Generalised Implicit Neural Representations

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal exists on some unknown topological space from which we sample a discrete graph. In the absence of a coordinate system to identify the sampled nodes, we propose approximating their location with a spectral embedding of the graph. This allows us to train INRs without knowing the underlying continuous domain, which is the case for most graph signals in nature, while also making the INRs equivariant under the symmetry group of the domain. We show experiments with our method on various real-world signals on non-Euclidean domains.