CNN MeaningApplying to MNIST

$0\mathrm{.}0/1\mathrm{.}0$ point $($graded$)$

If we explicitly apply the cubic feature mapping to the original $784-$dimensional raw pixel features, the resulting

representation would be of massive dimensionality. Instead, we will apply the cubic feature mapping to the $10-$

dimensional PCA representation of our training data which we will have to calculate just as we calculated the

$18-$dimensional representation in the previous problem. After applying the cubic feature mapping to the PCA

representations for both the train and test datasets, retrain the softmax regression model using these new

features and report the resulting test set error below.

Important: You will probably get a runtime warning for getting the log of $0,$ ignore. Your code should still run

and perform correctly.

Note: Use the same training parameters as the first softmax model given in

file and temperature $1.$

If you have done everything correctly, softmax regression should perform better $($on the test set$)$ using these

features than either the $18-$dimensional principal components or raw pixels. The error on the test set using

cubic features should only be around $0\mathrm{.}08,$ demonstrating the power of nonlinear classification models.

Error rate for $10-$dimensional cubic PCA features $=$

$1$ point possible $($graded$)$

If you are trying to recognize a large number of features, you should have a small number of filters.

true

false