6 papers
Central limit theorems for the eigenvalues of graph Laplacians on data clouds
Chenghui Li, Nicolás García Trillos, Housen Li +1
Given i.i.d.\ samples from a distribution supported on a low dimensional manifold embedded in Eucliden space, we consider the graph Laplacian ope…
Quantifying Structure in CLIP Embeddings: A Statistical Framework for Concept Interpretation
Jitian Zhao, Chenghui Li, Frederic Sala +1
Concept-based approaches, which aim to identify human-understandable concepts within a model's internal representations, are a promising method for interpreting embeddings from dee…
Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
Nicolás García Trillos, Chenghui Li, Raghavendra Venkatraman
We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution supported on a manifold . The operators discussed in the pape…
Consistency of augmentation graph and network approximability in contrastive learning
Chenghui Li, A. Martina Neuman
Contrastive learning leverages data augmentation to develop feature representation without relying on large labeled datasets. However, despite its empirical success, the theoretica…
A Divide-and-Conquer Approach to Persistent Homology
Chenghui Li, Jessi Cisewski-Kehe
Persistent homology is a tool of topological data analysis that has been used in a variety of settings to characterize different dimensional holes in data. However, persistent homo…
Spectral Neural Networks: Approximation Theory and Optimization Landscape
Chenghui Li, Rishi Sonthalia, Nicolas Garcia Trillos
There is a large variety of machine learning methodologies that are based on the extraction of spectral geometric information from data. However, the implementations of many of the…