A Learnable Radial Basis Positional Embedding for Coordinate-MLPs.

We propose a novel method to enhance the performance of coordinate-MLPs (also referred to as neural fields) by learning instance-specific positional embeddings. End-to-end optimization of positional embedding parameters along with network weights leads to poor generalization performance. Instead, we develop a generic framework to learn the positional embedding based on the classic graph-Laplacian regularization, which can implicitly balance the trade-off between memorization and generalization. This framework is then used to propose a novel positional embedding scheme, where the hyperparameters are learned per coordinate ( i.e instance) to deliver optimal performance. We show that the proposed embedding achieves better performance with higher stability compared to the well-established random Fourier features (RFF). Further, we demonstrate that the proposed embedding scheme yields stable gradients, enabling seamless integration into deep architectures as intermediate layers.