ReLUs Are Sufficient for Learning Implicit Neural Representations

Joseph Shenouda, Yamin Zhou, Robert D Nowak
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:44800-44814, 2024.

Abstract

Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations (INRs). Inspired by second order B-spline wavelets, we incorporate a set of simple constraints to the ReLU neurons in each layer of a deep neural network (DNN) to remedy the spectral bias. This in turn enables its use for various INR tasks. Empirically, we demonstrate that, contrary to popular belief, one can learn state-of-the-art INRs based on a DNN composed of only ReLU neurons. Next, by leveraging recent theoretical works which characterize the kinds of functions ReLU neural networks learn, we provide a way to quantify the regularity of the learned function. This offers a principled approach to selecting the hyperparameters in INR architectures. We substantiate our claims through experiments in signal representation, super resolution, and computed tomography, demonstrating the versatility and effectiveness of our method. The code for all experiments can be found at https://github.com/joeshenouda/relu-inrs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-shenouda24a, title = {{R}e{LU}s Are Sufficient for Learning Implicit Neural Representations}, author = {Shenouda, Joseph and Zhou, Yamin and Nowak, Robert D}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {44800--44814}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/shenouda24a/shenouda24a.pdf}, url = {https://proceedings.mlr.press/v235/shenouda24a.html}, abstract = {Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations (INRs). Inspired by second order B-spline wavelets, we incorporate a set of simple constraints to the ReLU neurons in each layer of a deep neural network (DNN) to remedy the spectral bias. This in turn enables its use for various INR tasks. Empirically, we demonstrate that, contrary to popular belief, one can learn state-of-the-art INRs based on a DNN composed of only ReLU neurons. Next, by leveraging recent theoretical works which characterize the kinds of functions ReLU neural networks learn, we provide a way to quantify the regularity of the learned function. This offers a principled approach to selecting the hyperparameters in INR architectures. We substantiate our claims through experiments in signal representation, super resolution, and computed tomography, demonstrating the versatility and effectiveness of our method. The code for all experiments can be found at https://github.com/joeshenouda/relu-inrs.} }
Endnote
%0 Conference Paper %T ReLUs Are Sufficient for Learning Implicit Neural Representations %A Joseph Shenouda %A Yamin Zhou %A Robert D Nowak %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-shenouda24a %I PMLR %P 44800--44814 %U https://proceedings.mlr.press/v235/shenouda24a.html %V 235 %X Motivated by the growing theoretical understanding of neural networks that employ the Rectified Linear Unit (ReLU) as their activation function, we revisit the use of ReLU activation functions for learning implicit neural representations (INRs). Inspired by second order B-spline wavelets, we incorporate a set of simple constraints to the ReLU neurons in each layer of a deep neural network (DNN) to remedy the spectral bias. This in turn enables its use for various INR tasks. Empirically, we demonstrate that, contrary to popular belief, one can learn state-of-the-art INRs based on a DNN composed of only ReLU neurons. Next, by leveraging recent theoretical works which characterize the kinds of functions ReLU neural networks learn, we provide a way to quantify the regularity of the learned function. This offers a principled approach to selecting the hyperparameters in INR architectures. We substantiate our claims through experiments in signal representation, super resolution, and computed tomography, demonstrating the versatility and effectiveness of our method. The code for all experiments can be found at https://github.com/joeshenouda/relu-inrs.
APA
Shenouda, J., Zhou, Y. & Nowak, R.D.. (2024). ReLUs Are Sufficient for Learning Implicit Neural Representations. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:44800-44814 Available from https://proceedings.mlr.press/v235/shenouda24a.html.

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