  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}.
