How does batch parallel training actually work?

[Martín Sevilla]

I was reading the documentation for Somoclu and it is stated that in order to make the algorithm parallelizable, a batch training mode has to be followed. The equation to update the weights is given in the 4th page of the document.

I don't understand why that formulation works. Shouldn't the factor (x- w) be used instead of just x to achieve convergence? What troubles me is that past values of the weights are not used in the update rule.

Does that equation make sense? If it does, why?