using back propagation you can build a nearly equivalent alternative which uses a kind of

reverse network and this is the dconfnet from reference and 26 so here the input is the trained

network and some image then you choose one activation and set all of the other activations

to zero then you build a reverse network and you can see the idea here that this is essentially

containing the same as the network but just in reverse sequence with so-called unpooling steps

and now with these unpooling steps and the reverse computation you can see that we can also produce

a kind of gradient estimate. The nice thing about this one is there's no training involved so you

just have to record the pooling location in the switches and the forward pass of the reverse

network effectively is the same as the backward pass of the network apart from the rectified

linear unit which we'll look at in a couple of slides. This is the construct and here we show

the visualizations of the top nine activations, the gradient and the corresponding patch. So for

example you can reveal with this one that this kind of feature map seems to focus on green patchy

areas and you could argue that this is more a kind of background feature that tries to detect grass

patches in the image. Anything we need. Right now we're inside a computer program. So what else?

Well there's guided backpropagation and guided backpropagation is a very similar concept and

the idea here is that you want to find positively correlated features so we are looking for positive

gradients because we assume that the features that are positive are the ones that the neuron

is interested in and the negative gradients are the ones that the neuron is not interested in. So

the idea is then to set all negative gradients in the backpropagation to zero and we can show

you now the different processes of the relu during the forward and backward passes with the different

kinds of gradient backpropagation techniques. Well of course if you have this input activations

then in the forward pass in the relu you would simply cancel out all the negative values and set

them to zero. Now what happens in the backpropagation for the three different alternatives? Let's look

at what the typical backpropagation does and note that we show here the negative entries that came

from the sensitivity in yellow and if you now try to backpropagate this you have to remember

which entries in the forward pass were negative and you set those values again to zero but you

keep everything that came from the sensitivity of the previous layer. Now if you do a deconf net you

don't need to remember the switches from the forward pass but you set all the entries that

are negative in the sensitivity to zero and backpropagate this way. Now the guided backpropagation

actually does both so it remembers the forward pass and sets all of those elements to zero and

it sets all of the elements of the sensitivities to zero so it's essentially a union of backpropagation

and deconf net in terms of canceling negative values and you can see that the guided backpropagation