Improved high-dimensional estimation with Langevin dynamics and stochastic weight averaging

ArXi:2603.06028v1 Announce Type: new Significant recent work has studied the ability of gradient descent to recover a hidden planted direction $\theta^\star \in S^{d-1}$ in different high-dimensional settings, including tensor PCA and single-index models. The key quantity that governs the ability of gradient descent to traverse these landscapes is the information exponent $k^\star$ (Ben Arous, ), which corresponds to the order of the saddle at initialization in the population landscape.