An input-to-state Lyapunov function is introduced to prove global asymptotic stability of RMSProp for constant step sizes and robustness to arbitrary bounded time-varying step size rules.
Adaptive subgradient methods for online learning and stochastic optimization
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FlowAdam adds clipped ODE integration to Adam with soft momentum injection for implicit regularization, cutting held-out error 10-22% on coupled matrix/tensor tasks while matching Adam on standard workloads.
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Global Stability and Step Size Robustness of RMSProp
An input-to-state Lyapunov function is introduced to prove global asymptotic stability of RMSProp for constant step sizes and robustness to arbitrary bounded time-varying step size rules.
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FlowAdam: Implicit Regularization via Geometry-Aware Soft Momentum Injection
FlowAdam adds clipped ODE integration to Adam with soft momentum injection for implicit regularization, cutting held-out error 10-22% on coupled matrix/tensor tasks while matching Adam on standard workloads.