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LogSumExp Smoothing Near-Optimal for Max Function Approximation

By PulseAugur Editorial · [1 sources] ·

A new paper published on arXiv presents an elementary proof that LogSumExp smoothing is nearly optimal for approximating the max function in $\mathbb{R}^d$. The research establishes a lower bound for overestimating smoothings, showing they must differ by at least approximately 0.8145 times the natural logarithm of d. While LogSumExp is close to this bound, the paper also introduces strictly stronger smoothings and, for small dimensions, proposes exactly optimal smoothings that meet the established lower bound. AI

IMPACT Provides theoretical underpinnings for optimization techniques used in machine learning models.

RANK_REASON Academic paper published on arXiv detailing mathematical proofs and new constructions. [lever_c_demoted from research: ic=1 ai=0.7]

Read on arXiv cs.LG →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

LogSumExp Smoothing Near-Optimal for Max Function Approximation

COVERAGE [1]

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

    An Elementary Proof of the Near Optimality of LogSumExp Smoothing

    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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