Deep Learning on Implicit Neural Datasets
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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→label) and segmentation (INR→INR) tasks.
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