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About this paper
Lukas Herrmann, Christoph Schwab, Jakob Zech
The authors construct neural and sparse polynomial surrogates for maps between infinite-dimensional function spaces. They encode inputs and outputs with stable basis or frame coefficients, approximate the coefficient map with ReLU networks or sparse multivariate polynomials, then decode the output. Under holomorphy and finite-regularity assumptions, both achieve algebraic worst-case rates; these are proved approximation bounds, not runtime or empirical performance.
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