GNF: Gaussian Neural Fields for Multidimensional Signal Representation and Reconstruction

Neural fields have emerged as a powerful framework for representing continuous multidimensional signals such as images and videos, 3D and 4D objects and scenes, and radiance fields. While efficient, achieving high-quality representation requires the use of wide and deep neural networks. These, however, are slow to train and evaluate. Although several acceleration techniques have been proposed, they either trade memory for faster training and/or inference, rely on thousands of fitted primitives with considerable optimization time, or compromise the smooth, continuous nature of neural fields. In this paper, we introduce Gaussian Neural Fields (GNF), a novel compact neural decoder that maps learned feature grids into continuous non-linear signals, such as RGB images, Signed Distance Functions (SDFs), and radiance fields, using a single compact layer of Gaussian kernels defined in a high-dimensional feature space. Our key observation is that neurons in traditional MLPs perform simple computations, usually a dot product followed by an activation function, necessitating wide and deep MLPs or high-resolution feature grids to model complex functions. In this paper, we show that replacing MLP-based decoders with Gaussian kernels whose centers are learned features yields highly accurate representations of 2D (RGB), 3D (geometry), and 5D (radiance fields) signals with just a single layer of such kernels. This representation is highly parallelizable, operates on low-resolution grids, and trains in under 15 seconds for 3D geometry and under 11 minutes for view synthesis. GNF matches the accuracy of deep MLP-based decoders with far fewer parameters and significantly higher inference throughput.