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]
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