Related papers: Persistent Topological Features in Large Language …
Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing…
As machine learning becomes increasingly integral to autonomous decision-making processes involving human interaction, the necessity of comprehending the model's outputs through conversational means increases. Most recently, foundation…
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…
Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Latent space matching, which consists of matching distributions of features in latent space, is a crucial component for tasks such as adversarial attacks and defenses, domain adaptation, and generative modelling. Metrics for probability…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
The social and economic importance of large bodies of programs and data that are potentially long-lived has attracted much attention in the commercial and research communities. Here we concentrate on a set of methodologies and technologies…
Using persistent homology to guide optimization has emerged as a novel application of topological data analysis. Existing methods treat persistence calculation as a black box and backpropagate gradients only onto the simplices involved in…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies. In this paper we use a…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
Language models exhibit strong robustness to paraphrasing, suggesting that semantic information may be encoded through stable internal representations, yet the structure and origin of such invariance remain unclear. We propose a local…
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a…
Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…
Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…
With the rise of large language models (LLMs) for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric…
The theory of multidimensional persistent homology was initially developed in the discrete setting, and involved the study of simplicial complexes filtered through an ordering of the simplices. Later, stability properties of…
Quantifying patterns in visual or tactile textures provides important information about the process or phenomena that generated these patterns. In manufacturing, these patterns can be intentionally introduced as a design feature, or they…
In standard persistent homology, a persistent cycle born and dying with a persistence interval (bar) associates the bar with a concrete topological representative, which provides means to effectively navigate back from the barcode to the…