arXiv subjects

Catherine Li

Publications and source records attributed to Catherine Li.

4 recordsLinked to original sources

arXiv2026

Level structures and cyclic power operations on the homology of $\mathbb{E}_\infty$ spaces

In this document, we discuss how cyclic power operations for periodic complex bordism can be understood through algebraic geometry, following from the theory of power operations for Morava $E$-theory developed by Ando, Hopkins, and Strickland. Using this perspective, we describe how one computes power operations on the $E$-homology of $BU$ and $BU\times \mathbb{Z}$, where $E$ is a 2-periodic even $\mathbb{E}_\infty$ ring. Then we provide some explicit example computations at $p=2$; in particular, we compute the action of the additive operations $\Delta$ on the indecomposables $\widehat{Q}(E_0(BU))$ for $E=KU, E_2$.

math.AT↗

arXiv2026

Sharpness-Aware Pretraining Mitigates Catastrophic Forgetting

Pretraining optimizers are tuned to produce the strongest possible base model, on the assumption that a stronger starting point yields a stronger model after subsequent changes like post-training and quantization. This overlooks the geometry of the base model which controls how much of the base model's capabilities survive subsequent parameter updates. We study three pretraining optimization approaches that bias optimization toward flatter minima: Sharpness-Aware Minimization (SAM), large learning rates, and shortened learning rate annealing periods. Across model sizes ranging from 20M to 150M parameters, we find that these interventions consistently improve downstream performance after post-training on five common datasets with up to 80% less forgetting. These principles hold at scale: a short SAM mid-training phase applied to an existing OLMo-2-1B checkpoint reduces forgetting by 31% after MetaMath post-training and by 40% after 4-bit quantization.

cs.LG↗

arXiv2025

In-Vivo Skin 3-D Surface Reconstruction and Wrinkle Depth Estimation using Handheld High Resolution Tactile Sensing

Three-dimensional (3-D) skin surface reconstruction offers promise for objective and quantitative dermatological assessment, but no portable, high-resolution device exists that has been validated and used for depth reconstruction across various body locations. We present a compact 3-D skin reconstruction probe based on GelSight tactile imaging with a custom elastic gel and a learning-based reconstruction algorithm for micron-level wrinkle height estimation. Our probe, integrated into a handheld probe with force sensing for consistent contact, achieves a mean absolute error of 12.55 micron on wrinkle-like test objects. In a study with 15 participants without skin disorders, we provide the first validated wrinkle depth metrics across multiple body regions. We further demonstrate statistically significant reductions in wrinkle height at three locations following over-the-counter moisturizer application. Our work offers a validated tool for clinical and cosmetic skin analysis, with potential applications in diagnosis, treatment monitoring, and skincare efficacy evaluation.

cs.CV↗

arXiv2023

Spatiotemporal risk prediction for infectious disease spread and mortality

With the outbreak of the COVID-19 pandemic, various studies have focused on predicting the trajectory and risk factors of the virus and its variants. Building on previous work that addressed this problem using genetic and epidemiological data, we introduce a method, Geo Score, that also incorporates geographic, socioeconomic, and demographic data to estimate infection and mortality risk by region and time. We employ gradient descent to find the optimal weights of the factors' significance in determining risk. Such spatiotemporal risk prediction is important for informed public health decision-making so that individuals are aware of the risks of travel during an epidemic or pandemic, and, perhaps more importantly, so that policymakers know how to triage limited resources during a crisis. We apply our method to New York City COVID-19 data from 2020, predicting ZIP code-level COVID-19 risk for 2021.

stat.AP↗