Geometric Analysis
Geometric analysis is a burgeoning field applying geometric concepts and tools to diverse problems in machine learning, computer vision, and other areas. Current research focuses on understanding the geometric properties of neural network architectures (e.g., convolutional networks, self-attention networks, and neural fields), analyzing the geometry of data manifolds and their impact on model performance, and developing novel algorithms leveraging geometric information for tasks like mesh reconstruction, image synthesis, and graph embedding. These advancements offer improved model interpretability, enhanced efficiency in complex tasks, and new approaches to solving problems in various scientific and engineering domains.
Papers
Geometry of naturalistic object representations in recurrent neural network models of working memory
Xiaoxuan Lei, Takuya Ito, Pouya Bashivan
Geometry of orofacial neuromuscular signals: speech articulation decoding using surface electromyography
Harshavardhana T. Gowda, Zachary D. McNaughton, Lee M. Miller
On the Geometry of Regularization in Adversarial Training: High-Dimensional Asymptotics and Generalization Bounds
Matteo Vilucchio, Nikolaos Tsilivis, Bruno Loureiro, Julia Kempe
MSGField: A Unified Scene Representation Integrating Motion, Semantics, and Geometry for Robotic Manipulation
Yu Sheng, Runfeng Lin, Lidian Wang, Quecheng Qiu, YanYong Zhang, Yu Zhang, Bei Hua, Jianmin Ji