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For higher dimensional functions, most of the points with zero gradient (stopping points) are saddle points.
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99.8% for 10 dimensions
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If you look at it from the perspective of maximizing utility function, the story goes like this
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Select the product with the largest utility function among those that are not too far removed from the current product.
- = Based on the gradient of the point represented by the current product, update in the direction with the greatest gradient
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Repeat that and you’ll reach the saddle point.
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Utility decreases if you go in the direction you have been going by the time you come to the saddle point.
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We need to go in a completely different direction.
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