Chasing the Constants and Its Implication in Private Learning

In this talk, we will discuss recent works that establish deep connections between private continual counting and a concept in matrix analysis (factorization norms) with its applications in private training. We then discuss the series of recent results that improve upon more than three decades-old results in matrix analysis. In particular, we will show an upper and lower bound on its norm with an additive gap of $0.14 + o(1)$. Moreover, the upper bound is achieved by an explicit factorization. Based on joint works with Hendrik Fichtenberger (Google), Monika Henzinger (ISTA), Nikita Kalinin (ISTA), and Sarvagya Upadhyay (Fujitsu Research Labs) and a topic of recent monologue (https://arxiv.org/abs/2506.08201)