Problem
Research questions and friction points this paper is trying to address.
polynomial threshold functions
noisy random lift
hypothesis testing
d-regular graph
Analysis of Polynomial Threshold Functions on Random Regular Graphs: Computational Complexity of Detecting Noisy Random Lift
🤖 AI Summary
本文分析了在随机正则图中检测噪声随机提升的问题，使用低度多项式阈值函数方法，并研究了短周期计数的分布。
📝 Abstract
In this work, we present the first analysis of low degree polynomial threshold functions for the natural hypothesis testing problem of detecting the noisy random lift of a base $d$-regular graph from a uniformly random $d$-regular graph. Along the way, we obtain a new result for the distribution of short cycle counts in noisy random lift up to logarithmic lengths, which generalizes results by McKay, Wormald, and Wysocka and by Johnson in the case of random regular graphs, and the result by Fortin and Rudinsky in the case of random lift.
Innovation
Methods, ideas, or system contributions that make the work stand out.
polynomial threshold functions
noisy random lift
short cycle counts
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