have that when they add more negative so when they increase the batch size that contrastive power increases they do analyze their gradient which I find it's pretty neat you can already see that if you formulate a loss of course the gradient is going to go in the negative direction but they make it clear that if you look at the gradient for the positive cases what appears is this one - pIJ quantity and the pIJ quantity is exactly the inner product between I and J normalized of course so if you minim so the gradient is going to point into