Your intuition is off, but only slightly. As the dimensionality increases, the number of stationary points (zero gradient) also increases. But they become overw

Your intuition is off, but only slightly. As the dimensionality increases, the number of stationary points (zero gradient) also increases. But they become overwhelmingly likely to be saddle points rather than minima. You can read more here [1]. [1] http://ganguli-gang.stanford.edu/pdf/14.SaddlePoint.NIPS.pdf http://ganguli-gang.stanford.edu/pdf/14.SaddlePoint.NIPS.pdf