Reproduce “Parallel Sampling from the Ising $p$-Spin Model” on OpenResearch
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About this paper
Nima Anari, Aniket Das, Alireza Haqi
The authors develop parallel samplers for random mixed-p-spin Gibbs distributions over spins. Their block sampler uses an Ising proposal and rejection sampling to achieve total-variation error at most ε with high probability, at parallel runtime O(n^{1/3} polylog(n/ε)). For zero external field, Picard-parallelized stochastic-localization sampling achieves O(ε) normalized 2-Wasserstein error in polylogarithmic runtime when ε>ε_n, where ε_n→0, under high-temperature conditions.
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