ReLUs Are Sufficient for Learning Implicit Neural Representations

• URL: http://arxiv.org/abs/2406.02529v1
• Date: Tue, 4 Jun 2024 17:51:08 GMT
• Title: ReLUs Are Sufficient for Learning Implicit Neural Representations
• Authors: Joseph Shenouda, Yamin Zhou, Robert D. Nowak,
• Abstract summary: We revisit the use of ReLU activation functions for learning implicit neural representations. 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) We demonstrate that, contrary to popular belief, one can learn state-of-the-art INRs based on a DNN composed of only ReLU neurons.
• Score: 17.786058035763254
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Topological Representations of Heterogeneous Learning Dynamics of Recurrent Spiking Neural Networks [16.60622265961373]
  Spiking Neural Networks (SNNs) have become an essential paradigm in neuroscience and artificial intelligence. Recent advances in literature have studied the network representations of deep neural networks.
  arXiv  Detail & Related papers  (2024-03-19T05:37:26Z)
• Manipulating Feature Visualizations with Gradient Slingshots [54.31109240020007]
  We introduce a novel method for manipulating Feature Visualization (FV) without significantly impacting the model's decision-making process. We evaluate the effectiveness of our method on several neural network models and demonstrate its capabilities to hide the functionality of arbitrarily chosen neurons.
  arXiv  Detail & Related papers  (2024-01-11T18:57:17Z)
• A Hybrid Neural Coding Approach for Pattern Recognition with Spiking Neural Networks [53.31941519245432]
  Brain-inspired spiking neural networks (SNNs) have demonstrated promising capabilities in solving pattern recognition tasks. These SNNs are grounded on homogeneous neurons that utilize a uniform neural coding for information representation. In this study, we argue that SNN architectures should be holistically designed to incorporate heterogeneous coding schemes.
  arXiv  Detail & Related papers  (2023-05-26T02:52:12Z)
• Permutation Equivariant Neural Functionals [92.0667671999604]
  This work studies the design of neural networks that can process the weights or gradients of other neural networks. We focus on the permutation symmetries that arise in the weights of deep feedforward networks because hidden layer neurons have no inherent order. In our experiments, we find that permutation equivariant neural functionals are effective on a diverse set of tasks.
  arXiv  Detail & Related papers  (2023-02-27T18:52:38Z)
• SignReLU neural network and its approximation ability [8.94250977764275]
  We explore the approximation ability of deep neural networks (DNNs) using a different activation function, called SignReLU. Our theoretical results demonstrate that SignReLU networks outperform rational and ReLU networks in terms of approximation performance.
  arXiv  Detail & Related papers  (2022-10-19T02:59:31Z)
• Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study [55.12108376616355]
  The study on NTK has been devoted to typical neural network architectures, but is incomplete for neural networks with Hadamard products (NNs-Hp) In this work, we derive the finite-width-K formulation for a special class of NNs-Hp, i.e., neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK.
  arXiv  Detail & Related papers  (2022-09-16T06:36:06Z)
• Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions [4.932130498861987]
  We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. Under suitable conditions, KNNs induce a faster decay of the loss than that by the feed-forward networks.
  arXiv  Detail & Related papers  (2021-05-20T04:54:57Z)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)
• A Deep Conditioning Treatment of Neural Networks [37.192369308257504]
  We show that depth improves trainability of neural networks by improving the conditioning of certain kernel matrices of the input data. We provide versions of the result that hold for training just the top layer of the neural network, as well as for training all layers via the neural tangent kernel.
  arXiv  Detail & Related papers  (2020-02-04T20:21:36Z)
• Non-linear Neurons with Human-like Apical Dendrite Activations [81.18416067005538]
  We show that a standard neuron followed by our novel apical dendrite activation (ADA) can learn the XOR logical function with 100% accuracy. We conduct experiments on six benchmark data sets from computer vision, signal processing and natural language processing.
  arXiv  Detail & Related papers  (2020-02-02T21:09:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.