Search Results for author:
Found 27 papers, 7 papers with code
Accurately Modeling Biased Random Walks on Weighted Graphs Using $\textit{Node2vec+}$
$\textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph.
MagNet: A Neural Network for Directed Graphs
In this paper, we propose MagNet, a spectral GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian.
Taxonomy of Benchmarks in Graph Representation Learning
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry.
Wavelet Scattering Regression of Quantum Chemical Energies
Sparse scattering regressions give state of the art results over two databases of organic planar molecules.
The Manifold Scattering Transform for High-Dimensional Point Cloud Data
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold.
Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms
As a result, the proposed construction unifies and extends known theoretical results for many of the existing graph scattering architectures.
Solid Harmonic Wavelet Scattering for Predictions of Molecule Properties
We present a machine learning algorithm for the prediction of molecule properties inspired by ideas from density functional theory.
Structural Risk Minimization for $C^{1,1}(\mathbb{R}^d)$ Regression
Recently, the following smooth function approximation problem was proposed: given a finite set $E \subset \mathbb{R}^d$ and a function $f: E \rightarrow \mathbb{R}$, interpolate the given information with a function $\widehat{f} \in \dot{C}^{1, 1}(\mathbb{R}^d)$ (the class of first-order differentiable functions with Lipschitz gradients) such that $\widehat{f}(a) = f(a)$ for all $a \in E$, and the value of $\mathrm{Lip}(\nabla \widehat{f})$ is minimal.
Quantum Energy Regression using Scattering Transforms
We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation.
Geometric Scattering for Graph Data Analysis
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.
Geometric Scattering on Manifolds
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.
Solid Harmonic Wavelet Scattering: Predicting Quantum Molecular Energy from Invariant Descriptors of 3D Electronic Densities
We introduce a solid harmonic wavelet scattering representation, invariant to rigid motion and stable to deformations, for regression and classification of 2D and 3D signals.
Graph Classification with Geometric Scattering
Furthermore, ConvNets inspired recent advances in geometric deep learning, which aim to generalize these networks to graph data by applying notions from graph signal processing to learn deep graph filter cascades.
Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction
Here this approach is extended for general steerable wavelets which are equivariant to translations and rotations, resulting in a sparse model of the target function.
Scattering Statistics of Generalized Spatial Poisson Point Processes
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.
Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks.
Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties
The dream of machine learning in materials science is for a model to learn the underlying physics of an atomic system, allowing it to move beyond interpolation of the training set to the prediction of properties that were not present in the original training data.
Wavelet invariants for statistically robust multi-reference alignment
After unbiasing the representation to remove the effects of the additive noise and random dilations, we recover an approximation of the power spectrum by solving a convex optimization problem, and thus reduce to a phase retrieval problem.
Texture synthesis via projection onto multiscale, multilayer statistics
We provide a new model for texture synthesis based on a multiscale, multilayer feature extractor.
Unbiasing Procedures for Scale-invariant Multi-reference Alignment
We propose a method that recovers the power spectrum of the hidden signal by applying a data-driven, nonlinear unbiasing procedure, and thus the hidden signal is obtained up to an unknown phase.
A Hybrid Scattering Transform for Signals with Isolated Singularities
We also show that the Gabor measurements used in the second layer can be used to synthesize sparse signals such as those produced by the first layer.
Towards a Taxonomy of Graph Learning Datasets
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data.
Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks
We further introduce an attention framework that allows the model to locally attend over combined information from different filters at the node level.
Time-inhomogeneous diffusion geometry and topology
From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel.
Geometric Scattering on Measure Spaces
Our proposed framework includes previous work on geometric scattering as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary.
NervePool: A Simplicial Pooling Layer
For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting.
Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment
Motivated by modern data applications such as cryo-electron microscopy, the goal of classic multi-reference alignment (MRA) is to recover an unknown signal $f: \mathbb{R} \to \mathbb{R}$ from many observations that have been randomly translated and corrupted by additive noise.
