Wavelets help compress neural networks efficiently.
problem Efficiently compressing linear layers in neural networks.
method Learnable wavelet transforms to compress RNNs.
result Wavelet compressed RNNs have fewer parameters and perform competitively.
Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.
problem Learning from raw time-series data efficiently and effectively.
method Constructing scale-translation equivariant neural networks based on wavelet symmetries.
result Wavelet Networks outperform conventional CNNs on raw waveforms and spectrograms.
VDWs enhance graph neural networks for analyzing complex data.
problem Analyzing data on non-Euclidean geometries.
method Incorporating vector diffusion wavelets into geometric graph neural networks.
result VDW-GNNs effectively analyze synthetic and real-world data.
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…
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
Wavelet Kolmogorov-Arnold Networks improve federated learning performance.
problem Improving performance in federated learning with heterogeneous data.
method Implemented Wav-KAN with CWT and DWT for multiresolution capability, integrating wavelet-based activation functions.
result Significant improvements in computational efficiency, robustness, and accuracy in federated learning.
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…
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 …
Express Wavenet reduces neural network parameters to 1% of standard networks.
problem Optical neural networks with high parameter count.
method Wavelet modulation, random shift wavelets, expressway structure.
result Express Wavenet achieves high accuracy with significantly fewer parameters.
AWD distills neural network info into interpretable wavelets.
problem Imbalanced interpretability and efficiency in deep learning models.
method Adaptive wavelet distillation (AWD) penalizes neural network attributions in wavelet domain.
result AWD yields a concise, efficient, and interpretable model.
Wav-KAN improves neural network interpretability and performance.
problem Challenges in interpretability, training speed, robustness, and performance of traditional neural networks.
method Integrates wavelet functions into the Kolmogorov-Arnold network structure for efficient data representation.
result Enhanced accuracy, faster training speeds, and increased robustness compared to existing methods.
Develops wavelet-based neural network approximation theory.
problem Analyzing neural network approximation capabilities over various activation functions.
method Wavelet frame theory on spaces of homogeneous type, sufficient conditions for approximation, error estimates.
result Derives sufficient conditions for neural networks to approximate any functions in a given space, including non-smooth activations.
MODWST improves classification tasks with wavelet scattering.
problem Signal classification challenges.
method Combines MODWT and WST for feature extraction.
result MODWST outperforms CNNs in limited data scenarios.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.
A new WNN framework selects wavelet bases for efficient learning.
problem Challenges in constructing accurate wavelet bases and high computational costs in WNN.
method Introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs.
result Significantly improves computational efficiency through a frequency estimator and wavelet-basis increase mechanism.
WCAM assesses neural network reliability by attributing decisions to wavelet scales.
problem Challenges in evaluating neural network reliability and feature robustness.
method Introduces WCAM, a wavelet-based attribution method to assess decision reliability.
result WCAM reveals where and on what scales a model focuses, enabling reliable decision assessment.
Enhances DSN with multi-family wavelet transforms and sparsity.
problem Improving interpretability and expressive power of DSN.
method Multi-family wavelet transforms and optimal thresholding.
result Enhanced robustness and diversity of scattering coefficients.
Enhanced image denoising with MWRDCNN using residual dense blocks.
problem Image denoising with improved performance and robustness.
method Multi-wavelet residual dense convolutional neural network (MWRDCNN) with residual dense blocks (RDBs).
result Significantly improved performance in image denoising compared to existing techniques.
WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.
problem Current noise generation models in GANs struggle with homogenizing noise, leading to low-fidelity samples.
method Proposes a multi-channel wavelet-based filtering method to homogenize noise in GANs.
result WaveletGAN generates high-fidelity samples with the smallest FIDs on Fashion-MNIST, KMNIST, and SVHN datasets.
Cake wavelets minimize orientation score uncertainty.
problem Minimizing uncertainty in orientation scores.
method Axiomatically derived wavelets for orientation score lifting.
result Uncertainty gap of cake wavelets is less than 1.1.
A new GNN module learns geometric scattering features for better graph classification and feature exploration.
problem Learning long-range graph relations and extracting meaningful features from graphs.
method Proposes a learnable geometric scattering (LEGS) module in graph neural networks (GNNs), incorporating wavelet filters.
result LEGS-based GNNs outperform existing methods in graph classification and feature extraction tasks.
Dual model predicts electricity spot prices using neural networks and wavelets.
problem Forecasting hourly electricity spot prices.
method Dual generalized long memory modelling with k-factor GARMA and G-GARCH models, using LLWNN and PSO for variance prediction.
result The hybrid k-factor GARMA-LLWNN model outperforms other methods in forecasting accuracy.
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…
CGNNs use wavelets for continuous function generation in infinite-dimensional spaces.
problem Generating continuous functions in infinite-dimensional spaces for applications like inverse problems.
method Inspired by DCGAN, CGNNs use wavelet multiresolution analysis with convolutional and nonlinear layers.
result CGNNs can be injective under certain conditions on filters and nonlinearity, leading to Lipschitz stability estimates.
WavPool improves deep neural networks with wavelet-based pooling.
problem Improving efficiency and performance of deep neural networks.
method Introducing WavPool, a wavelet-transform-based pooling layer.
result WavPool outperforms existing network architectures by 10% on CIFAR-10.
Improves CNN stability by translating classical signal denoising methods.
problem Stability of CNNs is poorly understood.
method Interprets classical signal denoising methods as ResNet architectures.
result Translates diffusivities, shrinkage functions, and regularizers into CNN activation functions.
RP-WNO extends WNO with uncertainty quantification, useful for scientists and engineers.
problem Uncertainty in predictions of deep learning models.
method Randomized Prior Wavelet Neural Operator (RP-WNO) with uncertainty quantification module.
result RP-WNO effectively estimates uncertainty in predictions.
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.
problem Interpreting complex biomedical signal models for high-stakes decisions.
method Wavelet features and knockoff variables for feature selection.
result Logistic regression outperforms neural networks in bacterial infection detection.
We discuss approximation of functions using deep neural nets. Given a function f on a d-dimensional manifold Γ⊂Rm, 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…
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
A method uses image processing and deep learning for financial market state prediction.
problem Low signal-to-noise ratio in financial time series data.
method Wavelet transform for denoising, convolutional neural network for pattern extraction.
result Competitive prediction accuracy of market states 'Up' and 'Down' on S&P 500 data.
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…
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…
A cost-effective method to generate high-resolution images using wavelet-based super-resolution.
problem High compute resources required for training state-of-the-art image generation models.
method Wavelet-based two-step training framework: low-frequency sampling followed by super-resolution.
result Achieves FID of 10.59 on ImageNet 512x512 with half the compute of BigGAN.
Compressive sensing is an impressive approach for fast MRI. It aims at reconstructing MR image using only a few under-sampled data in k-space, enhancing the efficiency of the data acquisition. In this study, we propose to learn priors based on undecimated wavelet transform and an iterative image reconstruction algorith…
Tensor network architecture for classification and regression using wavelet transformations.
problem Efficiently performing classification and regression tasks on complex data.
method Tensor network layers based on MERA and MPS, with adaptive fine-graining.
result Adaptive fine-graining improves model performance without loss in accuracy.
Wavelet Attribution Method (WAM) improves feature attribution for deep models.
problem Inability of pixel-based heatmaps to capture data structure and variability in feature attribution.
method Wavelet domain for feature attribution, leveraging spatial and scale-localized properties of wavelet coefficients.
result WAM provides quantitatively superior explanations across audio, image, and volume modalities.
New method selects diffusion scales for graph wavelets.
problem Choosing optimal diffusion scales for graph wavelets.
method Proposes an unsupervised method using information theory.
result Method selects diffusion scales for graph wavelets.
Stockformer uses wavelet transform and multi-task learning to predict stock returns and trends.
problem Challenges in predicting market dynamics due to policy uncertainty and economic events.
method Integrates wavelet transformation and multitask self-attention networks to capture market trends and fluctuations.
result Stockformer outperforms existing models on multiple real stock market datasets, demonstrating exceptional stability and reliability.
This paper proposes the use of wavelet methods to estimate U.S. core inflation. It explains wavelet methods and suggests they are ideally suited to this task. Comparisons are made with traditional CPI-based and regression-based measures for their performance in following trend inflation and predicting future inflation.…
A CNN-based method improves DTI of the human heart, compensating for motion.
problem Signal loss due to heart motion in DTI.
method Invertible Wavelet Scattering using CNN.
result Effective motion compensation and improved fiber structures.
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…
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…
Revisits SWIFT method for option pricing using Shannon wavelets.
problem Improving option pricing under known characteristic functions.
method SWIFT method based on Shannon wavelets.
result Exposes drawbacks and discusses improvements.
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
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…