Generalised Implicit Neural Representations

Daniele Grattarola, Pierre Vandergheynst

Keywords: implicit neural representations, neural fields

TL;DR: We train implicit neural representations for signals on non-Euclidean domains, showing experiments with biological, social, and meteorological data.

Abstract:

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 independent of any choice of coordinate system. We show experiments with our method on various real-world signals on non-Euclidean domains.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2205.15674/code)