AI RESEARCH
FlowBoost Reveals Phase Transitions and Spectral Structure in Finite Free Information Inequalities
arXiv CS.LG
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ArXi:2604.11922v1 Announce Type: cross Using FlowBoost, a closed-loop deep generative optimization framework for extremal structure discovery, we investigate $\ell^p$-generalizations of the finite free Stam inequality for real-rooted polynomials under finite free additive convolution $\boxplus_n$. At $p=2$, FlowBoost finds the Hermite pair as the unique equality case and reveals the spectral structure of the linearized convolution map at this extremal point.