Michael Perlmutter
Efficient neural network models that generate brain-like dynamic activity can be a valuable resource for generating synthetic data, analyzing differences in brain transients under conditions such as testing perturbation activity or…
A key challenge in deriving unified neural solvers for combinatorial optimization (CO) is efficient generalization of models between a given set of tasks to new tasks not used during the initial training process. To address it, we first…
We introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets…
Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to various powers, known as diffusion scales. Traditionally, these scales are chosen to be dyadic…
In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning on high-dimensional point clouds. Our work is motivated by single-cell data which can have very…
We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple…
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 our understanding of these networks' stability and invariance…
In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). Our filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and…
Graph neural networks (GNNs) have achieved great success for a variety of tasks such as node classification, graph classification, and link prediction. However, the use of GNNs (and machine learning more generally) to solve combinatorial…
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 graph neural networks (GNN) that can be applied to…
In order to better understand manifold neural networks (MNNs), we introduce Manifold Filter-Combine Networks (MFCNs). The filter-combine framework parallels the popular aggregate-combine paradigm for graph neural networks (GNNs) and…
In many data-driven applications, higher-order relationships among multiple objects are essential in capturing complex interactions. Hypergraphs, which generalize graphs by allowing edges to connect any number of nodes, provide a flexible…
Graph neural networks (GNNs) have emerged as a powerful tool for tasks such as node classification and graph classification. However, much less work has been done on signal classification, where the data consists of many functions (referred…
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-like operators to general manifolds. The initial work on this…
Here we consider the problem of denoising features associated to complex data, modeled as signals on a graph, via a smoothness prior. This is motivated in part by settings such as single-cell RNA where the data is very high-dimensional, but…
Directed graphs are a natural model for many phenomena, in particular scientific knowledge graphs such as molecular interaction or chemical reaction networks that define cellular signaling relationships. In these situations, source nodes…
We consider the problem of embedding point cloud data sampled from an underlying manifold with an associated flow or velocity. Such data arises in many contexts where static snapshots of dynamic entities are measured, including in…
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…
High-dimensional data arises in numerous applications, and the rapidly developing field of geometric deep learning seeks to develop neural network architectures to analyze such data in non-Euclidean domains, such as graphs and manifolds.…
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…