AI Networking Cookbook: Practical recipes for AI-assisted network automation and development
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This work develops an approach to the spectral norm of the matrix product $\Pi U_V$, based on entropy estimates for level sets of vectors $x\in V$, and shows that matching results hold for other random models with negatively associated entries.
A random $n\times k$ matrix $S$ is an \emph{$(r,\alpha)$-oblivious subspace injection} (OSI) if $\mathbb{E}\|S^\top x\|_2^2=\|x\|_2^2$ for every $x\in\mathbb{R}^n$, and for every fixed $r$-dimensional subspace $V\subset\mathbb{R}^n$, with probability close to one, one has $\alpha\|x\|_2^2\le\|S^\top x\|_2^2$ for all $x...
The main thrust of the result is that it is actually obtained by an efficient \textit{online} algorithm that minimizes prefix discrepancy, and is also essentially optimal, since online prefix discrepancy is known to scale as $\omega(\sqrt{d})$ for $d =o(\log T)$.
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