week 5?- CNN's

Question 1

what is a CNN convolutional layer

Answer 1

This layer applies convolutional filters (kernels) to the input data (e.g., an image) to detect local patterns such as edges, textures, or more complex features as the network deepens.
Each filter slides (or “convolves”) over the input image, performing a dot product between the filter and a small local region of the input image. This results in a feature map.
The convolutional operation allows the network to focus on local dependencies (spatial hierarchies), making it more efficient than fully connected networks.

Question 2

explain local dependencies and spatial hierachys in the convolutional layer

Answer 2

The convolutional operation focuses on local dependencies by looking at small, localized regions of the image and detecting basic features (e.g., edges, textures). This process builds up spatial hierarchies where simple features combine into more complex ones as the network goes deeper. This local, hierarchical approach makes CNNs more efficient than fully connected networks, as they require fewer parameters and computational resources while still being able to learn complex patterns from data.

Question 3

what is the sparesity aspect of the curse of dimensionality?

Answer 3

as dimensions increase, the number of data points becomes increasingly sparse

this makes it harder for ml agorithms to find meaningful patterns because there are fewer instances of meaningful data points

This means that models need more training data to find patterns

It also means that models are more likely to overfit to the data

Question 4

how to solve the curse of dimensionality in image classification by convoluting

Answer 4

just take a small portion of the image - e.g 9 pixels. however this doesn’t work if theres no single portion of the image that contains enough information for a classification

to get around this just do it for different portions of the image to get a feature map

then get the features out of the first feature map, and then do that again on a second feature map

this creates an MLP where each succesive layer learns to capture more pieces of information about the original image

because each feature map is smaller than the previous one, each layer condenses information about the original image. however, the smaller layers are also deeper

Question 5

why, in a CNN, is the classifier able to work with a significantly reduced quantity of information

Answer 5

because the feature maps contain compressed information, however this information is still reflective of the image as a whole

Question 6

why do CNNs work with images?

Answer 6

because local neighbourhoods in the image contain similar information

if the pixels were scrambled, the accuracy of CNNs would decrease to the same as an MLP. This is because MLP’s don’t take into account the ordering of the pixels

Question 7

what else can you use CNN’s for?

Answer 7

neural style transfer

Question 8

how does neural style transfer work

Answer 8

you train an image classifier on natural images to recognise patterns in images

Then you feed into it your image and your style target,

you have a content loss function and a style loss function

for the content, you extract the features at some point in the middle layers, before it reaches the actual classifiers. the content feature extraction ensures that the larger features of the image are present in the generative image. Content loss = mse

for the style, the correlation is computed with a gram matrix (correlation matrix). this tells us the correlations between different features in the style image. This tells us about style/texture, because style is determined by global patterns which are spatially independent. the style loss is then calculated as the difference in the gram matrix between the target image and the style image.

pixels are then adjusted to minimise in balance the content loss and the style loss functions

Question 9

why use the gram matrix in the style loss function, and not MSE

Answer 9

The Gram matrix is used in the style loss function because it captures the correlations between features (texture patterns) across the image, which is essential for transferring the style of one image to another. It focuses on global structure and spatial relationships between feature activations rather than pixel-wise differences.
MSE, on the other hand, is more suited for tasks where the exact values of features (such as pixel intensities or specific activations) are important, which is why it is more commonly used for content loss (where exact pixel similarity is desired).

Question 10

in neural transfer, what are the parameters of the model?

Answer 10

the pixels
so updating the parameters is equivalent to changing the pixels

Question 11

what is an application of neural style transfer in neuroscience?

Answer 11

super-resolution MRI scanners are expensive

hyperfine swoop scanners are much cheaper, however images are worse

you could use deep learning U-net techniques to improve the hyperfine images

Question 12

what is transposed convolution?

Answer 12

a way to increase the spatial resolution of feature maps/upsamples them

it is a reverse operation of convolution which downsamples.

you can go from compressed representation, to whole size images

if you add in style loss to the MSE loss when upsampling, you can end up with a much higher resolution image than previous

Question 13

what is a filter in a CNN

Answer 13

A filter in a Convolutional Neural Network (CNN) is a small matrix of weights that slides over the input data (e.g., an image) to detect specific features like edges, textures, or patterns. Filters learn these features during training, enabling the CNN to progressively recognize complex structures in deeper layers.

Question 14

in a CNN, how do the filters relate to the parameters of the model?

Answer 14

In a CNN, filters are paramaterised

This means that the weights in the filter matrix are actually parameters of the model that get optimised through backpropogation

Each neuron in the model is only connected to other nearby neurons, rather than each neuron being fully connected to each other (such as in MLPs). This improves the computational efficiency because fewer parameters are reequired, as the information is compressed into a smaller number of features.

Question 15

when would you choose a CNN over an MLP

Answer 15

CNN’s are good when the data contains spatial hierachys or local dependencies such as in images.

MLP’s may be better to observe global patterns, in more simply structured data

Question 16

how does log loss work?

Answer 16

Log loss, or logistic loss, measures the performance of a classification model by quantifying how far its predicted probabilities are from the true labels. For each prediction, it calculates a penalty: if the predicted probability of the true class is close to 1, the loss is small; if it’s far from 1, the loss grows exponentially.

penalizing predictions that deviate from the actual labels, with larger penalties for confident but incorrect predictions.

Question 17

what is a problem with using MLP’s for image classification

Answer 17

Images are highly dimensional. This leads to problems of sparsity, meaning you would need many more images to fill the image space.

Additionally, MLP’s don’t take into account local dependencies, which convey meaningful information about the data

Question 18

How do CNN’s work when combined with MLP’s?

Answer 18

CNN’s compress the information in the whole image, so the dimensions are reduced but it still captures information about the whole image.

This can then be fed into a MLP for classification, avoiding the problems associated with dimensionality.

Question 19

What is a U-net?

Answer 19

A U-Net is a type of neural network used for image segmentation, where it identifies specific regions in an image. It has two parts: one shrinks the image to learn important features, and the other expands it back to the original size while combining details to make accurate predictions.

Question 20

what is transposed convolution?

Answer 20

Applying convolutional filters in a reverse direction