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.
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…
New model distinguishes Poisson processes from self-similar ones.
problem Distinguishing Poisson point processes from self-similar processes.
method Machine learning model based on inhomogeneous, compound Poisson point process.
result The model can distinguish Poisson point processes from self-similar processes.
We present a sparse and invariant representation with low asymptotic complexity for robust unsupervised transient and onset zone detection in noisy environments. This unsupervised approach is based on wavelet transforms and leverages the scattering network from Mallat et al. by deriving frequency invariance. This frequ…
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 …
Kymatio simplifies scattering transforms for Python.
problem Signal processing and machine learning applications.
method Wavelet scattering transform implemented in Python.
result Efficient, GPU-accelerated implementation.
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.
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.
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.
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.
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.
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 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.
Study scattering rigidity for Hamiltonian systems, proving lens rigidity for non-trapping Finsler manifolds.
problem Scattering rigidity for Hamiltonian systems on manifolds with boundary.
method Linearization of travel times, X-ray transform over Hamiltonian curves, Hamiltonian light ray transform.
result Prove semiglobal lens rigidity of non-trapping Finsler manifolds.
Transformers predict scattering amplitudes in theoretical physics.
problem Computing exact coefficients of scattering amplitudes in N = 4 SYM theory.
method Applied Transformers to predict integer coefficients of scattering amplitudes.
result Transformers achieve high (> 98%) accuracy on predicting scattering amplitudes.
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.
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.
Method extracts features from signals for classification with explainability.
problem Lack of interpretability in signal classification models.
method Combining scattering transform and multiclass logistic regression with zeroth-order optimization.
result Uncovered the meaning of scattering transform coefficients.
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are certified stable to input deformations. This stability to deformations can be interp…
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.
Study on recovering Lorentzian metrics from scattering data.
problem Recovering Lorentzian metrics from scattering data on a boundary.
method Analyzing the role of boundary distance functions and linearizing the light ray transform.
result Scattering rigidity can be reduced to boundary rigidity of magnetic systems.
Bayesian Scattering offers a simple baseline for image data uncertainty.
problem Lack of interpretable, mathematically grounded uncertainty quantification methods for image data.
method Coupling wavelet scattering transform with a simple probabilistic head.
result Bayesian Scattering provides sensible uncertainty estimates under distribution shifts.
Study recovers Lorentzian metrics from boundary data, proving local rigidity.
problem Recovering a Lorentzian metric from scattering data on a boundary.
method Analyzes jet and real analyticity of metrics near lightlike points.
result Metric can be recovered up to gauge transformations near lightlike strictly convex points.
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.
Scattering theory developed for linearised gravity near Schwarzschild black hole.
problem Linear stability of Schwarzschild spacetime and scattering of gravitational waves.
method Physical-space Chandrasekhar transformation and Teukolsky-Starobinsky correspondence.
result Construction of scattering theory for spin 2 Teukolsky equations.
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.
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.
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be o…
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…
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
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.
3D scattering model predicts lithium-silicon formation energies.
problem Predicting formation energies of amorphous Li-Si materials.
method Steerable wavelet scattering for 3D signals, invariant to translations and rotations.
result State-of-the-art results compared to other machine learning methods.
NAST generalizes scattering transform for non-stationary time series analysis.
problem Analyzing non-stationary time series data.
method Neural activation of scattering transform with various activation functions and high pass filters.
result Central and non-central limit theorems for NAST of Gaussian processes.
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.
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. We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is re…
We design non-singular cloaks enabling objects to scatter waves like objects with smaller size and very different shapes. We consider the Schrodinger equation which is valid e.g. in the contexts of geometrical and quantum optics. More precisely, we introduce a generalized non-singular transformation for star domains, a…
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.
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 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…
Study fourth order Schrödinger equation on Cartan-Hadamard manifolds, proving existence, scattering, and blow-up results.
problem Fourth order Schrödinger equation with mixed dispersion on Cartan-Hadamard manifolds.
method Fourier transform for hyperbolic space, weighted Strichartz estimates for rotationally symmetric manifolds, localized virial argument.
result Existence, scattering, and blow-up results for the equation.
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.
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.
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.
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…
Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schrödinger …
The space-time monopole equation is obtained from a dimension reduction of the anti-self dual Yang-Mills equation on R2,2. A family of Ward equations is obtained by gauge fixing from the monopole equation. In this paper, we give an introduction and a survey of the space-time monopole equation. Included are altern…
The paper explores transformations between power law problems and geodesics on cones.
problem Solving power law problems and understanding their geometric properties.
method Geometric transformations and cone metrics.
result Derivation of Maclaurin duality and Jacobi-Maupertuis metric reformulation.