We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijec-tive neural operators through the lens of diffeomorphisms in infinite dimensions.

Other concurrent works address, e.g., learning from soft interventions with polynomial mixing [

Global stability and robustness guarantees in learned dynamical systems are essential to ensure well-behavedness of the systems in the face of uncertainty.

Neural Information Processing Systems http://nips.cc/

Lemma B.4. (Lemma 2.1.8 in [4]) For any diffeomorphismf Diffkc Rd and any δ > 0, there exists a finite sequence of(δ,k)-near-identity diffeomorphismsg1,,gs such that f = gs gs 1 g1. Let πi: Rd R denote the projection onto theith coordinate. Supposef: Rd Rd is compactly supported and sufficientlyCk-close to the identity. In this section, we analysis how to make the affine coupling flow with dimension-augmentation invertible. Tohandle this problem, we need to makesure thatRange(F)is tractable for easy sampling.

The derivation is based on Section 3.2.