While finite-dimensional irreducible representations (IRs) are attractive building blocks for equivariance due to their computationally exploitable structure, theyoften don'texist fornon-compact groups, precluding generalizations to most non-linear symmetries, let alone those ill-modeled by groups.

Specifically, we regularize the latent space such that maps between encodings preserve a learned inner product and commute with a learned functional operator, in the same manner as rigid-body transformations commute with the Laplacian.

Computational Geometry, and related fields.

Different from existing works that represent deformation fields by training a general-purpose neural network, we advocate for an approximation based on mesh-free methods. By letting the network learn deformation parameters at a sparse set of positions in space (nodes), we reconstruct the continuous deformation field in a closed-form with guaranteed smoothness.