28 accepted papers
Parameter-efficient fine-tuning (PEFT) has become the standard approach for adapting large language models under limited compute and memory budgets. Although previous methods improve efficiency through low-rank updates, quantization, or heuristic budget reallocation, they often decouple the allocati…
Large language models (LLMs) achieve remarkable performance through ever-increasing parameter counts, but scaling incurs steep computational costs. To better understand LLM scaling, we study representational differences between LLMs and their smaller counterparts, with the goal of replicating the re…
Single-cell transcriptomics and proteomics have become a great source for data-driven insights into biology, enabling the use of advanced deep learning methods to understand cellular heterogeneity and gene expression at the single-cell level. With the advent of spatial-omics data, we have the promis…
Embedding geometry plays a fundamental role in retrieval quality, yet dense retrievers for retrieval-augmented generation (RAG) remain largely confined to Euclidean space. However, natural language exhibits hierarchical structure from broad topics to specific entities that Euclidean embeddings fail …
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 may be effectively incorporated into a family of geometric g…
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 t…
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 gen…
Frontier large language models (LLMs) have shown great success in text modeling and generation tasks across domains. However, natural language exhibits inherent semantic hierarchies and nuanced geometric structure, which current LLMs do not capture completely owing to their reliance on Euclidean ope…
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 meth…
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 relatio…
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, a…
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…
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 poin…
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 to as signals) defined on the vertices of a single graph. T…
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 typically have distinct biophysical properties from sinks. Due…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology and physics. While it is thought that these methods preserve u…
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. To this end, we propose neural FIM, a method for com…
We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at…
In modern relational machine learning it is common to encounter large graphs that arise via interactions or similarities between observations in many domains. Further, in many cases the target entities for analysis are actually signals on such graphs. We propose to compare and organize such datasets…
We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) that learns stochastic, continuous population dynamics from static snapshot samples taken at sporadic timepoints. MIOFlow combines dynamic models, manifold learning, and optimal transport by training neural ordinary…
The last decade has witnessed a technological arms race to encode the molecular states of cells into DNA libraries, turning DNA sequencers into scalable single-cell microscopes. Single-cell measurement of chromatin accessibility (DNA), gene expression (RNA), and proteins has revealed rich cellular d…
We propose a new fast method of measuring distances between large numbers of related high dimensional datasets called the Diffusion Earth Mover’s Distance (EMD). We model the datasets as distributions supported on common data graph that is derived from the affinity matrix computed on the combined da…
It is increasingly common to encounter data in the form of cross-sectional population measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these me…
Functional magnetic resonance imaging (fMRI) is a crucial technology for gaining insights into cognitive processes in humans. Data amassed from fMRI measurements result in volumetric data sets that vary over time. However, analysing such data presents a challenge due to the large degree of noise and…
Interest in image-to-image translation has grown substantially in recent years with the success of unsupervised models based on the cycle-consistency assumption. The achievements of these models have been limited to a particular subset of domains where this assumption yields good results, namely hom…
Understanding why and how certain neural networks outperform others is key to guiding future development of network architectures and optimization methods. To this end, we introduce a novel visualization algorithm that reveals the internal geometry of such networks: Multislice PHATE (M-PHATE), the f…
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. This is in contrast to existing generative models that represent data density, and are strongly affected by noise…
It is increasingly common in many types of natural and physical systems (especially biological systems) to have different types of measurements performed on the same underlying system. In such settings, it is important to align the manifolds arising from each measurement in order to integrate such d…