Papers
arxiv:2206.01178

Discretization Invariant Networks for Learning Maps between Neural Fields

Published on Jun 2, 2022
Authors:
,

Abstract

Discretization invariant neural networks generalize discrete and continuous networks while maintaining consistent performance across different sampling methods, enabling robust learning from neural fields.

AI-generated summary

With the emergence of powerful representations of continuous data in the form of neural fields, there is a need for discretization invariant learning: an approach for learning maps between functions on continuous domains without being sensitive to how the function is sampled. We present a new framework for understanding and designing discretization invariant neural networks (DI-Nets), which generalizes many discrete networks such as convolutional neural networks as well as continuous networks such as neural operators. Our analysis establishes upper bounds on the deviation in model outputs under different finite discretizations, and highlights the central role of point set discrepancy in characterizing such bounds. This insight leads to the design of a family of neural networks driven by numerical integration via quasi-Monte Carlo sampling with discretizations of low discrepancy. We prove by construction that DI-Nets universally approximate a large class of maps between integrable function spaces, and show that discretization invariance also describes backpropagation through such models. Applied to neural fields, convolutional DI-Nets can learn to classify and segment visual data under various discretizations, and sometimes generalize to new types of discretizations at test time. Code: https://github.com/clintonjwang/DI-net.

Community

Sign up or log in to comment

Get this paper in your agent:

hf papers read 2206.01178
Don't have the latest CLI?
curl -LsSf https://hf.co/cli/install.sh | bash

Models citing this paper 0

No model linking this paper

Cite arxiv.org/abs/2206.01178 in a model README.md to link it from this page.

Datasets citing this paper 1

Spaces citing this paper 0

No Space linking this paper

Cite arxiv.org/abs/2206.01178 in a Space README.md to link it from this page.

Collections including this paper 0

No Collection including this paper

Add this paper to a collection to link it from this page.