5 min readNeural Networks
The Slowest Direction Sets the Pace
The step size you are allowed is fixed by the steepest direction and the number of steps you need is fixed by the flattest, so the cost of gradient descent is their ratio. The same least-squares fit, to the same ten decimal places, takes 1742 steps in one basis, 147 in a rescaled one and exactly 1 in an orthonormal one, and momentum buys back the square root of the ratio rather than the ratio.
Machine LearningMathematics