 Adaptive Subgradient Methods for Online Learning and Stochastic Optimization by John Duchi and others

John Duchi, Elad Hazan and Yoram Singer; Journal of Machine Learning Research12(61),2121–2159(2011). Primary PDF: jmlr.org/papers/volume12/duchi11a/duchi11a.pdf

First-page full bylines verified. Section1.1, printed pp2122–2124, Eq1 and Eq5: cumulative gradient outer-product matrix, diagonal specialization and additive stabilization outside its square root. Used for mathematical mechanisms, not benchmark or convergence claims beyond their stated hypotheses.