Smita Krishnaswamy

Neural signals are high-dimensional, noisy, and dynamic, making it challenging to extract interpretable features linked to behavior or disea… (voir plus)se. We introduce Neurospectrum, a framework that encodes neural activity as latent trajectories shaped by spatial and temporal structure. At each timepoint, signals are represented on a graph capturing spatial relationships, with a learnable attention mechanism highlighting important regions. These are embedded using graph wavelets and passed through a manifold-regularized autoencoder that preserves temporal geometry. The resulting latent trajectory is summarized using a principled set of descriptors - including curvature, path signatures, persistent homology, and recurrent networks -that capture multiscale geometric, topological, and dynamical features. These features drive downstream prediction in a modular, interpretable, and end-to-end trainable framework. We evaluate Neurospectrum on simulated and experimental datasets. It tracks phase synchronization in Kuramoto simulations, reconstructs visual stimuli from calcium imaging, and identifies biomarkers of obsessive-compulsive disorder in fMRI. Across tasks, Neurospectrum uncovers meaningful neural dynamics and outperforms traditional analysis methods.

2025-05-08

bioRxiv (prépublication)

ImmunoStruct: a multimodal neural network framework for immunogenicity prediction from peptide-MHC sequence, structure, and biochemical properties

Kevin Bijan Givechian

João Felipe Rocha

Edward Yang

Chen Liu

Kerrie Greene

Rex Ying

Etienne Caron

Akiko Iwasaki

2025-04-30

bioRxiv (prépublication)

ImmunoStruct: a multimodal neural network framework for immunogenicity prediction from peptide-MHC sequence, structure, and biochemical properties

Kevin Bijan Givechian

João Felipe Rocha

Edward Yang

Chen Liu

Kerrie Greene

Rex Ying

Etienne Caron

Akiko Iwasaki

2025-04-30

bioRxiv (prépublication)

InfoGain Wavelets: Furthering the Design of Diffusion Wavelets for Graph-Structured Data

David R. Johnson

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)

InfoGain Wavelets: Furthering the Design of Diffusion Wavelets for Graph-Structured Data

David R. Johnson

Michael Perlmutter

Diffusion wavelets extract information from graph signals at different scales of resolution by utilizing graph diffusion operators raised to… (voir plus) various powers, known as diffusion scales. Traditionally, the diffusion scales are chosen to be dyadic integers,

2025-04-01

arXiv (publié)

HiPoNet: A Multi-View Simplicial Complex Network for High Dimensional Point-Cloud and Single-Cell Data

Siddharth Viswanath

Hiren Madhu

Dhananjay Bhaskar

Jake Kovalic

David R. Johnson

Christopher Tape

Ian Adelstein

Rex Ying

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. Our work is motivated by single-cell data which can have very high-dimensionality --exceeding the capabilities of existing methods for point clouds which are mostly tailored for 3D data. Moreover, modern single-cell and spatial experiments now yield entire cohorts of datasets (i.e., one data set for 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 and topological information. In contrast, HiPoNet models the point-cloud as a set of higher-order simplicial complexes, with each particular complex being created using a reweighting of features. This method thus generates multiple constructs corresponding to different views of high-dimensional data, which in biology offers the possibility of disentangling distinct cellular processes. It then employs simplicial wavelet transforms to extract multiscale features, capturing both local and global topology from each view. We show that geometric and topological information is preserved in this framework both theoretically and empirically. We showcase the utility of HiPoNet on point-cloud level tasks, involving classification and regression of entire point-clouds in data cohorts. Experimentally, we find that HiPoNet outperforms other point-cloud and graph-based models on single-cell data. We also apply HiPoNet to spatial transcriptomics datasets using spatial coordinates 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)

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)

Principal Curvatures Estimation with Applications to Single Cell Data

Yanlei Zhang

Lydia Mezrag

Xingzhi Sun

Charles Xu

Kincaid MacDonald

Dhananjay Bhaskar

Guy Wolf

Bastian Rieck

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

Guy Wolf

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)

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

Xingzhi Sun

Danqi Liao

Kincaid MacDonald

Yanlei Zhang

Chen Liu

Guillaume Huguet

Guy Wolf

Ian Adelstein

Tim G. J. Rudner

2025-01-22

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