  Coordinate-based networks have emerged as a powerful tool for 3D
representation and scene reconstruction. These networks are trained to map
continuous input coordinates to the value of a signal at each point. Still,
current architectures are black boxes: their spectral characteristics cannot be
easily analyzed, and their behavior at unsupervised points is difficult to
predict. Moreover, these networks are typically trained to represent a signal
at a single scale, so naive downsampling or upsampling results in artifacts. We
introduce band-limited coordinate networks (BACON), a network architecture with
an analytical Fourier spectrum. BACON has constrained behavior at unsupervised
points, can be designed based on the spectral characteristics of the
represented signal, and can represent signals at multiple scales without
per-scale supervision. We demonstrate BACON for multiscale neural
representation of images, radiance fields, and 3D scenes using signed distance
functions and show that it outperforms conventional single-scale coordinate
networks in terms of interpretability and quality.
