Consider a convolutional neural network that is used to classify images into two classes. The structure of the network is as follows:

$$ INPUT: $100$x$100$ grayscale images.

$$ LAYER $1$: Convolutional layer with $1005$x$5$ convolutional filters.

$$ LAYER $2$: Convolutional layer with $1005$x$5$ convolutional filters.

$$ LAYER $3$: A max pooling layer that down$-$samples Layer $2$ by a factor of $4($from $100$x$100->50$x$50)$

$$ LAYER $4$: Dense layer with $100$ units

$$ LAYER $5$: Dense layer with $100$ units

$$ LAYER $6$: Single output unit

$($a$)$ How many weights does this network have?

$($b$)$ What is $$stochastic$$ about stochastic gradient descent?

$($c$)$ Assume this network is trained using stochastic gradient descent on a fixed training set. Is there a guarantee that the algorithm will converge to an optimal set of weights given enough epochs of training?

$($d$)$ As with any learning algorithm, designers of deep neural networks face a bias$/$variance trade$-$off. Given your answer to part $($a$),$ would you say that high bias or high variance is a bigger concern? How might we address the concern? In Figure $1$ we see that the ordering of the three methods with respect to mean absolute error is different from the ordering with respect to test set R$2.$ How can this be$?$