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The talk will focus on limit theorems for stochastic gradient descent (SGD) and on how the choice of step size affects its convergence. We will begin by discussing the convergence of deterministic gradient descent with a constant step size, then review the classical Robbins–Monro result for SGD, and finally turn to several results from our joint work [1] concerning the convergence of SGD with a constant step size that tends to zero.

References:

D. Dudukalov, A. Logachov, V. Lotov, T. Prasolov, E. Prokopenko & A. Tarasenko, Convergence, Sticking and Escape: Stochastic Dynamics Near Critical Points in SGD, arXiv preprint, 2025, arXiv: 2505.18535

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/4TGPAsgr42lx.
Meeting code: 865-161-635
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Modern multi-modal learning often relies on the premise that jointly analyzing multiple, related datasets can yield more powerful inferences than processing each one in isolation. We study this through the lens of a pair of spiked random matrices with correlated spikes. By proposing a novel subgraph counts algorithm, we show that the correlation between the spikes can be exploited for inference even in certain regimes where inference in each individual matrix is believed to be computationally intractable. Furthermore, we provide evidence for a matching computational lower bound based on the low-degree polynomial framework, suggesting our algorithm is optimal. Our results thus establish a new computational phase transition in correlated spiked models, delineating the boundary between what is efficiently possible and what is not. Based on arXiv:2511.06040.