Smita Krishnaswamy

Michael Perlmutter

2025-04-08

ArXiv (prépublication)

Accelerated learning of a noninvasive human brain-computer interface via manifold geometry

Erica Lindsey Busch

E. Chandra Fincke

Guillaume Lajoie

Nicholas B Turk-Browne

2025-04-03

bioRxiv (prépublication)

HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

Siddharth Viswanath

Hiren Madhu

Dhananjay Bhaskar

Jake Kovalic

David R. Johnson

Rex Ying

Christopher Tape

Ian Adelstein

Michael Perlmutter

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning o… (voir plus)n high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods point cloud tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multi-scale features - capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

2025-02-11

ArXiv (prépublication)

HiPoNet: A Topology-Preserving Multi-View Neural Network For High Dimensional Point Cloud and Single-Cell Data

Siddharth Viswanath

Hiren Madhu

Dhananjay Bhaskar

Jake Kovalic

Dave Johnson

Rex Ying

Christopher Tape

Ian Adelstein

Michael Perlmutter

In this paper, we propose HiPoNet, an end-to-end differentiable neural network for regression, classification, and representation learning o… (voir plus)n high-dimensional point clouds. Single-cell data can have high dimensionality exceeding the capabilities of existing methods point cloud tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e. one on every patient), necessitating models that can process large, high-dimensional point clouds at scale. Most current approaches build a single nearest-neighbor graph, discarding important geometric information. In contrast, HiPoNet forms higher-order simplicial complexes through learnable feature reweighting, generating multiple data views that disentangle distinct biological processes. It then employs simplicial wavelet transforms to extract multi-scale features - capturing both local and global topology. We empirically show that these components preserve topological information in the learned representations, and that HiPoNet significantly outperforms state-of-the-art point-cloud and graph-based models on single cell. We also show an application of HiPoNet on spatial transcriptomics datasets using spatial co-ordinates as one of the views. Overall, HiPoNet offers a robust and scalable solution for high-dimensional data analysis.

2025-02-11

ArXiv (prépublication)

Principal Curvatures Estimation with Applications to Single Cell Data

Yanlei Zhang

Lydia Mezrag

Xingzhi Sun

Charles Xu

Kincaid MacDonald

Dhananjay Bhaskar

Bastian Rieck

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datas… (voir plus)ets. A common method in manifold learning consists in hypothesizing that datasets lie on a lower dimensional manifold. This allows to study the geometry of point clouds by extracting meaningful descriptors like curvature. In this work, we will present Adaptive Local PCA (AdaL-PCA), a data-driven method for accurately estimating various notions of intrinsic curvature on data manifolds, in particular principal curvatures for surfaces. The model relies on local PCA to estimate the tangent spaces. The evaluation of AdaL-PCA on sampled surfaces shows state-of-the-art results. Combined with a PHATE embedding, the model applied to single-cell RNA sequencing data allows us to identify key variations in the cellular differentiation.

2025-02-06

ArXiv (prépublication)

Principal Curvatures Estimation with Applications to Single Cell Data

Yanlei Zhang

Lydia Mezrag

Xingzhi Sun

Charles Xu

Kincaid MacDonald

Dhananjay Bhaskar

Bastian Rieck

2025-02-06

ArXiv (prépublication)

Geometry-Aware Generative Autoencoder for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds

Xingzhi Sun

Danqi Liao

Kincaid MacDonald

Yanlei Zhang

Guillaume Huguet

Ian Adelstein

Tim G. J. Rudner

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportu… (voir plus)nities for scientific discovery, but it also presents unique computational and statistical challenges. Traditional methods struggle with geometry-aware data generation, interpolation along meaningful trajectories, and transporting populations via feasible paths. To address these issues, we introduce Geometry-Aware Generative Autoencoder (GAGA), a novel framework that combines extensible manifold learning with generative modeling. GAGA constructs a neural network embedding space that respects the intrinsic geometries discovered by manifold learning and learns a novel warped Riemannian metric on the data space. This warped metric is derived from both the points on the data manifold and negative samples off the manifold, allowing it to characterize a meaningful geometry across the entire latent space. Using this metric, GAGA can uniformly sample points on the manifold, generate points along geodesics, and interpolate between populations across the learned manifold. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over SOTA in single-cell population-level trajectory inference.

2025-01-22

aistats.org/AISTATS/2025/Conference (poster)

openreview.net

Geometry-Aware Generative Autoencoders for Warped Riemannian Metric Learning and Generative Modeling on Data Manifolds

Xingzhi Sun

Danqi Liao

Kincaid MacDonald

Yanlei Zhang

Guillaume Huguet

Chen Liu

Ian Adelstein

Tim G. J. Rudner

2025-01-22

aistats.org/AISTATS/2025/Conference (poster)

openreview.net

Mapping the gene space at single-cell resolution with gene signal pattern analysis

Aarthi Venkat

Martina Damo

Samuel Leone

Scott E. Youlten

Nikhil S. Joshi

Eric Fagerberg

John Attanasio

Michael Perlmutter

In single-cell sequencing analysis, several computational methods have been developed to map the cellular state space, but little has been d… (voir plus)one to map or create embeddings of the gene space. Here, we formulate the gene embedding problem, design tasks with simulated single-cell data to evaluate representations, and establish ten relevant baselines. We then present a graph signal processing approach we call gene signal pattern analysis (GSPA) that learns rich gene representations from single-cell data using a dictionary of diffusion wavelets on the cell-cell graph. GSPA enables characterization of genes based on their patterning on the cellular manifold. It also captures how localized or diffuse the expression of a gene is, for which we present a score called the gene localization score. We motivate and demonstrate the efficacy of GSPA as a framework for a range of biological tasks, such as capturing gene coexpression modules, condition-specific enrichment, and perturbation-specific gene-gene interactions. Then, we showcase the broad utility of gene rep-resentations derived from GSPA, including for cell-cell communication (GSPA-LR), spatial transcriptomics (GSPA-multimodal), and patient response (GSPA-Pt) analysis.

2024-12-20

Nature Computational Science (publié)

Beta cells are essential drivers of pancreatic ductal adenocarcinoma development

Cathy C. Garcia

Aarthi Venkat

Daniel C. McQuaid

Sherry Agabiti

Alex Tong

Rebecca L. Cardone

Rebecca Starble

Akin Sogunro

Jeremy B. Jacox

Christian F. Ruiz

Richard G. Kibbey

Mandar Deepak Muzumdar

Pancreatic endocrine-exocrine crosstalk plays a key role in normal physiology and disease. For instance, endocrine islet beta (β) cell secr… (voir plus)etion of insulin or cholecystokinin (CCK) promotes progression of pancreatic adenocarcinoma (PDAC), an exocrine cell-derived tumor. However, the cellular and molecular mechanisms that govern endocrine-exocrine signaling in tumorigenesis remain incompletely understood. We find that β cell ablation impedes PDAC development in mice, arguing that the endocrine pancreas is critical for exocrine tumorigenesis. Conversely, obesity induces β cell hormone dysregulation, alters CCK-dependent peri-islet exocrine cell transcriptional states, and enhances islet proximal tumor formation. Single-cell RNA-sequencing, in silico latent-space archetypal and trajectory analysis, and genetic lineage tracing in vivo reveal that obesity stimulates postnatal immature β cell expansion and adaptation towards a pro-tumorigenic CCK+ state via JNK/cJun stress-responsive signaling. These results define endocrine-exocrine signaling as a driver of PDAC development and uncover new avenues to target the endocrine pancreas to subvert exocrine tumorigenesis.

2024-12-03

bioRxiv (prépublication)

Exploring the Manifold of Neural Networks Using Diffusion Geometry

Elliott Abel

Peyton Crevasse

Yvan Grinspan

Selma Mazioud

Folu Ogundipe

Kristof Reimann

Ellie Schueler

Andrew J. Steindl

Ellen Zhang

Dhananjay Bhaskar

Siddharth Viswanath

Yanlei Zhang

Tim G. J. Rudner

Ian Adelstein

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we … (voir plus)apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.

2024-11-19

ArXiv (prépublication)

Exploring the Manifold of Neural Networks Using Diffusion Geometry

Elliott Abel

Peyton Crevasse

Yvan Grinspan

Selma Mazioud

Folu Ogundipe

Kristof Reimann

Ellie Schueler

Andrew J. Steindl

Ellen Zhang

Dhananjay Bhaskar

Siddharth Viswanath

Yanlei Zhang

Tim G. J. Rudner

Ian Adelstein

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we … (voir plus)apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.

2024-11-19

ArXiv (prépublication)