1. The small subset is to test that your training pipeline works and converges near 0 loss.

2. Sure, but for most new hacks like mixup, randaugment and etc the results usually transfer over. Problem with deep learning is that most of the new results don't replicate so it's good to have a way to quickly validate things.

3. The lower level features are usually pretty data agnostic and transfer well to new tasks.

1. Gradient descent almost always finds a non optimum local min (it is not guaranteed to find a global min).

Isn’t the current best practice to train highly over-parametrized models to zero training error? That’d be a global optima, no?

Unless we’re talking about the optima of test error.

If you find a zero in a non negative function, I would call that a global minima, yes.

Yeah but depending on the data you might have even worse results, selecting the right subset to be representative is really important.

Would a random sample be representative? Statistically this seems to be the case for any large N. In fact it's not clear to me that any other sample would be more representative.

Many public datasets have skewed classes so if you take a random approach you're not gonna have a good result. And N might not be big enough anyway.