GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.
Unified graph scattering transforms improve theoretical properties of graph neural networks.
problem Improving theoretical guarantees for graph neural networks.
method Introducing windowed and non-windowed geometric scattering transforms for graphs.
result Unified family of graph scattering transforms with provable stability and invariance.
Geometric wavelet scattering on manifolds improves neural network understanding.
problem Improving neural network understanding on manifold and graph domains.
method Defining a geometric scattering transform based on wavelet filters and nonlinearities.
result Generalizes deformation stability and local translation invariance to manifolds.
Graph scattering transforms are stable to metric perturbations of network topology.
problem Stability of graph data representations under metric perturbations.
method Extending scattering transforms to network data using multiresolution graph wavelets and graph convolutions.
result Graph scattering transforms are stable to metric perturbations of the underlying network topology.
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An expected scattering defines a contractive representation of a high-dimensional probabil…
Scattering networks improve image representation learning without deep learning.
problem Improving image representation learning without deep learning.
method Scattering networks as generic representations in scattering space.
result Scattering networks achieve competitive results in supervised and unsupervised learning.
Geometric scattering on manifolds improves neural network performance.
problem Improving neural network performance on manifold data.
method Generalized Euclidean scattering transform to compact manifolds.
result Geometric scattering provides localized isometry invariant descriptions of manifold signals.
Scattering networks maximize separation on low-dimensional data.
problem Maximizing separation capacity on low-dimensional datasets.
method Characterize and bound separation capacity for feature extractors, then apply to scattering networks with specific criteria.
result Design criteria for scattering networks to maximize separation on low-dimensional data.
Proposes Haar Scattering Networks for better feature extraction.
problem Improving feature extraction in various signal processing and system identification tasks.
method Building function approximators on top of Haar Scattering Networks.
result Demonstrates the architecture's effectiveness in multiple fields.
WideBNet learns inverse scattering from wide-band data efficiently and stably.
problem Learning the inverse scattering map from wide-band scattering data.
method Combines butterfly factorization, FFT, and deep learning.
result WideBNet requires fewer training points and has stable training dynamics.
A deep network classifies images by scattering and dictionary learning.
problem Classifying images with high accuracy using deep learning.
method Sparse scattering transform followed by ℓ1 dictionary learning in a deep convolutional network. result Higher classification accuracy than AlexNet on ImageNet dataset.
Deep learning solves wave-based inverse problems, including super-resolution imaging.
problem Solving inverse wave scattering problems across all length scales.
method Wide-band butterfly network coupled with dynamic noise injection.
result Framework successfully solves super-resolution imaging problems.
Generative models are created by inverting a wavelet Scattering transform.
problem Understanding and simplifying the mathematics behind generative models.
method Inverts a fixed embedding operator using a wavelet Scattering transform.
result Scattering generators produce similar results to GANs and VAEs without optimization.
Scattering GCN improves graph neural networks by filtering oversmoothing.
problem Oversmoothing in GCNs limits their ability to distinguish graph nodes.
method Augmenting GCNs with geometric scattering transforms and residual convolutions.
result Scattering GCN outperforms GAT in semi-supervised node classification.
Enhances CNN feature extractors' separation capacity analysis.
problem Understanding the separation capacity of CNNs.
method Extending Cover's function-counting theory, analyzing scattering networks.
result Identifies factors affecting scattering networks' separation capacity.
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.
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.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
problem Mie scattering obscures biochemically relevant spectral information in FTIR spectra of biological samples.
method Deep neural networks to approximate the preprocessing function that removes Mie scattering.
result The model is faster and more generalizable across different tissue types.
Paper extends scattering network for fast, scalable feature extraction.
problem Efficiently extracting features from structured inputs.
method Derives a Fourier domain model for scattering network with higher order nonlinearities.
result Achieves linear time complexity for fast computations.
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.
Unified geometric scattering model for measure spaces.
problem Improving CNNs for non-Euclidean data.
method Unified geometric scattering model for measure spaces.
result Unified model includes previous work and applies to more general settings.
New MHSNs extract multiscale features from complex data for robust classification.
problem Signal classification and domain classification on complex data.
method Layered structure with multiscale basis dictionaries, pooling operations, and invariant features.
result High-accuracy classification with fewer parameters than traditional graph neural networks.
Haar scattering networks improve pattern recognition across various tasks.
problem Improving pattern recognition in diverse tasks like regression and classification.
method Stacking convolutional filters based on Haar wavelets followed by non-linear operators.
result Outperformed best algorithms in 4 out of 18 data classification problems.
New deep learning model estimates scattering timescale of FRBs efficiently.
problem Estimating scattering timescale of fast radio bursts (FRBs) is a bottleneck.
method Multimodal Transformer Based Generic Mixture Density Network (MT-GMDN) that ingests dynamic spectrum and timeseries profile.
result Achieves 94% R2 on expected value of τ for measurable scattering. Geometric scattering for graph data enhances feature retention and classification.
problem Tackling the generalization of scattering transforms to graph data.
method Analogous to ConvNets, we develop geometric scattering for graph data, focusing on feature stability under graph deformations.
result Extracted features retain informative variability and relations in graph data, aiding classification and exploration.
FAT-GAN simulates electron-proton scattering without theoretical assumptions.
problem Efficiently training GANs to simulate complex particle distributions.
method Developed FAT-GAN using transformed and augmented features to improve GAN performance.
result FAT-GAN accurately reproduces electron momenta distributions in electron-proton scattering.
A new hybrid GNN framework tackles oversmoothing in graph data.
problem Oversmoothing in graph convolutional networks limits their expressive power and generalization.
method Combines traditional GCN filters with band-pass filters defined via geometric scattering and introduces an attention framework.
result Improves expressive power and generalization of graph convolutional networks.
New method uses GANs and proper scoring rules for robust scatter estimation.
problem Robust scatter estimation in statistics.
method General learning via classification framework based on proper scoring rules.
result Proposed robust scatter estimators achieve minimax rate under Huber's contamination model.
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes o…
Predict cell loads in cellular networks using statistical learning of geometric marks.
problem Predicting cell loads in cellular networks using geometric marks.
method Statistical regression model and scattering moments of random measures.
result Scattering moments can capture similar geometry information as baseline approach and improve performance.
Transfer learning improves lensless imaging through scattering media with fewer samples.
problem Training deep neural networks (DNNs) for lensless imaging through scattering media requires large datasets, leading to poor cross-dataset performance.
method Proposed transfer learning approach using LISMU-FCN and LISMU-OCN architectures with a balance loss function.
result Transfer learning enables imaging across similar and significantly different datasets with fewer samples.
New methods implement manifold scattering transform for high-dimensional point cloud data.
problem Classifying data on complex, non-linear manifolds.
method Adapting diffusion maps theory for numerical implementation.
result Effective for signal and manifold classification tasks.
Approach detects sleep arousal with high accuracy.
problem Detecting sleep arousals in polysomnographic recordings.
method Scattering Transform and Recurrent Neural Networks (RNN) for sequence learning.
result AUROC of 88.0% and AUPRC of 42.1% on 10% test set.
A new graph generation model uses Mallat's scattering transform.
problem Unclear mathematical properties and difficulty in training good generative models for graphs.
method Proposes a graph generation model using a Gaussianized graph scattering transform.
result Demonstrates state-of-the-art performance in link prediction and graph/signal generation.
Proves two non-trapping obstacles coincide if scattering rays have similar travelling times or scattering length spectra.
problem Identifying non-trapping obstacles based on scattering properties.
method Proves two obstacles coincide if their scattering rays have similar travelling times or scattering length spectra under weak non-degeneracy conditions.
result Two non-trapping obstacles coincide if their scattering rays have similar travelling times or scattering length spectra.
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.
First-order scattering reduces CNN input size while maintaining classification accuracy.
problem Reducing the input size of CNNs for faster inference and lower memory usage.
method First-order scattering transform applied to CNN inputs.
result Cascaded CNN with scattering transform achieves similar ImageNet classification performance.
Model predicts stable molecules with AI and physics constraints.
problem Designing stable molecules with limited data.
method Graph Scattering Variational Autoencoder with physical constraints.
result Model generates stable molecules with desired properties.
New method uses overcomplete frames for better acoustic scene analysis.
problem Improving acoustic scene analysis in real-world applications.
method Risk minimization-based overcomplete frame thresholding.
result Validated on bird activity detection task using wavelets.
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be computable. This paper will demonstrate the potential of the scattering symplect…
Paper explains scattering diagrams' role in mirror symmetry.
problem Reconstruction problem in mirror symmetry.
method Introduction of scattering diagrams and their role in SYZ and HMS conjectures.
result Scattering diagrams help in understanding mirror symmetry.
New method uses broken scattering to uniquely identify Finsler manifolds.
problem Identifying Finsler manifolds from scattering data.
method Uses broken scattering relation to compare geodesics.
result Two reversible Finsler manifolds with the same broken scattering relation are isometric.
New method learns soliton dynamics from scattering data without assuming known equations.
problem Deriving soliton dynamics from scattering data without prior knowledge.
method Combining IST with weak-form system identification for data-driven discovery.
result Effective soliton dynamics models derived from observed scattering data.
Deep learning improves PS pixel selection in SAR interferometry.
problem Selecting persistent scatterer pixels for geophysical parameter estimation in multi-temporal SAR interferometry.
method Proposed two deep learning architectures: CNN-ISS and CLSTM-ISS trained on phase history to classify PS and non-PS pixels.
result CLSTM-ISS outperforms conventional methods in PS pixel selection and classification accuracy.
Scattering representations simplify SBI for images without extra compression.
problem Efficiently performing simulation-based inference on images with limited data.
method Use scattering representations for compression and learning, combined with spatial averaging and expressive density estimators.
result Scattering representations provide more information than traditional methods, without requiring additional simulations.
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
problem Defocusing semilinear wave equations on Schwarzschild spacetime.
method Combining energy and pointwise decay results with Sobolev embedding, constructing scattering operator.
result Construction of a scattering operator mapping past to future scattering data.
Paper develops formulas for shape derivatives in wave scattering.
problem Computing high order shape derivatives for wave scattering is challenging.
method Introduces elegant recurrence formulas using differential forms and Lie derivatives.
result Unified framework for computing high order shape perturbations in scattering problems.
Physics-informed neural networks improve baryonic predictions from dark matter simulations.
problem Recreating hydrodynamic simulations from dark matter requires expensive and time-consuming computations.
method Combining neural network architectures with physical constraints and using Kullback-Leibler divergence for prediction comparison.
result Improved accuracy of baryonic predictions based on dark matter halo properties, successful recovery of the metallicity relation, and preserved scatter.