Sparse convolutional architectures combined with deep networks approximate nonlinear functionals with improved rates that reduce exponential dimension dependence in spaces with fast frequency decay or mixed smoothness.
This implies that sup f∈F |P(f)−Φ( ˜f m)|≲m − β 4 (2a−3)(logm) β 4 (2a−1)+β(d−1)(a+b)+ β 2 ≲(logK) −β(a− 3 2 )(log logK) β(a+(d−1)(a+b)− 1 2 )
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Sparse-Aware Neural Networks for Nonlinear Functionals: Mitigating the Exponential Dependence on Dimension
Sparse convolutional architectures combined with deep networks approximate nonlinear functionals with improved rates that reduce exponential dimension dependence in spaces with fast frequency decay or mixed smoothness.