87 citations · 450 across the 34 of their papers we have counts for
35 papers
Bispectrum Unbiasing for Dilation-Invariant Multi-reference Alignment
Liping Yin, Anna Little, Matthew Hirn
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 \math…
NervePool: A Simplicial Pooling Layer
Sarah McGuire Scullen, Ernst Röell, Elizabeth Munch +2
For deep learning problems on graph-structured data, pooling layers are important for down sampling, reducing computational cost, and to minimize overfitting. We define a pooling l…
On Generalizations of the Nonwindowed Scattering Transform
Albert Chua, Matthew Hirn, Anna Little
In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as $\Lb^q(\mathbb{R}^n)$ norms of a cascade of continuous wavelet transforms (or dyadic…
Geometric Scattering on Measure Spaces
Joyce Chew, Matthew Hirn, Smita Krishnaswamy +5
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in o…
The Manifold Scattering Transform for High-Dimensional Point Cloud Data
Joyce Chew, Holly R. Steach, Siddharth Viswanath +5
The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-l…
Taxonomy of Benchmarks in Graph Representation Learning
Renming Liu, Semih Cantürk, Frederik Wenkel +9
Graph Neural Networks (GNNs) extend the success of neural networks to graph-structured data by accounting for their intrinsic geometry. While extensive research has been done on de…
Time-inhomogeneous diffusion geometry and topology
Guillaume Huguet, Alexander Tong, Bastian Rieck +5
Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifo…
Overcoming Oversmoothness in Graph Convolutional Networks via Hybrid Scattering Networks
Frederik Wenkel, Yimeng Min, Matthew Hirn +2
Geometric deep learning has made great strides towards generalizing the design of structure-aware neural networks from traditional domains to non-Euclidean ones, giving rise to gra…
Towards a Taxonomy of Graph Learning Datasets
Renming Liu, Semih Cantürk, Frederik Wenkel +10
Graph neural networks (GNNs) have attracted much attention due to their ability to leverage the intrinsic geometries of the underlying data. Although many different types of GNN mo…
A Hybrid Scattering Transform for Signals with Isolated Singularities
Michael Perlmutter, Jieqian He, Mark Iwen +1
The scattering transform is a wavelet-based model of Convolutional Neural Networks originally introduced by S. Mallat. Mallat's analysis shows that this network has desirable stabi…
Accurately Modeling Biased Random Walks on Weighted Graphs Using
Renming Liu, Matthew Hirn, Arjun Krishnan
Node embedding is a powerful approach for representing the structural role of each node in a graph. is a widely used method for node embedding that works by exp…
Unbiasing Procedures for Scale-invariant Multi-reference Alignment
Matthew Hirn, Anna Little
This article discusses a generalization of the 1-dimensional multi-reference alignment problem. The goal is to recover a hidden signal from many noisy observations, where each nois…
Texture synthesis via projection onto multiscale, multilayer statistics
Jieqian He, Matthew Hirn
We provide a new model for texture synthesis based on a multiscale, multilayer feature extractor. Within the model, textures are represented by a set of statistics computed from Re…
MagNet: A Neural Network for Directed Graphs
Xitong Zhang, Yixuan He, Nathan Brugnone +2
The prevalence of graph-based data has spurred the rapid development of graph neural networks (GNNs) and related machine learning algorithms. Yet, despite the many datasets natural…
Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties
Paul Sinz, Michael W. Swift, Xavier Brumwell +4
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…
Understanding Graph Neural Networks with Generalized Geometric Scattering Transforms
Michael Perlmutter, Alexander Tong, Feng Gao +2
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 g…
Wavelet invariants for statistically robust multi-reference alignment
Matthew Hirn, Anna Little
We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference a…
Coarse Graining of Data via Inhomogeneous Diffusion Condensation
Nathan Brugnone, Alex Gonopolskiy, Mark W. Moyle +7
Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here…
Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds
Michael Perlmutter, Feng Gao, Guy Wolf +1
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geo…
Scattering Statistics of Generalized Spatial Poisson Point Processes
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. Like the wav…
Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction
Xavier Brumwell, Paul Sinz, Kwang Jin Kim +2
A general machine learning architecture is introduced that uses wavelet scattering coefficients of an inputted three dimensional signal as features. Solid harmonic wavelet scatteri…
Kymatio: Scattering Transforms in Python
Mathieu Andreux, Tomás Angles, Georgios Exarchakis +15
The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software packag…
Geometric Scattering on Manifolds
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…
Geometric Scattering for Graph Data Analysis
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…