Discretization Invariant Learning on Neural Fields

With the ability to generate and store continuous data in the form of neural fields (NFs), there is a need for neural networks that can process such fields in a manner that is invariant to the discretization of the data domain. We introduce INR-Net, a framework for learning discretization invariant maps on NFs of any type. Driven by numerical integration, INR-Net can universally approximate a large class of maps between $L^2$ functions. We demonstrate our framework on NF classification, and examine the network's ability to generalize to different discretizations.