Search Results for author: Matthew Hirn

Found 22 papers, 4 papers with code

Time-inhomogeneous diffusion geometry and topology

no code implementations28 Mar 2022 Guillaume Huguet, Alexander Tong, Bastian Rieck, Jessie Huang, Manik Kuchroo, Matthew Hirn, Guy Wolf, Smita Krishnaswamy

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.

Denoising Topological Data Analysis

Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks

no code implementations22 Jan 2022 Frederik Wenkel, Yimeng Min, Matthew Hirn, Michael Perlmutter, Guy Wolf

However, current GNN models (and GCNs in particular) are known to be constrained by various phenomena that limit their expressive power and ability to generalize to more complex graph datasets.

Towards a Taxonomy of Graph Learning Datasets

no code implementations27 Oct 2021 Renming Liu, Semih Cantürk, Frederik Wenkel, Dylan Sandfelder, Devin Kreuzer, Anna Little, Sarah McGuire, Leslie O'Bray, Michael Perlmutter, Bastian Rieck, Matthew Hirn, Guy Wolf, Ladislav Rampášek

Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data.

Graph Learning

A Hybrid Scattering Transform for Signals with Isolated Singularities

no code implementations10 Oct 2021 Michael Perlmutter, Jieqian He, Mark Iwen, Matthew Hirn

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.

Accurately Modeling Biased Random Walks on Weighted Graphs Using $\textit{Node2vec+}$

1 code implementation15 Sep 2021 Renming Liu, Matthew Hirn, Arjun Krishnan

$\textit{Node2vec}$ is a widely used method for node embedding that works by exploring the local neighborhoods via biased random walks on the graph.

Unbiasing Procedures for Scale-invariant Multi-reference Alignment

no code implementations2 Jul 2021 Matthew Hirn, Anna Little

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.

Translation

Texture synthesis via projection onto multiscale, multilayer statistics

no code implementations22 May 2021 Jieqian He, Matthew Hirn

We provide a new model for texture synthesis based on a multiscale, multilayer feature extractor.

Image Generation Texture Synthesis

MagNet: A Neural Network for Directed Graphs

1 code implementation NeurIPS 2021 Xitong Zhang, Yixuan He, Nathan Brugnone, Michael Perlmutter, Matthew Hirn

In this paper, we propose MagNet, a spectral GNN for directed graphs based on a complex Hermitian matrix known as the magnetic Laplacian.

Link Prediction Node Classification

Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties

no code implementations1 Jun 2020 Paul Sinz, Michael W. Swift, Xavier Brumwell, Jialin Liu, Kwang Jin Kim, Yue Qi, Matthew Hirn

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.

feature selection

Understanding Graph Neural Networks with Asymmetric Geometric Scattering Transforms

no code implementations14 Nov 2019 Michael Perlmutter, Feng Gao, Guy Wolf, Matthew Hirn

As a result, the proposed construction unifies and extends known theoretical results for many of the existing graph scattering architectures.

Wavelet invariants for statistically robust multi-reference alignment

1 code implementation24 Sep 2019 Matthew Hirn, Anna Little

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.

Translation

Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

no code implementations24 May 2019 Michael Perlmutter, Feng Gao, Guy Wolf, Matthew Hirn

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks.

Translation

Graph Classification with Geometric Scattering

no code implementations ICLR 2019 Feng Gao, Guy Wolf, Matthew Hirn

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.

Classification General Classification +2

Scattering Statistics of Generalized Spatial Poisson Point Processes

no code implementations10 Feb 2019 Michael Perlmutter, Jieqian He, Matthew Hirn

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.

Point Processes

Geometric Scattering on Manifolds

no code implementations15 Dec 2018 Michael Perlmutter, Guy Wolf, Matthew Hirn

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.

Translation

Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction

no code implementations21 Nov 2018 Xavier Brumwell, Paul Sinz, Kwang Jin Kim, Yue Qi, Matthew Hirn

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.

Formation Energy

Geometric Scattering for Graph Data Analysis

no code implementations ICLR 2019 Feng Gao, Guy Wolf, Matthew Hirn

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.

General Classification Graph Classification +1

Solid Harmonic Wavelet Scattering for Predictions of Molecule Properties

no code implementations1 May 2018 Michael Eickenberg, Georgios Exarchakis, Matthew Hirn, Stéphane Mallat, Louis Thiry

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

no code implementations29 Mar 2018 Adam Gustafson, Matthew Hirn, Kitty Mohammed, Hariharan Narayanan, Jason Xu

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.

Solid Harmonic Wavelet Scattering: Predicting Quantum Molecular Energy from Invariant Descriptors of 3D Electronic Densities

no code implementations NeurIPS 2017 Michael Eickenberg, Georgios Exarchakis, Matthew Hirn, Stephane Mallat

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.

General Classification

Wavelet Scattering Regression of Quantum Chemical Energies

1 code implementation16 May 2016 Matthew Hirn, Stéphane Mallat, Nicolas Poilvert

Sparse scattering regressions give state of the art results over two databases of organic planar molecules.

Quantum Energy Regression using Scattering Transforms

no code implementations6 Feb 2015 Matthew Hirn, Nicolas Poilvert, Stéphane Mallat

We present a novel approach to the regression of quantum mechanical energies based on a scattering transform of an intermediate electron density representation.

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