In the diagram below, although the flow of information happens from the input to output layer, the labeling of weights appears reverse. Eg: For the arrow flowing from X3 to the fourth hidden layer node has the weight labeled as W(1,0) and W(4,3) instead of W(0,1) and W(3,4) which would indicate data flowing from the 3rd node of the 0'th layer to the 4th node of the 1st layer.
One of my neural networks teachers did not emphasize on this convention at all. Another teacher made it a point to emphasize on it.
Is there a reason there is such an un-intuitive convention and is there really a convention?