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An Improved Example for an Autoconvolution Inequality
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AI
DOI：10.1080/10586458.2025.2607423.png)
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Abstract
En 中文
We give a nonnegative step function with 575 equally spaced intervals such that & Vert;f & lowast;f & Vert;L2(R)2 & Vert;f & lowast;f & Vert;L infinity(R)& Vert;f & lowast;f & Vert;L1(R)>= 0.901564. This improves upon a recent result of Deepmind's AlphaEvolve from May 2025, which found a nonnegative step function with 50 equally space intervals for which the left hand side is >= 0.8962. Our function was found using simulated annealing and gradient based methods.
Keywords:
autoconvolution
gradient ascent
H & ouml
lder's inequality
simulated annealing
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