5 papers
Jacobian estimates and geometric inequalities under intermediate Ricci curvature
Kwok-Kun Kwong, Jihye Lee, Fabio Ricci
We prove a Jacobian estimate underlying both the Heintze--Karcher comparison and the Alexandrov--Bakelman--Pucci method for submanifolds of arbitrary codimension. The estimate reta…
A Fourier perspective on the learning dynamics of neural networks: from sample complexities to mechanistic insights
Fabiola Ricci, Claudia Merger, Sebastian Goldt
Neural networks trained with gradient-based methods exhibit a strong simplicity bias: they learn simpler statistical features of their data before moving to more complex features.…
Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions
Fabiola Ricci, Lorenzo Bardone, Sebastian Goldt
Deep neural networks learn structured features from complex, non-Gaussian inputs, but the mechanisms behind this process remain poorly understood. Our work is motivated by the obse…
Isoperimetric profile function comparisons with Integral Ricci curvature bounds
Jihye Lee, Fabio Ricci
We prove comparison results for the Isoperimetric profile function in the setting of manifolds with integral bounds on the Ricci curvature. We extend previous work of Ni and Wang a…
The Log-Sobolev inequality for a submanifold in manifolds with asymptotic non-negative intermediate Ricci curvature
Jihye Lee, Fabio Ricci
We prove a sharp Log-Sobolev inequality for submanifolds of a complete non-compact Riemannian manifold with asymptotic non-negative intermediate Ricci curvature and Euclidean volum…