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Found 54 papers, 19 papers with code
Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy
Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions.
Bayesian Formulations for Graph Spectral Denoising
In particular, we present algorithms for the cases where the signal is perturbed by Gaussian noise, dropout, and uniformly distributed noise.
BLIS-Net: Classifying and Analyzing Signals on Graphs
We make several crucial changes to the original geometric scattering architecture which we prove increase the ability of our network to capture information about the input signal and show that BLIS-Net achieves superior performance on both synthetic and real-world data sets based on traffic flow and fMRI data.
Graph topological property recovery with heat and wave dynamics-based features on graphs
In this paper, we propose Graph Differential Equation Network (GDeNet), an approach that harnesses the expressive power of solutions to PDEs on a graph to obtain continuous node- and graph-level representations for various downstream tasks.
Directed Scattering for Knowledge Graph-based Cellular Signaling Analysis
We show this method outperforms numerous others on tasks such as embedding directed graphs and learning cellular signaling networks.
A Flow Artist for High-Dimensional Cellular Data
Existing embedding techniques either do not utilize velocity information or embed the coordinates and velocities independently, i. e., they either impose velocities on top of an existing point embedding or embed points within a prescribed vector field.
Manifold Filter-Combine Networks
We introduce a class of manifold neural networks (MNNs) that we call Manifold Filter-Combine Networks (MFCNs), that aims to further our understanding of MNNs, analogous to how the aggregate-combine framework helps with the understanding of graph neural networks (GNNs).
Inferring dynamic regulatory interaction graphs from time series data with perturbations
Complex systems are characterized by intricate interactions between entities that evolve dynamically over time.
Graph Fourier MMD for Signals on Graphs
GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation between the pair of distributions on the graph.
Neural FIM for learning Fisher Information Metrics from point cloud data
Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature.
Assessing Neural Network Representations During Training Using Data Diffusion Spectra
We also see that there is an increase in DSMI with the class label over time.
A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction
Finally, we show that parameters of our more general method can be configured to give results similar to PHATE (a state-of-the-art diffusion based manifold learning method) as well as SNE (an attraction/repulsion neighborhood based method that forms the basis of t-SNE).
Geodesic Sinkhorn for Fast and Accurate Optimal Transport on Manifolds
Efficient computation of optimal transport distance between distributions is of growing importance in data science.
CUTS: A Framework for Multigranular Unsupervised Medical Image Segmentation
To address this, we present CUTS (Contrastive and Unsupervised Training for multi-granular medical image Segmentation), a fully unsupervised deep learning framework for medical image segmentation to better utilize the vast majority of imaging data that are not labeled or annotated.
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.
Learnable Filters for Geometric Scattering Modules
We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters.
Manifold Interpolating Optimal-Transport Flows for Trajectory Inference
In GAE the latent space distance between points is regularized to match a novel multiscale geodesic distance on the data manifold that we define.
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.
Diffusion Curvature for Estimating Local Curvature in High Dimensional Data
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature.
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.
ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins
Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods.
Learning shared neural manifolds from multi-subject FMRI data
In order to understand the connection between stimuli of interest and brain activity, and analyze differences and commonalities between subjects, it becomes important to learn a meaningful embedding of the data that denoises, and reveals its intrinsic structure.
MURAL: An Unsupervised Random Forest-Based Embedding for Electronic Health Record Data
In particular, in EHR data, some variables are {\em missing not at random (MNAR)} but deliberately not collected and thus are a source of information.
Molecular Graph Generation via Geometric Scattering
We guide the latent representation of an autoencoder by capturing graph structure information with the geometric scattering transform and apply penalties that structure the representation also by molecular properties.
Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance
We propose to compare and organize such datasets of graph signals by using an earth mover's distance (EMD) with a geodesic cost over the underlying graph.
Exploring epithelial-cell calcium signaling with geometric and topological data analysis
However the function of calcium signaling in epithelial cells is not well understood.
Diffusion Earth Mover's Distance and Distribution Embeddings
Here, Diffusion EMD can derive distances between patients on the manifold of cells at least two orders of magnitude faster than equally accurate methods.
Multimodal Data Visualization and Denoising with Integrated Diffusion
We propose a method called integrated diffusion for combining multimodal datasets, or data gathered via several different measurements on the same system, to create a joint data diffusion operator.
Exploring the Geometry and Topology of Neural Network Loss Landscapes
This suggests that qualitative and quantitative examination of the loss landscape geometry could yield insights about neural network generalization performance during training.
Data-Driven Learning of Geometric Scattering Networks
We propose a new graph neural network (GNN) module, based on relaxations of recently proposed geometric scattering transforms, which consist of a cascade of graph wavelet filters.
Image-to-image Mapping with Many Domains by Sparse Attribute Transfer
Unsupervised image-to-image translation consists of learning a pair of mappings between two domains without known pairwise correspondences between points.
Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistence
We observe significant differences in both brain state trajectories and overall topological activity between adults and children watching the same movie.
Uncovering the Folding Landscape of RNA Secondary Structure with Deep Graph Embeddings
We propose a geometric scattering autoencoder (GSAE) network for learning such graph embeddings.
Making Logic Learnable With Neural Networks
We show the utility of our pipeline on a network that is trained on biomedical data.
TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics
To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time.
Improving Multi-Manifold GANs with a Learned Noise Prior
Generative adversarial networks (GANs) learn to map samples from a noise distribution to a chosen data distribution.
Beyond GANs: Transforming without a Target Distribution
While generative neural networks can learn to transform a specific input dataset into a specific target dataset, they require having just such a paired set of input/output datasets.
Visualizing the PHATE of Neural Networks
We demonstrate M-PHATE with two vignettes: continual learning and generalization.
Coarse Graining of Data via Inhomogeneous Diffusion Condensation
Here, we consider multiple levels of abstraction via a multiresolution geometry of data points at different granularities.
Fixing Bias in Reconstruction-based Anomaly Detection with Lipschitz Discriminators
We show that this procedure successfully detects unseen anomalies with guarantees on those that have a certain Wasserstein distance from the data or corrupted training set.
Manifold Alignment via Feature Correspondence
We leverage this assumption to estimate relations between intrinsic manifold dimensions, which are given by diffusion map coordinates over each of the datasets.
Graph Spectral Regularization For Neural Network Interpretability
First, we show a synthetic example that the graph-structured layer can reveal topological features of the data.
Enhancing experimental signals in single-cell RNA-sequencing data using graph signal processing
Single-cell RNA-sequencing (scRNA-seq) is a powerful tool for analyzing biological systems.
TraVeLGAN: Image-to-image Translation by Transformation Vector Learning
The achievements of these models have been limited to a particular subset of domains where this assumption yields good results, namely homogeneous domains that are characterized by style or texture differences.
Compressed Diffusion
Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions.
Finding Archetypal Spaces Using Neural Networks
Here, we propose a reformulation of the problem such that the goal is to learn a non-linear transformation of the data into a latent archetypal space.
Generating and Aligning from Data Geometries with Generative Adversarial Networks
Unsupervised domain mapping has attracted substantial attention in recent years due to the success of models based on the cycle-consistency assumption.
Geometry Based Data Generation
We propose a new type of generative model for high-dimensional data that learns a manifold geometry of the data, rather than density, and can generate points evenly along this manifold.
Harmonic Alignment
We use this to relate the diffusion coordinates of each dataset through our assumption of partial feature correspondence.
Interpretable Neuron Structuring with Graph Spectral Regularization
Taking inspiration from spatial organization and localization of neuron activations in biological networks, we use a graph Laplacian penalty to structure the activations within a layer.
Modeling Dynamics of Biological Systems with Deep Generative Neural Networks
DyMoN is well-suited to the idiosyncrasies of biological data, including noise, sparsity, and the lack of longitudinal measurements in many types of systems.
Geometry-Based Data Generation
Then, it generates new points evenly along the manifold by pulling randomly generated points into its intrinsic structure using a diffusion kernel.
MAGAN: Aligning Biological Manifolds
We present a new GAN called the Manifold-Aligning GAN (MAGAN) that aligns two manifolds such that related points in each measurement space are aligned together.
Modeling Global Dynamics from Local Snapshots with Deep Generative Neural Networks
In order to model the dynamics of such systems given snapshot data, or local transitions, we present a deep neural network framework we call Dynamics Modeling Network or DyMoN.
