no code implementations • 4 Feb 2021 • Vamsi Pritham Pingali
We prove that a "cushioned" Hermitian-Einstein-type equation proposed by Demailly in an approach towards a conjecture of Griffiths on the existence of a Griffiths positively curved metric on a Hartshorne ample vector bundle, has an essentially unique solution when the bundle is stable.
Differential Geometry
no code implementations • 1 Jan 2021 • Yikai Zhang, Samuel Bald, Wenjia Zhang, Vamsi Pritham Pingali, Chao Chen, Mayank Goswami
We provide empirical evidence that this condition holds for several loss functions, and provide theoretical evidence that the known tight SGD stability bounds for convex and non-convex loss functions can be circumvented by HC loss functions, thus partially explaining the generalization of deep neural networks.