Adding momentum - sigmoid units, Computer Engineering

Adding Momentum - Sigmoid units:

However imagine a ball rolling down a hill as it does so then it gains momentum in which its speed increases and it becomes more difficult to stop. Alternatively as it rolls down the hill towards the valley floor as the global minimum, then it might occasionally wander into local hollows. Moreover,, there it may be that the momentum it has obtained stays it rolling up and out of the hollow and back on track to the valley floor. 

Hence the crude analogy describes one heuristic technique for avoiding local minima that called adding momentum, funnily enough. Thus the method is simple as: now for each weight remember as the previous value of Δ that was added on to the weight in the last epoch. Rather then, where updating that weight for the current epoch, add on a little of the previous Δ. Now how small to make the additional extra is controlled through a parameter α that's called the momentum which is set to a value between 0 and 1. 

Alternatively to see why this might help bypass local minima so note there that if the weight change carries on in the direction it was going in the previous epoch and then the movement will be a little much more pronounced in the current epoch. Thus this effect will be compounded as the search continues in the same direction. Where the trend finally reverses so then the search may be at the global minimum case there it is hoped that the momentum won't be enough to take it anywhere other than where it is belongs. Conversely the search may be at a fairly narrow local minimum. So next there in this case, even though the back propagation algorithm which dictates Δ will change direction then it may be that the additional extra from the previous epoch as the momentum may be enough to  counteract this effect for a few steps. Then we can saythese few steps may be all that is utilised to bypass the local minimum.

Posted Date: 1/11/2013 7:23:47 AM | Location : United States

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