Abstract:This work studies operators mapping vector and scalar fields defined over a manifold M, and which commute with its group of diffeomorphisms Diff(M). We prove that in the case of scalar fields L p ω (M, R), those operators correspond to point-wise non-linearities, recovering and extending known results on R d . In the context of Neural Networks defined over M, it indicates that point-wise nonlinear operators are the only universal family that commutes with any group of symmetries, and justifies their systematic… Show more
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