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📗 [4 points] Compute the activation map based on the image and the filter using zero padding. Remember to flip the filter first.
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] What is the convolution between the image and the filter using zero padding? Remember to flip the filter first.
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] What is the convolution between the image and the filter using zero padding? Remember to flip the filter first.
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] A convolutional neural network has input image of size x that is connected to a convolutional layer that uses a x filter, no padding of the image, and a stride of 1. There are activation maps. The convolutional layer is then connected to a pooling layer that uses x max pooling, a stride of (non-overlapping), and no padding of the convolutional layer. The pooling layer is then fully connected to an output layer that contains output units. There are no hidden layers between the pooling layer and the output layer. How many different weights must be learned in this whole network, not including any bias.
📗 Answer: .
📗 [4 points] A convolutional neural network has input image of size x that is connected to a convolutional layer that uses a x filter, zero padding of the image, and a stride of 1. There are activation maps. (Here, zero-padding implies that these activation maps have the same size as the input images.) The convolutional layer is then connected to a pooling layer that uses x max pooling, a stride of (non-overlapping, no padding) of the convolutional layer. The pooling layer is then fully connected to an output layer that contains output units. There are no hidden layers between the pooling layer and the output layer. How many different weights must be learned in this whole network, not including any bias.
📗 Answer: .
📗 [4 points] A convolutional neural network has input image of size x that is connected to a convolutional layer that uses a x filter, zero padding of the image, and a stride of 1. There are activation maps. (Here, zero-padding implies that these activation maps have the same size as the input images.) The convolutional layer is then connected to a pooling layer that uses x max pooling, a stride of (non-overlapping, no padding) of the convolutional layer. The pooling layer is then fully connected to an output layer that contains output units. There are no hidden layers between the pooling layer and the output layer. How many different weights must be learned in this whole network, not including any bias.
📗 Answer: .
📗 [4 points] In a convolutional neural network, suppose the activation map of a convolution layer is . What is the activation map after a non-overlapping (stride 2) 2 by 2 average-pooling layer?
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] In a convolutional neural network, suppose the activation map of a convolution layer is . What is the activation map after a non-overlapping (stride 2) 2 by 2 max-pooling layer?
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] In a convolutional neural network, suppose the activation map of a convolution layer is . What is the activation map after a non-overlapping (stride 2) 2 by 2 max-pooling layer?
📗 Answer (matrix with multiple lines, each line is a comma separated vector): .
📗 [4 points] Consider an unbiased estimator \(X\) for a parameters \(\theta\). We have \(\mathbb{E}\left[X\right]\) = , \(Var\left[X\right]\) = , \(\mathbb{E}\left[Y\right]\) = , \(Var\left[Y\right]\) = . We would like a modified estimator \(Z = X - Y\) to have a reduced variance compared to \(X\). For what covariance \(Cov\left[X, Y\right]\) can we achieve \(Var\left[Z\right] \leq Var\left[X\right]\)? Note: there are many possible answers, enter only one of them.
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