Generalised Implicit Neural Representations
This work addresses the challenge of representing signals on unknown topological spaces, such as graph data in nature, which is incremental by extending INRs to non-Euclidean settings.
The paper tackles the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains by approximating node locations with spectral embeddings when coordinates are unknown, enabling INR training without prior knowledge of the underlying domain. Experiments demonstrate the method's applicability to various real-world graph signals.
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.