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For conceptual questions that somehow involve the PyTorch library, but note that programming questions are off-topic here.

2 votes
Accepted

"Tweaking" the cost function to penalize rarer cases more severely

Yes, you can use weighted MSE by applying different coefficients to each data point. Here is an implementation given by Francisco Massa at https://discuss.pytorch.org/t/how-to-implement-weighted-mean- …
Jaume Oliver Lafont's user avatar
1 vote

How do we determine the slope for leakyrelu activation function?

When this slope in the negative part is learned, the activation function is called Parametric ReLU or PReLU. https://pytorch.org/docs/stable/generated/torch.nn.PReLU.html
Jaume Oliver Lafont's user avatar