Q$8.$ Which ones of the following statements are true? $($Check all that apply.$)$

$($a$)$ After training a neural network, you observe a large gap between the training accuracy $(100\%)$ and the test accuracy $(42\%).$ Which of the following methods is commonly used to reduce this gap?

i$.$ Generative Adversarial Networks

ii$.$ Dropout

iii. Sigmoid Activation

iv$.$ RMSprop optimizer

$($b$)$ Which of the following is true about Batch$-$norm?

i$.$ Batchnorm is another way of performing dropout.

ii$.$ Batchnorm makes training faster.

iii. In Batchnorm, the mean is computed over the features.

iv$.$ Batchnorm is a non$-$linear transformation to center the dataset around the origin

v$.$ Batchnorm is taking the tradeoff between the number of epochs and

the minimum batch size.

$($c$)$ Suppose when you are training your convolutional neural network, you find that the training loss just doesnt go down after initialization. What changes will likely fix this problem?

i$.$ Change the network architecture.

ii$.$ Change learning rates.

iii. Ensure training data is being read correctly.

iv$.$ Use dropout.

v$.$ Normalize the inputs to the network.

vi$.$ Add l$2$ regularization.

$($d$)$ Let us compare and contrast convolutions with fully connected layers. Suppose the input is an n n image with c channels. First, consider a convolution with kernel width, height, and stride all equal to

$1.$ Let m denote the number of output filters. Second, consider a convolution with kernel width and height equal to n$,$ with stride $1$ and m output filters. Which of the following are true statements?

i$.$ The first convolutional layer is equivalent to a fully connected layer.

ii$.$ The second convolutional layer is equivalent to a fully connected layer.

iii. The second convolutional layer has fewer parameters than the first.

iv$.$ Both convolutions are a form of dimensionality reduction if m $<$ c$.$