Supremum Norm
Defined as the supremum of the absolute value of a function over its entire domain, it measures the maximum deviation of the function. In function spaces, the supremum norm is stronger than the L2 or Wasserstein distance, requiring simultaneous approximation at all points.
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For polynomial activation functions and arbitrary compact input sets, this lifting gives a rate of m^{-1/2} under the supremum norm, with an explicit constant.
The supremum norm is defined as the maximum deviation of a function over its entire domain, is stronger than L2 or W2, and requires all points to be approximated simultaneously.
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For polynomial activation functions and arbitrary compact input sets, this lifting gives a rate of m^{-1/2} under the supremum norm, with an explicit constant.
50%UnverifiedThe supremum norm is defined as the maximum deviation of a function over its entire domain, is stronger than L2 or W2, and requires all points to be approximated simultaneously.
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