4e8eaf897c638d519710b1691121f8cb-Supplemental.pdf

Supplementary material for'Locality defeats the curse of dimensionality in convolutional teacher-student scenarios' In this appendix we provide additional details about the derivation of Eq. (8) within the framework's are free to take any value. Finally, Eq. (8) is obtained by noticing that, under our assumptions on the decay of If all the parameters are initialised independently from a standard Normal distribution, Eq. (13) is In this section we prove the eigendecompositions introduced in Lemma 3.3 and Lemma 3.4, then extend them to overlapping-patches kernel (cf. We start by proving orthonormality of the eigenfunctions. Then, we prove that the eigenfunctions and the eigenvalues defined in Eq. (17) satisfy the kernel We start again by proving the orthonormality of the eigenfunctions. Then, we prove that the eigenfunctions and the eigenvalues defined in Eq. (19) satisfy the kernel In this section Lemma 3.3 and Lemma 3.4 are extended to kernels with overlapping patches, having (u 1) 's, we have introduced an apex We start by proving the orthonormality of the eigenfunctions.