相关论文: What Topological and Geometric Structure Do Biolog…

Methods allowing the synthesis of realistic cell shapes could help generate training data sets to improve cell tracking and segmentation in biomedical images. Deep generative models for cell shape synthesis require a light-weight and…

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…

The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows…

Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…

We prove that for a broad class of permutation-equivariant learning rules (including SGD, Adam, and others), the training process induces a bi-Lipschitz mapping between neurons and strongly constrains the topology of the neuron distribution…

Deep sequence models are said to store atomic facts predominantly in the form of associative memory: a brute-force lookup of co-occurring entities. We identify a dramatically different form of storage of atomic facts that we term as…

Structural knowledge graph foundation models aim to generalize reasoning to completely new graphs with unseen entities and relations. A key limitation of existing approaches like Ultra is their reliance on a single relational transformation…

Single-cell RNA sequencing (scRNA-seq) data exhibit strong and reproducible statistical structure. This has motivated the development of large-scale foundation models, such as TranscriptFormer, that use transformer-based architectures to…

A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of the bosonic, (0,1)- and…

Structural Health Monitoring (SHM) is a critical task for ensuring the safety and reliability of civil infrastructures, typically realized on bridges and viaducts by means of vibration monitoring. In this paper, we propose for the first…

In this work, we build a generic architecture of Convolutional Neural Networks to discover empirical properties of neural networks. Our first contribution is to introduce a state-of-the-art framework that depends upon few hyper parameters…

Deep learning has made significant progress in protein structure prediction, advancing the development of computational biology. However, despite the high accuracy achieved in predicting single-chain structures, a significant number of…

Since its foundations, more than one hundred years ago, the field of structural biology has strived to understand and analyze the properties of molecules and their interactions by studying the structure that they take in 3D space. However,…

This paper investigates the relationship between convolutional neural network (CNN) topology and image recognition performance through a comparative study of the VGG, ResNet, and GoogLeNet architectural families. Utilizing a unified…

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

Earth observation foundation models encode land surface information into dense embedding vectors, yet the geometric structure of these representations and its implications for downstream reasoning remain underexplored. We characterize the…

Identifying driver genes is crucial for understanding oncogenesis and developing targeted cancer therapies. Driver discovery methods using protein or pathway networks rely on traditional network science measures, focusing on nodes, edges,…

We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first…

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…