Equivariant Wavelets: Fast Rotation and Translation Invariant Wavelet Scattering Transforms

Towards an Optimal Estimation of Cosmological Parameters with the Wavelet Scattering Transform

“…Using equivariant wavelets applied on 2D images, some residual power was found to lie in the coefficients usually discarded 6 . In addition, [44] did not find a clear divide in the usefulness of the various second order coefficients, as can be seen from Fig. 11 of that work.…”

“…[39,40]. We note, however, that this is not necessarily always the case, as evidenced by [44]. Using equivariant wavelets applied on 2D images, some residual power was found to lie in the coefficients usually discarded 6 .…”

“…Furthermore, in direct analogy to the chemistry investigations mentioned above, one may further optimize the performance of the WST for LSS applications in particular, using wavelets designed to leverage existing symmetries (as for example in Ref. [44]). We plan to explore these issues in upcoming work.…”

“…If one wants to further reduce the dimensionality of the problem, coefficients with a greater degree of isotropy, S Iso , can be constructed [36,37,39], by averaging over all l's for a given j combination, thus reducing the total number of S 1 + S 2 coefficients by a factor of (L + 1). For a more sophisticated attempt at preserving isotropy, we refer the readers to [44]. Unless stated otherwise, we hereafter choose the pair of values J = 4 and L = 4 as our baseline case, which corresponds to a total of 76 coefficients and 16 isotropic ones.…”

Inferring dark matter substructure with astrometric lensing beyond the power spectrum

“…The use of architectures that can equivariantly handle vector inputs [52] can aid in learning more efficient representations of the astrometric map. Using convolutions based on fixed rather than learned filters can additionally reduce model complexity and produce more interpretable representations [53][54][55][56][57].…”