Construction shows n-neuron asymmetric Hopfield networks support exp(Ω(n/(log n)^2)) limit-cycle attractors of length exp(Ω(√n/log n)) each, robust to 1/2-o(1) noise.
URL https://drops.dagstuhl.de/entities/document/ 10.4230/LIPIcs.OPODIS.2022.23
2 Pith papers cite this work. Polarity classification is still indexing.
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Consensus time in 3-Majority is ilde{\Theta}(\min\{1/\|\alpha^{(0)}\|_\infty, \sqrt{n}\}) and in 2-Choices is \tilde{\Theta}(1/\|\alpha^{(0)}\|_\infty) w.h.p., governed by maximum initial opinion density for every starting configuration.
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Beyond Fixed Points: Superpolynomial Capacity of Asymmetric Hopfield Networks
Construction shows n-neuron asymmetric Hopfield networks support exp(Ω(n/(log n)^2)) limit-cycle attractors of length exp(Ω(√n/log n)) each, robust to 1/2-o(1) noise.
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Consensus Time in 3-Majority and 2-Choices Is Determined by the Maximum Initial Opinion Density
Consensus time in 3-Majority is ilde{\Theta}(\min\{1/\|\alpha^{(0)}\|_\infty, \sqrt{n}\}) and in 2-Choices is \tilde{\Theta}(1/\|\alpha^{(0)}\|_\infty) w.h.p., governed by maximum initial opinion density for every starting configuration.