7. Examples on infinite-dimensional spaces🔗

The exact targets and integral networks have genuinely infinite-dimensional inputs. Their finite-width approximants use finitely many linear measurements. We establish the Gaussian integral before computing a target transform, and the hinge identity before using Gaussian-parameter networks. Explicit operator layers and equivariance then lead to convolution and Dirichlet examples. Section 8 checks approximation and transform formulas numerically.

1. 7.1. A Gaussian integral and a target with a closed-form transform
2. 7.2. Gaussian-parameter networks on l2
3. 7.3. Neural-operator layers
4. 7.4. Periodic convolution layers
5. 7.5. Dirichlet solution layers