9 problems

Let $X_1,\ldots,X_n$ be independent sensing matrices of the form … Consider the quadratic-neural-network sensing model with these matrices and fixed output weights. Gaussian-univer…

Perfect-recovery-threshold conjecture. The perfect-recovery threshold is

Consider the gradient flow dynamics in the absence of regularization, under Assumption 2, and let $\alpha_\mathrm{inter}(\kappa,\kappa^*,\Delta)$ be the interpolation threshold. Un…

Let $\alpha_\mathrm{inter}(\kappa,\kappa^*,\Delta)$ denote the interpolation threshold characterized in Proposition 1. When $\kappa\geq 1$, this threshold is the smallest value of…

Asymptotic local-PL curvature conjecture. Let $\varepsilon>0$. There exist $C_1,C_2>0$ depending only on the data and the initialization such that, for

The paper considers gradient-flow dynamics for general neural networks and the differential equations governing those dynamics, whose differential Galois group measures the algebra…

Adaptivity conjecture. Decoupling the learning scales in this way should be more adaptive to the problem than learning the two layers jointly.

Let $M$ be a smooth submanifold of $\mathbb{R}^D$, let $G:M\to\mathbb{R}^d$ be a smooth parametrization, and let $\mathrm{Lie}^{\geq 2}(\partial G)$ denote the span of Lie brackets…

Let $N$ be the number of layers in a deep linear network, and let $L^N$ denote its factorized square-loss objective. Assume that $XX^T$ has full rank, define … let…