Related papers: TopoFisher: Learning Topological Summary Statistic…

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

We propose a novel unsupervised learning approach to 3D shape correspondence that builds a multiscale matching pipeline into a deep neural network. This approach is based on smooth shells, the current state-of-the-art axiomatic…

Commonly, learning-based topological navigation approaches produce a local policy while preserving some loose connectivity of the space through a topological map. Nevertheless, spurious or missing edges in the topological graph often lead…

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…

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…

First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic…

Extracting maximum cosmological information from current and upcoming large-scale structure data requires going beyond summary statistics as currently used in likelihood-based inference. Simulation-Based Inference (SBI) promises to enable…

Data quality is crucial for the successful training, generalization and performance of machine learning models. We propose to measure the quality of a subset concerning the dataset it represents, using topological data analysis techniques.…

The high-pressure transportation process of pipeline necessitates an accurate hydraulic transient simulation tool to prevent slack line flow and over-pressure, which can endanger pipeline operations. However, current numerical solution…

We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…

Text summarization aims to condense long documents and retain key information. Critical to the success of a summarization model is the faithful inference of latent representations of words or tokens in the source documents. Most recent…

The Fisher information metric is an important foundation of information geometry, wherein it allows us to approximate the local geometry of a probability distribution. Recurrent neural networks such as the Sequence-to-Sequence (Seq2Seq)…

A central challenge in data visualization is to understand which data samples are required to generate an image of a data set in which the relevant information is encoded. In this work, we make a first step towards answering the question of…

As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…

Artificial neural networks can learn complex, salient data features to achieve a given task. On the opposite end of the spectrum, mathematically grounded methods such as topological data analysis allow users to design analysis pipelines…

Recovering point clouds involves the sequential process of sampling and restoration, yet existing methods struggle to effectively leverage both topological and geometric attributes. To address this, we propose an end-to-end architecture…

The estimation of continuous parameters from measured data plays a central role in many fields of physics. A key tool in understanding and improving such estimation processes is the concept of Fisher information, which quantifies how…

Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been…

Network compression has been widely studied since it is able to reduce the memory and computation cost during inference. However, previous methods seldom deal with complicated structures like residual connections, group/depth-wise…

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…