Fourier Neural Networks for Function Approximation

• URL: http://arxiv.org/abs/2111.08438v1
• Date: Thu, 21 Oct 2021 09:30:26 GMT
• Title: Fourier Neural Networks for Function Approximation
• Authors: R Subhash Chandra Bose, Kakarla Yaswanth
• Abstract summary: It is proved extensively that neural networks are universal approximators. It is specifically proved that for a narrow neural network to approximate a function which is otherwise implemented by a deep Neural network, the network take exponentially large number of neurons.
• Score: 2.840363325289377
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The success of Neural networks in providing miraculous results when applied to a wide variety of tasks is astonishing. Insight in the working can be obtained by studying the universal approximation property of neural networks. It is proved extensively that neural networks are universal approximators. Further it is proved that deep Neural networks are better approximators. It is specifically proved that for a narrow neural network to approximate a function which is otherwise implemented by a deep Neural network, the network take exponentially large number of neurons. In this work, we have implemented existing methodologies for a variety of synthetic functions and identified their deficiencies. Further, we examined that Fourier neural network is able to perform fairly good with only two layers in the neural network. A modified Fourier Neural network which has sinusoidal activation and two hidden layer is proposed and the results are tabulated.

Related papers

• Graph Neural Networks for Learning Equivariant Representations of Neural Networks [55.04145324152541]
  We propose to represent neural networks as computational graphs of parameters. Our approach enables a single model to encode neural computational graphs with diverse architectures. We showcase the effectiveness of our method on a wide range of tasks, including classification and editing of implicit neural representations.
  arXiv  Detail & Related papers  (2024-03-18T18:01:01Z)
• Addressing caveats of neural persistence with deep graph persistence [54.424983583720675]
  We find that the variance of network weights and spatial concentration of large weights are the main factors that impact neural persistence. We propose an extension of the filtration underlying neural persistence to the whole neural network instead of single layers. This yields our deep graph persistence measure, which implicitly incorporates persistent paths through the network and alleviates variance-related issues.
  arXiv  Detail & Related papers  (2023-07-20T13:34:11Z)
• Exploring the Approximation Capabilities of Multiplicative Neural Networks for Smooth Functions [9.936974568429173]
  We consider two classes of target functions: generalized bandlimited functions and Sobolev-Type balls. Our results demonstrate that multiplicative neural networks can approximate these functions with significantly fewer layers and neurons. These findings suggest that multiplicative gates can outperform standard feed-forward layers and have potential for improving neural network design.
  arXiv  Detail & Related papers  (2023-01-11T17:57:33Z)
• Spiking neural network for nonlinear regression [68.8204255655161]
  Spiking neural networks carry the potential for a massive reduction in memory and energy consumption. They introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. A framework for regression using spiking neural networks is proposed.
  arXiv  Detail & Related papers  (2022-10-06T13:04:45Z)
• Consistency of Neural Networks with Regularization [0.0]
  This paper proposes the general framework of neural networks with regularization and prove its consistency. Two types of activation functions: hyperbolic function(Tanh) and rectified linear unit(ReLU) have been taken into consideration.
  arXiv  Detail & Related papers  (2022-06-22T23:33:39Z)
• Why Quantization Improves Generalization: NTK of Binary Weight Neural Networks [33.08636537654596]
  We take the binary weights in a neural network as random variables under rounding, and study the distribution propagation over different layers in the neural network. We propose a quasi neural network to approximate the distribution propagation, which is a neural network with continuous parameters and smooth activation function.
  arXiv  Detail & Related papers  (2022-06-13T06:11:21Z)
• Stochastic Neural Networks with Infinite Width are Deterministic [7.07065078444922]
  We study neural networks, a main type of neural network in use. We prove that as the width of an optimized neural network tends to infinity, its predictive variance on the training set decreases to zero.
  arXiv  Detail & Related papers  (2022-01-30T04:52:31Z)
• The Connection Between Approximation, Depth Separation and Learnability in Neural Networks [70.55686685872008]
  We study the connection between learnability and approximation capacity. We show that learnability with deep networks of a target function depends on the ability of simpler classes to approximate the target.
  arXiv  Detail & Related papers  (2021-01-31T11:32:30Z)
• Theoretical Analysis of the Advantage of Deepening Neural Networks [0.0]
  It is important to know the expressivity of functions computable by deep neural networks. By the two criteria, we show that to increase layers is more effective than to increase units at each layer on improving the expressivity of deep neural networks.
  arXiv  Detail & Related papers  (2020-09-24T04:10:50Z)
• Graph Structure of Neural Networks [104.33754950606298]
  We show how the graph structure of neural networks affect their predictive performance. A "sweet spot" of relational graphs leads to neural networks with significantly improved predictive performance. Top-performing neural networks have graph structure surprisingly similar to those of real biological neural networks.
  arXiv  Detail & Related papers  (2020-07-13T17:59:31Z)
• Towards Understanding Hierarchical Learning: Benefits of Neural Representations [160.33479656108926]
  In this work, we demonstrate that intermediate neural representations add more flexibility to neural networks. We show that neural representation can achieve improved sample complexities compared with the raw input. Our results characterize when neural representations are beneficial, and may provide a new perspective on why depth is important in deep learning.
  arXiv  Detail & Related papers  (2020-06-24T02:44:54Z)

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.