Recall the rotation based pretext task for self$-$supervised pretraining on image data. Suggest a way to realize a similar rotation based pretext task for audio data.

Consider a convolutional layer with $30$ convolution filters of size $33.$ What will be the amount of reduction $(\%)$ in number of trainable parameters if the flattened convolutions are used?

$[$True$/$False$]$ Co$-$occurrence matrix based word embedding is an example of local representation. $($Justify your answer$)$

Consider the error surfaces of a simple problem with two trainable weights $w_1$ and $w_2$ shown below. The left one is observed when supervised training is used to optimize the weights whereas the right one corresponds to unsupervised pretraining. Two solutions obtained at different runs of unsupervised pretraining are marked with brown and red stars $(***).$ Which one of these two solutions is useful for subsequent supervised finetuning? Justify your answer.

Show that for a rectangular weight matrix $Win{R}^{mn}$ such that $m>>n,$ a compression rate

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of $O(\frac{n}{r})$ can be achieved using singular value decomposition where $r$ denotes the number of non$-$zero singular values preserved during low rank approximation of $W.$

$6.$ Consider an exhibition where different products are presented with never$-$seen$-$before shapes and designs. You have collected few pictures of these products and are asked to design a classifier to classify each product into a different class. You decide to use a domain adaptation approach with help of hand drawn sketches. Among the different domain adaptation approaches we discussed in the class, which one is the best choice for the considered problem and why?

$7.$ Recall our discussion on causal mechanisms and answer whether semisupervised learning be effective on the following two prediction problems? Justify your answer.

Performance prediction using the system attributes such as vendor name, model no$.,$ RAM capacity etc.

Tumor type prediction from its features such as size, shape, location etc.

Which of the following can be used as pretext tasks for self$-$supervised pretraining in computer vision applications? Justify your answer.

Colour image to grayscale image prediction.

Image inpainting.