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About this paper
Anupama Sridhar, Alexander Johansen
Stanford University researchers developed a theoretical framework to prove global convergence and generalization guarantees for the Adam optimizer in deep ReLU networks, which are known for their non-smooth and non-convex loss landscapes. This framework, based on a novel analysis of region-crossing complexity and Kakeya-based generalization bounds, demonstrates that Adam's iterates converge to a true global minimizer with exponential rates after initial stabilization.
Key insights
- Empirically-motivated refinements drastically reduce the theoretical region-crossing complexity of Adam's trajectory in ReLU networks from exponential to near-linear in the effective dimension.
- Adam exhibits a two-phase convergence: an initial sublinear phase leading to activation mask stabilization, followed by exponential convergence to a local minimizer within the stable activation cone.
- The Uniform Low-Barrier (ULB) connectivity property of the loss landscape is crucial for guaranteeing global optimality, ensuring all local minima are effectively global minima.
Summary by alphaXiv.
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