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English(EN) An Elementary Proof of the Near Optimality of LogSumExp Smoothing

LogSumExp平滑在最大函数逼近中近乎最优

作者 PulseAugur 编辑部 · [1 个来源] ·

一篇新发表在arXiv上的论文提供了一个初等证明，证明了LogSumExp平滑在$\\mathbb{R}^d$中逼近最大函数时近乎最优。该研究为高估平滑度设定了一个下界，表明它们必须至少相差d的自然对数的约0.8145倍。虽然LogSumExp接近这个界限，但该论文也引入了严格更强的平滑方法，并针对低维度提出了完全最优的平滑方法，这些方法达到了已设定的下界。 AI

影响 为机器学习模型中使用的优化技术的理论基础提供了支持。

排序理由 发表在arXiv上的学术论文，详细介绍了数学证明和新构造。[lever_c_demoted from research: ic=1 ai=0.7]

在 arXiv cs.LG 阅读 →

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LogSumExp平滑在最大函数逼近中近乎最优

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发表在arXiv上的学术论文，详细介绍了数学证明和新构造。[lever_c_demoted from research: ic=1 ai=0.7]
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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Thabo Samakhoana, Benjamin Grimmer ·

    LogSumExp平滑的近乎最优性的初等证明

    arXiv:2512.10825v3 Announce Type: replace-cross Abstract: We consider the design of smoothings of the (coordinate-wise) max function in $\mathbb{R}^d$ in the infinity norm. The LogSumExp function $f(x)=\ln(\sum^d_i\exp(x_i))$ provides a classical smoothing, differing from the max…

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