Liangchen Liu

we are all travelers, in the

wilderness of this world

Hello! I can also go by Lewis. I’m a fourth-year Ph.D.candidate in the Department of Mathematics at the University of Texas at Austin. I’m grateful for working with and being supported by Prof.Richard Tsai under the Scientific AI Research group.

My research interests primarily center around studying the impact of the geometry of the data distribution on (machine learning) algorithms, through the applications of tools from differential geometry and geometric probability.

I’m also into cooking, British rock, bouldering, escape room, and Hearthstone.

news

Oct 1, 2024	Currently stuyding the discrete notions of (Ricci) curvatures on graphs. Fun stuffs!
May 3, 2024	You know what? The learning rate in gradient descent can go beyond the largest eigenvalue!
Jul 25, 2023	Attended the 40th ICML 2023, exciting to meet so many new people with many interesting works!
Jul 18, 2023	The RaySense paper has been accepted for publication in CAMC for the special issue to honor Prof. Stanley Osher’s 80th birthday.
Jun 18, 2023	The paper Linear Regression on Manifold Structured Data was accepted to the TAGML workshop in ICML2023, and it will be published in PMLR.

publications

2024

Data-induced multiscale losses and efficient multirate gradient descent schemes

Liangchen Liu, Juncai He, and Richard Tsai

arXiv preprint arXiv:2402.03021, 2024

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We investigate the impact of multiscale data (large variations in scale across different directions) on machine learning algorithms and reveal multiscale structures in the loss landscape. We also introduce a novel gradient descent algorithm for this scenario adopting a combination of large and small learning rates, and provide convergence guarantees.

2023

Linear Regression on Manifold Structured Data: the Impact of Extrinsic Geometry on Solutions

Liangchen Liu, Juncai He, and Richard Tsai

arXiv preprint arXiv:2307.02478, 2023

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We study linear regression applied to data structured on a manifold. We reveal the impact of the data manifold’s extrinsic geometry on the regression by deriving explicit solution formulas and numerical experiments. Our findings reveal the role of data manifold geometry in ensuring the stability of regression models for out-of-distribution inferences.

2019

Nearest neighbor sampling of point sets using rays (RaySense)

Liangchen Liu, Louis Ly, Colin Macdonald, and 1 more author

arXiv preprint arXiv:1911.10737, 2019

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We propose a new framework for the sampling, compression, and analysis of distributions of point sets and other geometric objects. We provide theoretical explanations to its properties along with guarantees for line integral approximation