17 papers
Scalable Graph Coreset Selection via Greedy Sampling
Zhaiming Shen, Alexander Cloninger
The paper introduces a greedy column‑selective algorithm that samples representative nodes from large graphs using only small random subsets of Laplacian columns, avoiding eigendec…
Robust Tangent Space Estimation via Laplacian Eigenvector Gradient Orthogonalization
Dhruv Kohli, Sawyer J. Robertson, Gal Mishne +1
Estimating the tangent spaces of a data manifold is a fundamental problem in geometric data analysis. The standard approach, Local Principal Component Analysis (LPCA), struggles in…
Transformers for Learning on Noisy and Task-Level Manifolds: Approximation and Generalization Insights
Zhaiming Shen, Alex Havrilla, Rongjie Lai +2
Transformers serve as the foundational architecture for large language and video generation models, such as GPT, BERT, SORA and their successors. Empirical studies have demonstrate…
Does Sparse Connectivity Improve Generalization? Convolutional Networks Below the Edge of Stability
Tongtong Liang, Esha Singh, Rahul Parhi +2
Gradient descent on overparameterized neural networks typically operates at the Edge of Stability (EoS), where the largest Hessian eigenvalue hovers around a step-size-dependent th…
Generalization Below the Edge of Stability: The Role of Data Geometry
Tongtong Liang, Alexander Cloninger, Rahul Parhi +1
Understanding generalization in overparameterized neural networks hinges on the interplay between the data geometry, neural architecture, and training dynamics. In this paper, we t…
Resistance Distance and Linearized Optimal Transport on Graphs
Sawyer Robertson, Zhengchao Wan, Alexander Cloninger
We study the linearization of a discrete transportation distance between probability distributions on finite weighted graphs originally due to Maas (``Gradient flows of the entropy…