Research map / Learning theory and algorithms / Sample complexity
Optimal Minimum Width for the Universal Approximation of Continuously Differentiable Functions by Deep Narrow MLPs
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Studies the minimum width for deep narrow MLPs to universally approximate C^1 functions in the W^{1,∞} Sobolev norm, a theoretical question about approximation capacity.
Problem
Determining the optimal minimum width of deep, narrow MLPs that can universally approximate C^1 functions under the W^{1,∞} Sobolev norm, which is less understood than the continuous-function case.
Approach
Extends optimal-width universal approximation results from continuous functions to C^1 functions measured in the W^{1,∞} norm, characterizing the minimal width needed for deep narrow MLPs.
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