arXiv subjects

Chenguang Xu

Publications and source records attributed to Chenguang Xu.

3 recordsLinked to original sources

arXiv2024

Persistence module and Schubert calculus

A multiplication on persistence diagrams is introduced by means of Schubert calculus. The key observation behind this multiplication comes from the fact that the representation space of persistence modules has the structure of the Schubert decomposition of a flag. In particular, isomorphism classes of persistence modules correspond to Schubert cells, thereby the Schubert calculus naturally defines a multiplication on persistence diagrams. The meaning of the multiplication on persistence diagrams is carried over from that on Schubert calculus, i.e., algebro-geometric intersections of varieties of persistence modules.

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arXiv2023

Refinement of Interval Approximations for Fully Commutative Quivers

A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative quiver's representation via synthesizing interpretations obtained from intervals. Additionally, it provides a mechanism to tune the balance between approximation resolution and computational complexity. This framework is evaluated on commutative ladders of both finite-type and infinite-type. For the former, we discover an efficient method for the indecomposable decomposition leveraging solely one-parameter persistent homology. For the latter, we introduce a new invariant that reveals persistence in the second parameter by connecting two standard persistence diagrams using interval approximations. We subsequently present several models for constructing commutative ladder filtrations, offering fresh insights into random filtrations and demonstrating our toolkit's effectiveness in analyzing the topology of materials.

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arXiv2021

Proposing an Interactive Audit Pipeline for Visual Privacy Research

In an ideal world, deployed machine learning models will enhance our society. We hope that those models will provide unbiased and ethical decisions that will benefit everyone. However, this is not always the case; issues arise during the data preparation process throughout the steps leading to the models' deployment. The continued use of biased datasets and processes will adversely damage communities and increase the cost of fixing the problem later. In this work, we walk through the decision-making process that a researcher should consider before, during, and after a system deployment to understand the broader impacts of their research in the community. Throughout this paper, we discuss fairness, privacy, and ownership issues in the machine learning pipeline; we assert the need for a responsible human-over-the-loop methodology to bring accountability into the machine learning pipeline, and finally, reflect on the need to explore research agendas that have harmful societal impacts. We examine visual privacy research and draw lessons that can apply broadly to artificial intelligence. Our goal is to systematically analyze the machine learning pipeline for visual privacy and bias issues. We hope to raise stakeholder (e.g., researchers, modelers, corporations) awareness as these issues propagate in this pipeline's various machine learning phases.

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