Guo, Fang, and Lu recently proved the Koml\'os conjecture: for vectors $v_1,\ldots,v_n\in\mathbb R^d$ of Euclidean norm at most one, there are signs $\varepsilon_j\in\{-1,1\}$ with $\|\sum_j\varepsilon_jv_j\|_\infty\le3\sqrt{2\pi}$. We give a short proof of the bound $3\pi$ that keeps the geometric lifting framework of...
We develop a novel approach to matrix discrepancy based on matrix small-ball estimates. Specifically, we use a determinantal weight (obtained from the log-barrier) to scale the small-ball probability into a partition function of a tilt of the Gaussian measure. We then employ matrix-weighted Poincar\'e inequalities to c...
The dynamics of Stochastic Gradient Descent is studied by modeling the stochastic gradient flow as a percolation process, in which nested architectural symmetries force subnetworks to merge in discrete blocks rather than by single-edge attachment.
Sai Niranjan Ramachandran, Suvrit Sra· 0 citations
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