arXiv subjects

Smita Krishnaswamy

Publications and source records attributed to Smita Krishnaswamy.

At least 37 records · Page 2Linked to original sources

arXiv2025

Low-dimensional embeddings of high-dimensional data

Large collections of high-dimensional data have become nearly ubiquitous across many academic fields and application domains, ranging from biology to the humanities. Since working directly with high-dimensional data poses challenges, the demand for algorithms that create low-dimensional representations, or embeddings, for data visualization, exploration, and analysis is now greater than ever. In recent years, numerous embedding algorithms have been developed, and their usage has become widespread in research and industry. This surge of interest has resulted in a large and fragmented research field that faces technical challenges alongside fundamental debates, and it has left practitioners without clear guidance on how to effectively employ existing methods. Aiming to increase coherence and facilitate future work, in this review we provide a detailed and critical overview of recent developments, derive a list of best practices for creating and using low-dimensional embeddings, evaluate popular approaches on a variety of datasets, and discuss the remaining challenges and open problems in the field.

cs.LG↗

arXiv2025

STAGED: A Multi-Agent Neural Network for Learning Cellular Interaction Dynamics

The advent of single-cell technology has significantly improved our understanding of cellular states and subpopulations in various tissues under normal and diseased conditions by employing data-driven approaches such as clustering and trajectory inference. However, these methods consider cells as independent data points of population distributions. With spatial transcriptomics, we can represent cellular organization, along with dynamic cell-cell interactions that lead to changes in cell state. Still, key computational advances are necessary to enable the data-driven learning of such complex interactive cellular dynamics. While agent-based modeling (ABM) provides a powerful framework, traditional approaches rely on handcrafted rules derived from domain knowledge rather than data-driven approaches. To address this, we introduce Spatio Temporal Agent-Based Graph Evolution Dynamics(STAGED) integrating ABM with deep learning to model intercellular communication, and its effect on the intracellular gene regulatory network. Using graph ODE networks (GDEs) with shared weights per cell type, our approach represents genes as vertices and interactions as directed edges, dynamically learning their strengths through a designed attention mechanism. Trained to match continuous trajectories of simulated as well as inferred trajectories from spatial transcriptomics data, the model captures both intercellular and intracellular interactions, enabling a more adaptive and accurate representation of cellular dynamics.

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arXiv2025

SlepNet: Spectral Subgraph Representation Learning for Neural Dynamics

Graph neural networks have been useful in machine learning on graph-structured data, particularly for node classification and some types of graph classification tasks. However, they have had limited use in representing patterning of signals over graphs. Patterning of signals over graphs and in subgraphs carries important information in many domains including neuroscience. Neural signals are spatiotemporally patterned, high dimensional and difficult to decode. Graph signal processing and associated GCN models utilize the graph Fourier transform and are unable to efficiently represent spatially or spectrally localized signal patterning on graphs. Wavelet transforms have shown promise here, but offer non-canonical representations and cannot be tightly confined to subgraphs. Here we propose SlepNet, a novel GCN architecture that uses Slepian bases rather than graph Fourier harmonics. In SlepNet, the Slepian harmonics optimally concentrate signal energy on specifically relevant subgraphs that are automatically learned with a mask. Thus, they can produce canonical and highly resolved representations of neural activity, focusing energy of harmonics on areas of the brain which are activated. We evaluated SlepNet across three fMRI datasets, spanning cognitive and visual tasks, and two traffic dynamics datasets, comparing its performance against conventional GNNs and graph signal processing constructs. SlepNet outperforms the baselines in all datasets. Moreover, the extracted representations of signal patterns from SlepNet offers more resolution in distinguishing between similar patterns, and thus represent brain signaling transients as informative trajectories. Here we have shown that these extracted trajectory representations can be used for other downstream untrained tasks. Thus we establish that SlepNet is useful both for prediction and representation learning in spatiotemporal data.

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arXiv2025

DYMAG: Rethinking Message Passing Using Dynamical-systems-based Waveforms

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 rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

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arXiv2025

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

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 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.

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arXiv2025

ImageFlowNet: Forecasting Multiscale Image-Level Trajectories of Disease Progression with Irregularly-Sampled Longitudinal Medical Images

Advances in medical imaging technologies have enabled the collection of longitudinal images, which involve repeated scanning of the same patients over time, to monitor disease progression. However, predictive modeling of such data remains challenging due to high dimensionality, irregular sampling, and data sparsity. To address these issues, we propose ImageFlowNet, a novel model designed to forecast disease trajectories from initial images while preserving spatial details. ImageFlowNet first learns multiscale joint representation spaces across patients and time points, then optimizes deterministic or stochastic flow fields within these spaces using a position-parameterized neural ODE/SDE framework. The model leverages a UNet architecture to create robust multiscale representations and mitigates data scarcity by combining knowledge from all patients. We provide theoretical insights that support our formulation of ODEs, and motivate our regularizations involving high-level visual features, latent space organization, and trajectory smoothness. We validate ImageFlowNet on three longitudinal medical image datasets depicting progression in geographic atrophy, multiple sclerosis, and glioblastoma, demonstrating its ability to effectively forecast disease progression and outperform existing methods. Our contributions include the development of ImageFlowNet, its theoretical underpinnings, and empirical validation on real-world datasets. The official implementation is available at https://github.com/KrishnaswamyLab/ImageFlowNet.

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arXiv2025

DiffKillR: Killing and Recreating Diffeomorphisms for Cell Annotation in Dense Microscopy Images

The proliferation of digital microscopy images, driven by advances in automated whole slide scanning, presents significant opportunities for biomedical research and clinical diagnostics. However, accurately annotating densely packed information in these images remains a major challenge. To address this, we introduce DiffKillR, a novel framework that reframes cell annotation as the combination of archetype matching and image registration tasks. DiffKillR employs two complementary neural networks: one that learns a diffeomorphism-invariant feature space for robust cell matching and another that computes the precise warping field between cells for annotation mapping. Using a small set of annotated archetypes, DiffKillR efficiently propagates annotations across large microscopy images, reducing the need for extensive manual labeling. More importantly, it is suitable for any type of pixel-level annotation. We will discuss the theoretical properties of DiffKillR and validate it on three microscopy tasks, demonstrating its advantages over existing supervised, semi-supervised, and unsupervised methods. The code is available at https://github.com/KrishnaswamyLab/DiffKillR.

cs.CV↗

arXiv2025

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

Rapid growth of high-dimensional datasets in fields such as single-cell RNA sequencing and spatial genomics has led to unprecedented opportunities 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 using geodesic-guided flows. GAGA shows competitive performance in simulated and real-world datasets, including a 30% improvement over the state-of-the-art methods in single-cell population-level trajectory inference.

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arXiv2025

Principal Curvatures Estimation with Applications to Single Cell Data

The rapidly growing field of single-cell transcriptomic sequencing (scRNAseq) presents challenges for data analysis due to its massive datasets. 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.

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arXiv2025

Geometric Scattering on Measure Spaces

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 properties. Subsequently, there has been widespread interest in extending the success of CNNs to data sets with non-Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. In this paper, we introduce a general, unified model for 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. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, directed graphs, and on high-dimensional single-cell data.

stat.ML↗

arXiv2025

Manifold Filter-Combine Networks

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 naturally suggests many interesting families of MNNs which can be interpreted as manifold analogues of various popular GNNs. We propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating an underlying manifold by a sparse graph. We then prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity, and we numerically demonstrate its effectiveness on real-world and synthetic data sets.

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arXiv2024

Exploring the Manifold of Neural Networks Using Diffusion Geometry

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we 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.

cs.LG↗

arXiv2024

Convergence of Manifold Filter-Combine Networks

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 naturally suggests many interesting families of MNNs which can be interpreted as the manifold analog of various popular GNNs. We then propose a method for implementing MFCNs on high-dimensional point clouds that relies on approximating the manifold by a sparse graph. We prove that our method is consistent in the sense that it converges to a continuum limit as the number of data points tends to infinity.

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arXiv2024

Latent Representation Learning for Multimodal Brain Activity Translation

Neuroscience employs diverse neuroimaging techniques, each offering distinct insights into brain activity, from electrophysiological recordings such as EEG, which have high temporal resolution, to hemodynamic modalities such as fMRI, which have increased spatial precision. However, integrating these heterogeneous data sources remains a challenge, which limits a comprehensive understanding of brain function. We present the Spatiotemporal Alignment of Multimodal Brain Activity (SAMBA) framework, which bridges the spatial and temporal resolution gaps across modalities by learning a unified latent space free of modality-specific biases. SAMBA introduces a novel attention-based wavelet decomposition for spectral filtering of electrophysiological recordings, graph attention networks to model functional connectivity between functional brain units, and recurrent layers to capture temporal autocorrelations in brain signal. We show that the training of SAMBA, aside from achieving translation, also learns a rich representation of brain information processing. We showcase this classify external stimuli driving brain activity from the representation learned in hidden layers of SAMBA, paving the way for broad downstream applications in neuroscience research and clinical contexts.

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arXiv2024

Looking through the mind's eye via multimodal encoder-decoder networks

In this work, we explore the decoding of mental imagery from subjects using their fMRI measurements. In order to achieve this decoding, we first created a mapping between a subject's fMRI signals elicited by the videos the subjects watched. This mapping associates the high dimensional fMRI activation states with visual imagery. Next, we prompted the subjects textually, primarily with emotion labels which had no direct reference to visual objects. Then to decode visual imagery that may have been in a person's mind's eye, we align a latent representation of these fMRI measurements with a corresponding video-fMRI based on textual labels given to the videos themselves. This alignment has the effect of overlapping the video fMRI embedding with the text-prompted fMRI embedding, thus allowing us to use our fMRI-to-video mapping to decode. Additionally, we enhance an existing fMRI dataset, initially consisting of data from five subjects, by including recordings from three more subjects gathered by our team. We demonstrate the efficacy of our model on this augmented dataset both in accurately creating a mapping, as well as in plausibly decoding mental imagery.

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arXiv2024

Hyperedge Representations with Hypergraph Wavelets: Applications to Spatial Transcriptomics

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 and powerful framework for modeling such higher-order relationships. In this work, we introduce hypergraph diffusion wavelets and describe their favorable spectral and spatial properties. We demonstrate their utility for biomedical discovery in spatially resolved transcriptomics by applying the method to represent disease-relevant cellular niches for Alzheimer's disease.

stat.ML↗

arXiv2024

CUTS: A Deep Learning and Topological Framework for Multigranular Unsupervised Medical Image Segmentation

Segmenting medical images is critical to facilitating both patient diagnoses and quantitative research. A major limiting factor is the lack of labeled data, as obtaining expert annotations for each new set of imaging data and task can be labor intensive and inconsistent among annotators. We present CUTS, an unsupervised deep learning framework for medical image segmentation. CUTS operates in two stages. For each image, it produces an embedding map via intra-image contrastive learning and local patch reconstruction. Then, these embeddings are partitioned at dynamic granularity levels that correspond to the data topology. CUTS yields a series of coarse-to-fine-grained segmentations that highlight features at various granularities. We applied CUTS to retinal fundus images and two types of brain MRI images to delineate structures and patterns at different scales. When evaluated against predefined anatomical masks, CUTS improved the dice coefficient and Hausdorff distance by at least 10% compared to existing unsupervised methods. Finally, CUTS showed performance on par with Segment Anything Models (SAM, MedSAM, SAM-Med2D) pre-trained on gigantic labeled datasets.

cs.CV↗

arXiv2024

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. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification tasks.

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