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On September 7, 2026, arXiv cs.LG published the paper “Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension”. This study proposes an adaptive batch-based Lipschitz contraction method that can be implemented without prior knowledge of the zooming dimension. By combining batch processing mechanisms with adaptive adjustment strategies, this method dynamically adapts to the scaling requirements of different dimensions during the optimization process, thereby improving the stability and convergence efficiency of model training.
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2026-09-04
Dimension-Adaptive Batched Lipschitz Na…
Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension
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2026-09-07
Dimension-Adaptive Batched Lipschitz Na…
arXiv:2609.05214v1 提出 Count-Adaptive BLiN 算法，消除了对缩放维度 $d_z$ 的依赖。该算法通过从幸存立方体数量中选择下一条边长，无需使用 $d_z$ 或缩放常数 $C_z$，即可在 $\math…
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Dimension-Adaptive Batched Lipschitz Narrowing Without Knowing the Zooming Dimension
arXiv:2609.05214v1 提出 Count-Adaptive BLiN 算法，消除了对缩放维度 $d_z$ 的依赖。该算法通过从幸存立方体数量中选择下一条边长，无需使用 $d_z$ 或缩放常数 $C_z$，即可在 $\mathcal O_d(\log\log T)$ 批次下达到 $\widetilde{\mathcal O}_d(T^{(d_z+1)/(d_z+2)})$ 的 regret。结合原论文定理 10 中的自适应网格下界，当 $d_z$ 未知时，最优批量复杂度仍为 $\Theta_d(\log\log T)$。