5 papers
On the cover time of Brownian motion on the Brownian continuum random tree
George Andriopoulos, David A. Croydon, Vlad Margarint +1
Upon almost-every realisation of the Brownian continuum random tree (CRT), it is possible to define a canonical diffusion process or `Brownian motion'. The main result of this arti…
Geometric Analysis of Neural Regression Collapse via Intrinsic Dimension
George Andriopoulos, Zixuan Dong, Bimarsha Adhikari +1
Neural multivariate regression underpins a wide range of domains, including control, robotics, and finance, yet the geometry of its learned representations remains poorly character…
Neural Multivariate Regression: Qualitative Insights from the Unconstrained Feature Model
George Andriopoulos, Soyuj Jung Basnet, Juan Guevara +2
The Unconstrained Feature Model (UFM) is a mathematical framework that enables closed-form approximations for minimal training loss and related performance measures in deep neural…
Cross Entropy versus Label Smoothing: A Neural Collapse Perspective
Li Guo, George Andriopoulos, Zifan Zhao +3
Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC),…
The Prevalence of Neural Collapse in Neural Multivariate Regression
George Andriopoulos, Zixuan Dong, Li Guo +2
Recently it has been observed that neural networks exhibit Neural Collapse (NC) during the final stage of training for the classification problem. We empirically show that multivar…