Homework 2

We shall train affine models on the CIFAR-10 dataset:
https://huggingface.co/datasets/uoft-cs/cifar10
If you get low accuracy values, do not fret. This is a more difficult task than MNIST. Just make sure your values are over what would be expected from random choice.

1. Load the dataset. Note that it includes a "train" and a "test" split.
2. Perform a train-validation split on its "train" split.
   1. Make the validation set as big as the "test" split.
   2. Make the random split using a fixed seed for reproducibility.
3. Transform the train, validation and test sets to pairs of feature matrices and label vectors, in torch.Tensor format.
4. Save the 6 tensors you get in a dictionary, with torch.save.
5. Optional (no grade, but can help): Make your code so that at start if it finds a file at the location you would save the preprocessed tensors to, it skips preprocessing and loads the tensors directly.
   1. You can use os.path.exists for this.
6. Train logistic regression models on the dataset:
   1. Using Negative Log Likelihood as loss.
   2. Using 7 different learning rates: 10 ** i where i = -2, -1.5, ..., 1.
   3. Make a line plot with
      1. log10 of the learning rates, that is -2, -1.5, ..., 1 on the horizontal axis and
      2. the validation accuracies on the vertical axis.
7. Repeat step 7 with Brier Score as the loss function: This is the squared distance between:
   1. The model output as 10 probability values. To take softmax of a torch.Tensor, you can use the softmax method. In the dim keyword, you can specify along which dimension you want to take the softmax.
   2. A one-hot vector. Besides the approach of Notebook 0206, you can also use torch.nn.functional.one_hot.
8. Optional (no grade, but can help): To help with points 7 and 8, make a train function that has
   1. the learning rate and the loss function as input and
   2. outputs the validation accuracy.