5 problems

Let $f,g:\mathbb{R}^d\to\mathbb{R}$ be two continuous functions, and let $\Gamma,\Gamma^\prime$ be their respective graphs. Write…

Consider large neural networks trained by an optimization process, their local minima, and their generalization performance on a test set. Equivalent-minima conjecture. Large neura…

Consider the loss landscape of a recurrent neural network and its minima, between which continuous paths may be constructed. Felix et al.'s manifold conjecture. The loss minima are…

Let a deep neural network (a deepnet) be trained to a converged solution, and consider the curvature of its loss at that solution. Hochreiter et al.'s conjecture. The generalizatio…

Benign-landscape conjecture. In many situations, nonlinear activation functions should give rise to “nice” landscape properties, or even to the complete absence of spurious local m…