Ok, I found out what the issue was. For future reference to people that also don’t understand like myself:
Apparently, you cannot pass a tensor to the mp.Process that has data shared with other processes. If I add a line and substitute the mp.Process argumentsd accordingly,
data_i = data[rank]
p = mp.Process(target=init_process, args=(rank, size, data_i, run))

Then the processes can use that data.
Still, I am not sure then why in the example repo 8 of the multiprocessing pest practices 6 they can pass the dataset
dataset1 = datasets.MNIST('../data', train=True, download=True,
                       transform=transform)

If there is some knowledgeable user, would be helpful if they can explain this a bit more.