46 citations · 49 across the 9 of their papers we have counts for
10 papers
Topological Interpretations of GPT-3
Tianyi Sun, Bradley Nelson
This is an experiential study of investigating a consistent method for deriving the correlation between sentence vector and semantic meaning of a sentence. We first used three stat…
Greedy Matroid Algorithm And Computational Persistent Homology
Tianyi Sun, Bradley Nelson
An important problem in computational topology is to calculate the homology of a space from samples. In this work, we develop a statistical approach to this problem by calculating…
Parameterized Vietoris-Rips Filtrations via Covers
Bradley J. Nelson
A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the developm…
What is an equivariant neural network?
Lek-Heng Lim, Bradley J. Nelson
We explain equivariant neural networks, a notion underlying breakthroughs in machine learning from deep convolutional neural networks for computer vision to AlphaFold 2 for protein…
Topology-Preserving Dimensionality Reduction via Interleaving Optimization
Bradley J. Nelson, Yuan Luo
Dimensionality reduction techniques are powerful tools for data preprocessing and visualization which typically come with few guarantees concerning the topological correctness of a…
Topological Regularization for Dense Prediction
Deqing Fu, Bradley J. Nelson
Dense prediction tasks such as depth perception and semantic segmentation are important applications in computer vision that have a concrete topological description in terms of par…
Accelerating Iterated Persistent Homology Computations with Warm Starts
Yuan Luo, Bradley J. Nelson
Persistent homology is a topological feature used in a variety of applications such as generating features for data analysis and penalizing optimization problems. We develop an app…
Clustering of Electromagnetic Showers and Particle Interactions with Graph Neural Networks in Liquid Argon Time Projection Chambers Data
Francois Drielsma, Qing Lin, Pierre Côte de Soux +7
Liquid Argon Time Projection Chambers (LArTPCs) are a class of detectors that produce high resolution images of charged particles within their sensitive volume. In these images, th…
Persistent and Zigzag Homology: A Matrix Factorization Viewpoint
Gunnar Carlsson, Anjan Dwaraknath, Bradley J. Nelson
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundame…
A Topology Layer for Machine Learning
Rickard Brüel-Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath +3
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topolog…