Abstract

Implicit neural representations (INRs) have become fast, lightweight tools for storing continuous data, but to date there is no general method for learning directly with INRs as a data representation. We introduce a principled deep learning framework for learning and inference directly with INRs of any type without reverting to grid-based features or operations. Our INR-Nets evaluate INRs on a low discrepancy sequence, enabling quasi-Monte Carlo (QMC) integration throughout the network. We prove INR-Nets are universal approximators on a large class of maps between $L^2$ functions. Additionally, INR-Nets have convergent gradients under the empirical measure, enabling backpropagation. We design INR-Nets as a continuous generalization of discrete networks, enabling them to be initialized with pre-trained models. We demonstrate learning of INR-Nets on classification (INR$\to$label) and segmentation (INR$\to$INR) tasks.