A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified graph scattering transforms improve theoretical properties of graph neural networks.
Graph scattering transforms are stable to metric perturbations of network topology.
Unified geometric scattering model for measure spaces.
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and gra…
We explore the generalization of scattering transforms from traditional (e.g., image or audio) signals to graph data, analogous to the generalization of ConvNets in geometric deep learning, and the utility of extracted graph features in graph data analysis. In particular, we focus on the capacity of these features to r…
A new GNN module learns geometric scattering features for better graph classification and feature exploration.
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…
GSAN learns adaptive node representations using geometric scattering and attention.
Scattering GCN improves graph neural networks by filtering oversmoothing.
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…
Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is di…
New MHSNs extract multiscale features from complex data for robust classification.
Model predicts stable molecules with AI and physics constraints.
MODWST improves classification tasks with wavelet scattering.
A deep learning model organizes RNA graphs to reveal folding patterns and properties.
New methods implement manifold scattering transform for high-dimensional point cloud data.
New method selects diffusion scales for graph wavelets.
Study scattering rigidity for Hamiltonian systems, proving lens rigidity for non-trapping Finsler manifolds.
Transformers predict scattering amplitudes in theoretical physics.
The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software package, an easy-to-use, high-performance Python implementation of the scattering transform in 1D, 2D, and 3D that is compatible with modern deep …
New method learns soliton dynamics from scattering data without assuming known equations.
Method extracts features from signals for classification with explainability.
A deep network classifies images by scattering and dictionary learning.
Study on recovering Lorentzian metrics from scattering data.
Bayesian Scattering offers a simple baseline for image data uncertainty.
Study recovers Lorentzian metrics from boundary data, proving local rigidity.
FAT-GAN simulates electron-proton scattering without theoretical assumptions.
Scattering theory developed for linearised gravity near Schwarzschild black hole.
Deep neural networks correct Mie scattering in FTIR spectra of biological samples.
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.
Enhances DSN with multi-family wavelet transforms and sparsity.
A new hybrid GNN framework tackles oversmoothing in graph data.
NAST generalizes scattering transform for non-stationary time series analysis.
New deep learning model estimates scattering timescale of FRBs efficiently.
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 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.
In this paper we construct a learning architecture for high dimensional time series sampled by sensor arrangements. Using a redundant wavelet decomposition on a graph constructed over the sensor locations, our algorithm is able to construct discriminative features that exploit the mutual information between the sensors…
A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scattering transforms of three dimensional signals were previously introduced in a machine learning framework for the regression of properties of sm…
CSTs improve stability in covariance spectrum analysis without training.
We study the first-order scattering transform as a candidate for reducing the signal processed by a convolutional neural network (CNN). We show theoretical and empirical evidence that in the case of natural images and sufficiently small translation invariance, this transform preserves most of the signal information nee…
We present a machine learning model for the analysis of randomly generated discrete signals, modeled as the points of an inhomogeneous, compound Poisson point process. Like the wavelet scattering transform introduced by Mallat, our construction is naturally invariant to translations and reflections, but it decouples th…
A CNN-based method improves DTI of the human heart, compensating for motion.
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 …