 Batch size

Batch size counts the examples combined in a mini-batch. In the simple stochastic gradient descent loop where each group produces one parameter update, it controls how many examples contribute to that update. It differs from a training epoch, which counts a pass over the available training data.^[ref]

For an original counting example, partition ten examples with nominal batch size $b=4$ and retain the remainder. The actual sizes are $4,4,2$, giving $\lceil 10/4\rceil =3$ updates per training epoch. Discarding the remainder instead gives two updates and uses only eight examples. More generally the retained-remainder update count is $\lceil n/b\rceil$ for $n$ examples, provided there is one update per group.

Batch size also changes gradient sampling noise. If independently sampled component gradients at a fixed parameter have scalar variance ${\sigma }^2$, their sample mean hasFor an original exact example, suppose one component gradient is equally likely to be 0 or 2. Its mean is 1 and variance is 1. A two-example mini-batch gradient takes values $0,1,2$ with probabilities $1/4,1/2,1/4$, giving variance $1/2$. This calculation holds parameters fixed and assumes independent sampling; sampling without replacement has a finite population correction.

With gradient accumulation, several groups may contribute before an update. Two full four-example groups then involve eight examples per update if their gradients are normalized consistently. State whether a reported size counts the processed group or all examples contributing to an update. Lower sampling variance alone does not establish faster training for a fixed computation budget.