I suspect actually there is some connection between optimal batch size and the proofs of this paper regarding how deep NN will provably converge to zero trainin

I suspect actually there is some connection between optimal batch size and the proofs of this paper regarding how deep NN will provably converge to zero training loss with gradient descent (not stochastic gradient descent). https://arxiv.org/abs/1811.03804 https://arxiv.org/abs/1811.03804