arXiv research

New MHSNs extract multiscale features from complex data for robust classification.

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…

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computation…

New sigma models compute graviton scattering amplitudes from quaternionic geometry.

Automatic Music Transcription (AMT) is one of the oldest and most well-studied problems in the field of music information retrieval. Within this challenging research field, onset detection and instrument recognition take important places in transcription systems, as they respectively help to determine exact onset times…

Let $g$ and $\tilde{g}$ be Riemannian metrics on a noncompact manifold $M$, which are conformally equivalent. We show that under a very mild \emph{first order} control on the conformal factor, the wave operators corresponding to the Hodge-Laplacians $Δ_g$ and $Δ_{\tilde{g}}$ acting on differential forms exist and are c…

Neural network approach simplifies multiscale problem homogenization.

New method for manifold topological learning avoids remeshing issues.

Study examines money flow network among firms' accounts in a Japanese region.

We study approximations of non-Gaussian stationary processes having long range correlations with microcanonical models. These models are conditioned by the empirical value of an energy vector, evaluated on a single realization. Asymptotic properties of maximum entropy microcanonical and macrocanonical processes and the…

The de Rham-Hodge theory is a landmark of the 20$^\text{th}$ Century's mathematics and has had a great impact on mathematics, physics, computer science, and engineering. This work introduces an evolutionary de Rham-Hodge method to provide a unified paradigm for the multiscale geometric and topological analysis of evolv…

DMGNN predicts 3D human motions using adaptive multiscale graphs.

Novel graph network learns hierarchical network structure.

For a compact manifold, which has a part isometric to a cylinder of finite length, we consider an adiabatic limit procedure, in which the length of the cylinder tends to infinity. We study the asymptotic of the spectrum of Hodge-Laplacian and the asymptotic of the $L^2$-metric on de Rham cohomology. As an application, …

GSAN learns adaptive node representations using geometric scattering and attention.

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…

The paper extends entropy maximization to multiscale settings and applies it to neural networks.

The paper proves wave operator existence and completeness for Hodge Laplacians.

Scattering networks maximize separation on low-dimensional data.

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…

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…

iLED framework offers interpretable dynamics for multiscale systems.

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stabili…

MsIGN tackles high-dimensional Bayesian inference using multiscale structure.

Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve competitive results both for supervised and unsupervised learning tasks, while making pr…

Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales, which do not comply with the nature of dynamical temporal patterns among sequences…

WideBNet learns inverse scattering from wide-band data efficiently and stably.

Deep learning solves wave-based inverse problems, including super-resolution imaging.

Scattering GCN improves graph neural networks by filtering oversmoothing.

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…

Enhances CNN feature extractors' separation capacity analysis.

MODWST improves classification tasks with wavelet scattering.

Enhances DSN with multi-family wavelet transforms and sparsity.

Deep neural networks correct Mie scattering in FTIR spectra of biological samples.

Extracts causal brain dynamics across multiple scales.

GINNs combine deep learning with PGMs for physics-based multiscale systems.

PINNs solve neuronal parameter and state estimation problems with limited data.

Paper introduces MGLasso for multiscale graph inference in clustering and network analysis.

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

Deep neural network algorithms are difficult to analyze because they lack structure allowing to understand the properties of underlying transforms and invariants. Multiscale hierarchical convolutional networks are structured deep convolutional networks where layers are indexed by progressively higher dimensional attrib…

A new autoencoder architecture captures multiscale data.

Unified geometric scattering model for measure spaces.

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 a sparse scattering deep convolutional neural network, which provides a simple model to analyze properties of deep representation learning for classification. Learning a single dictionary matrix with a classifier yields a higher classification accuracy than AlexNet over the ImageNet 2012 dataset. The netwo…

Deep neural network approximates flow averages for rough walls in multiscale simulations.

We introduce a multiscale supervised dimension reduction method for SPatial Interaction Network (SPIN) data, which consist of a collection of spatially coordinated interactions. This type of predictor arises when the sampling unit of data is composed of a collection of primitive variables, each of them being essentiall…

New deep learning model estimates scattering timescale of FRBs efficiently.

Develops DSD for analyzing multiscale biological networks.