Two adaptive kernel selection techniques for Kernelized Diffusion Maps are developed, backed by proofs of Lipschitz dependence on kernel weights, spectral projector continuity under gap conditions, residual control, and exponential consistency of the selector.
org/abs/2309.04522
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VRAdam hybridizes Adam's per-parameter adaptation with a physics-inspired velocity regularizer to stabilize training at the edge of stability, delivering better empirical performance than AdamW and O(ln(N)/sqrt(N)) convergence bounds under mild assumptions.
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Adaptive Kernel Selection for Kernelized Diffusion Maps
Two adaptive kernel selection techniques for Kernelized Diffusion Maps are developed, backed by proofs of Lipschitz dependence on kernel weights, spectral projector continuity under gap conditions, residual control, and exponential consistency of the selector.
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A Physics-Inspired Optimizer: Velocity Regularized Adam
VRAdam hybridizes Adam's per-parameter adaptation with a physics-inspired velocity regularizer to stabilize training at the edge of stability, delivering better empirical performance than AdamW and O(ln(N)/sqrt(N)) convergence bounds under mild assumptions.