Derives ODE limits of Adam-DA showing that first- and second-order momentum parameters reverse their convergence roles in zero-sum games compared to minimization, validated on GAN experiments.
Reddi and Satyen Kale and Sanjiv Kumar , booktitle =
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Muon does not converge on convex Lipschitz functions regardless of learning rate, while error feedback restores theoretical convergence but degrades performance on CIFAR-10 and nanoGPT tasks.
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Understanding Dynamics of Adam in Zero-Sum Games: An ODE Approach
Derives ODE limits of Adam-DA showing that first- and second-order momentum parameters reverse their convergence roles in zero-sum games compared to minimization, validated on GAN experiments.
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Muon Does Not Converge on Convex Lipschitz Functions
Muon does not converge on convex Lipschitz functions regardless of learning rate, while error feedback restores theoretical convergence but degrades performance on CIFAR-10 and nanoGPT tasks.
- Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization