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About this paper
Gabin Maxime Nguegnang, Bubacarr Bah, Holger Rauhut, Ulrich Terstiege
The authors prove almost-sure convergence properties for stochastic gradient descent on deep linear networks with a regularized squared-loss objective. They establish boundedness of the iterates and connect them to the objective’s gradient flow under specified diminishing step sizes. The regularized loss converges, gradients vanish, and distance to the critical-point set tends to zero; convergence for the unregularized loss remains open.
Summary by alphaXiv.
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