(10 points) Understanding receptive fields In a fully connected network, the value/output of every unit (i.e. neuron) depends on the entire input to the network. However, in convolutional neural networks, we typically use filters smaller in size than the input and hence the value of a neuron depends on a part of the input. This region of input space that affects the value of a neuron is called receptive field of the neuron. In other words, we say that the receptive field of a neuron is n if it's output depends on an nn patch of the input. More rigorously, receptive field is a region of space and must be represented as nn. However, when we consider square kernels, we can denote it using a single variable, since both dimensions are equal. Receptive fields are key to diagnosing potential issue with CNNs. They also help us identify any blind spots in the input and ensure visibility of all input pixels at the output so that no relevant information is missed out while making a prediction. Consider a toy CNN with 3 convolution layers (CL), powered by ReLU activations, a fully connected layer followed by the output, as shown below: (Output)(Softmax)Loss The kernel size of these layers are CL1:m1m1,CL2:m2m2,CL3:m3m3 and stride is set to 1 for all layers. (Note: For the following questions it maybe be helpful to draw a couple of layers of a simple network to visualize the neurons' fields of view) (a) (1 point) What is the receptive field of each neuron in (CL1) ? (b) (2 points) What is the receptive field of each neuron in (CL2) ? (c) (3 points) Suppose we introduced a stride of s1,s2,s3 on conv layers CL1,CL2 and CL3 respectively, how would this affect the receptive fields of CL1 and CL2 ? (d) (2 points) Based on the patterns you observed in the previous question, write down a generalized expression for the receptive field of a neuron in the kth layer of a CNN with n convolution layers (take mi and si as the kernel size and stride of each layer). (e) (2 points) Mention two ways to increase the receptive field of neurons in a CNN