arXiv research

Wavelets help compress neural networks efficiently.

VDWs enhance graph neural networks for analyzing complex data.

Paper introduces rational Gaussian wavelets for efficient signal approximation.

Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.

In this work we propose a method for learning wavelet filters directly from data. We accomplish this by framing the discrete wavelet transform as a modified convolutional neural network. We introduce an autoencoder wavelet transform network that is trained using gradient descent. We show that the model is capable of le…

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform. Different from graph Fourier transform, graph wavelet transform can be obtained …

AWD distills neural network info into interpretable wavelets.

Develops wavelet-based neural network approximation theory.

Wav-KAN improves neural network interpretability and performance.

The wavelet transform has seen success when incorporated into neural network architectures, such as in wavelet scattering networks. More recently, it has been shown that the dual-tree complex wavelet transform can provide better representations than the standard transform. With this in mind, we extend our previous meth…

Wavelet Kolmogorov-Arnold Networks improve federated learning performance.

WCAM assesses neural network reliability by attributing decisions to wavelet scales.

Express Wavenet is an improved optical diffractive neural network. At each layer, it uses wavelet-like pattern to modulate the phase of optical waves. For input image with n2 pixels, express wavenet reduce parameter number from O(n2) to O(n). Only need one percent of the parameters, and the accuracy is still very high.…

Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.

A new WNN framework selects wavelet bases for efficient learning.

WavPool improves deep neural networks with wavelet-based pooling.

MODWST improves classification tasks with wavelet scattering.

Dual model predicts electricity spot prices using neural networks and wavelets.

RP-WNO extends WNO with uncertainty quantification, useful for scientists and engineers.

We discuss approximation of functions using deep neural nets. Given a function $f$ on a $d$-dimensional manifold $Γ\subset \mathbb{R}^m$, we construct a sparsely-connected depth-4 neural network and bound its error in approximating $f$. The size of the network depends on dimension and curvature of the manifold $Γ$, the…

We develop a neural network model to classify liver cancer patients into high-risk and low-risk groups using genomic data. Our approach provides a novel technique to classify big data sets using neural network models. We preprocess the data before training the neural network models. We first expand the data using wavel…

Networks with large receptive field (RF) have shown advanced fitting ability in recent years. In this work, we utilize the short-term residual learning method to improve the performance and robustness of networks for image denoising tasks. Here, we choose a multi-wavelet convolutional neural network (MWCNN), one of the…

CGNNs use wavelets for continuous function generation in infinite-dimensional spaces.

A new GNN module learns geometric scattering features for better graph classification and feature exploration.

Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer…

Recent years have witnessed the unprecedented rising of time series from almost all kindes of academic and industrial fields. Various types of deep neural network models have been introduced to time series analysis, but the important frequency information is yet lack of effective modeling. In light of this, in this pap…

Logistic regression with wavelets achieves bacterial infection detection accuracy.

MathNet uses wavelets for graph representation and learning.

A method uses image processing and deep learning for financial market state prediction.

We present a logarithmic-scale efficient convolutional neural network architecture for edge devices, named WaveletNet. Our model is based on the well-known depthwise convolution, and on two new layers, which we introduce in this work: a wavelet convolution and a depthwise fast wavelet transform. By breaking the symmetr…

Study shows neural network parameters converge to ridgelet spectrum.

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric…

Model based iterative reconstruction (MBIR) algorithms for low-dose X-ray CT are computationally expensive. To address this problem, we recently proposed a deep convolutional neural network (CNN) for low-dose X-ray CT and won the second place in 2016 AAPM Low-Dose CT Grand Challenge. However, some of the texture were n…

The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducin…

Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction …

Deep neural networks have presented impressive performance in biometric applications. However, their performance is highly at risk when facing carefully crafted input samples known as adversarial examples. In this paper, we present three defense strategies to detect adversarial iris examples. These defense strategies a…

Convolutional neural networks (CNNs) often perform well, but their stability is poorly understood. To address this problem, we consider the simple prototypical problem of signal denoising, where classical approaches such as nonlinear diffusion, wavelet-based methods and regularisation offer provable stability guarantee…

We study the possibility of completing data bases of a sample of governance, diversification and value creation variables by providing a well adapted method to reconstruct the missing parts in order to obtain a complete sample to be applied for testing the ownership-structure/diversification relationship. It consists o…

This research predicts Bitcoin prices using wavelet and deep stacking approach.

Representation costs in data science: Unifying function-space views of parametric methods

Kernel extreme learning machine (KELM) is a novel feedforward neural network, which is widely used in classification problems. To some extent, it solves the existing problems of the invalid nodes and the large computational complexity in ELM. However, the traditional KELM classifier usually has a low test accuracy when…

A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized i…

Low-cost water-level tracking using LTE power metrics and wavelet analysis.

Wavelet Attribution Method (WAM) improves feature attribution for deep models.

Paper introduces a neural framework for accurate energy forecasting.

Noise-resilient method improves Hurst exponent estimation accuracy in noisy data.

Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements. This success can be attributed in part to their ability to represent and generate…

Enhances DSN with multi-family wavelet transforms and sparsity.