论文标题
普遍的隐式神经代表
Generalised Implicit Neural Representations
论文作者
论文摘要
我们考虑学习隐式神经表示（INRS）的问题，以了解非欧几里得领域的信号。在欧几里得的情况下，对INR进行了培训，以常规晶格的信号的离散采样进行训练。在这里，我们假设连续信号存在于一些未知的拓扑空间上，从中我们采样了离散图。在没有坐标系来识别采样节点的情况下，我们建议使用图形的光谱嵌入近似它们的位置。这使我们能够在不知道基本连续域的情况下训练INR，这对于自然界中的大多数图形信号就是这种情况，同时也使INR独立于任何选择坐标系。我们通过我们的方法展示了非欧几里得领域各种现实世界信号的实验。
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.
