# Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives

Source: [Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives](<https://www.sota2.com/research/paper/68fa6d101e209131cea37644>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-26T00:24:36.116Z

Authors: Wentao Yuan, Qingtian Zhu, Xiangyue Liu, Yikang Ding, Haotian Zhang, Chi Zhang

Published: 2022-07-21T10:12:41.000Z

## Abstract

Recently, Implicit Neural Representations (INRs) parameterized by neural networks have emerged as a powerful and promising tool to represent different kinds of signals due to its continuous, differentiable properties, showing superiorities to classical discretized representations. However, the training of neural networks for INRs only utilizes input-output pairs, and the derivatives of the target output with respect to the input, which can be accessed in some cases, are usually ignored. In this paper, we propose a training paradigm for INRs whose target output is image pixels, to encode image derivatives in addition to image values in the neural network. Specifically, we use finite differences to approximate image derivatives. We show how the training paradigm can be leveraged to solve typical INRs problems, i.e., image regression and inverse rendering, and demonstrate this training paradigm can improve the data-efficiency and generalization capabilities of INRs. The code of our method is available at \\url{https://github.com/megvii-research/Sobolev\_INRs}.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Scattered-domain fitting on Scattered-domain blobs sampling 256x256, N=8,192 (test)](<https://www.sota2.com/research/sota/scattered-domain-fitting-on-scattered-domain-blobs-sampling-256x256-n-8-192-test.md>): Scattered-domain fitting; Scattered-domain blobs sampling 256x256, N=8,192 (test); PSNR: 23.02.

- [Scattered-domain fitting on Scattered-domain ramp sampling 256x256, N=8,192 (test)](<https://www.sota2.com/research/sota/scattered-domain-fitting-on-scattered-domain-ramp-sampling-256x256-n-8-192-test.md>): Scattered-domain fitting; Scattered-domain ramp sampling 256x256, N=8,192 (test); PSNR: 22.74.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2207.10395>)

[PDF](<https://arxiv.org/pdf/2207.10395.pdf>)