[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119684-en":3,"doc-seo-119684-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},119684,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems","Machine-learning-assisted Monte Carlo methods are assessed on a class of sampling problems that are exponentially hard for conventional local Monte Carlo at sufficiently low temperatures. The study focuses on the antiferromagnetic Potts model on a random graph, equivalent to graph coloring in the zero-temperature limit. Multiple machine-learning-assisted MCMC strategies are tested and all are found to fail. The results provide reliable benchmarks for future smart sampling algorithms and highlight practical learning issues such as mode collapse when the target distribution has multiple peaks.","Machine-learning-assisted Monte Carlo fails at sampling computationally hard  \nproblems  \nSimone Ciarella, 1, ∗ Jeanne Trinquier,2, 1, ∗ Martin Weigt,2 and Francesco Zamponi 1  \n1 Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL,  \nCNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France  \n2 Sorbonne Université, CNRS, Institut de Biologie Paris Seine,  \nBiologie Computationnelle et Quantitative LCQB, F-75005 Paris, France  \n(Dated: November 10, 2022)  \narXiv :2210 . 11145v2 [ cond-mat .dis-nn] 8 Nov 2022  \nSeveral strategies have been recently proposed in order to improve Monte Carlo sampling efficiency using machine learning tools. Here, we challenge these methods by considering a class of problems that are known to be exponentially hard to sample using conventional local Monte Carlo at low enough temperatures. In particular, we study the antiferromagnetic Potts model on a random graph, which reduces to the coloring of random graphs at zero temperature. We test several machinelearning-assisted Monte Carlo approaches, and we find that they all fail. Our work thus provide good benchmarks for future proposals for smart sampling algorithms.  \nI. INTRODUCTION  \nA. Motivations  \nSampling from a given target probability distribution Pt (σ1 , · · · , σN ) over N degrees of freedom can become extremely hard when N is large. A universal (i.e. systemindependent) strategy for sampling consists in starting from a random configuration of σ = {σi }i=1 , ··· ,N, and generating a local Monte Carlo Markov Chain (MCMC), by sequentially proposing an update of one of the σi , and accepting or rejecting it with a proper probability (e.g. Metropolis-Hastings), until convergence [1] . However, for large N, the convergence time of the MCMC can grow exponentially in N, because of non-trivial longrange correlations that make local decorrelation extremely hard [2] .  \nA solution to this problem consists in identifying the proper set of correlated variables, and proposing global updates of such variables together, in such a way to speedup convergence [3] . However, this process is not universal, because it relies on the proper identification of systemdependent correlations, which is not always possible. For instance, in disordered systems such as spin glasses, the nature of correlated domains is extremely elusive and proper global moves are not easy to identify [4, 5] . Another approach, which has been particularly successful in atomistic models of glasses, consists in unconstraining some degrees of freedom, evolve them and constrain them back [6–10], but again it is model-specific. Alternative proposals based on a renormalization group approach [11, 12] also rely on the identification of system-dependent collective variables.  \nA recently developed line of research, see e.g. [13–20], proposed to solve the problem in an elegant and universal way, by machine learning proper MCMC moves. In a  \n∗ These authors contributed equally. Email: [simone.ciarella@ens.fr](simone.ciarella@ens.fr), [jeanne.trinquier@ens.fr](jeanne.trinquier@ens.fr)  \nnutshell, the idea is to learn an auxiliary probability distribution Pa (σ), which (i) can be sampled efficiently (e.g. linearly in N) and (ii) provides a good approximation of the target probability. Then, the hope is to use the auxiliary distribution to propose smart MCMC moves. Using this strategy with autoregressive architectures that ensure efficient sampling, some authors found convergence speedup [13, 14 , 16], but others found less promising results [20] .  \nIn order to make these studies more systematic, and really assess the performance of the method, it is important to have good benchmarks, i.e. problems that are guaranteed to be really hard to sample by local MCMC. In the early 90s, the very same problem had to be faced to assess the performance of local search algorithms that looked for solution of optimization or satisfiability problems [21] . In that case, the problem of generating","cbCaihXtR0brl6r7","https://ap.wps.com/l/cbCaihXtR0brl6r7","pdf",3720988,1,22,"English","en",105,"# Introduction\n## Motivations\n## State of the art","[{\"question\":\"Why does local Monte Carlo sampling become extremely hard for large systems?\",\"answer\":\"As the number of degrees of freedom grows, MCMC convergence time can scale exponentially due to long-range correlations that prevent efficient local decorrelation.\"},{\"question\":\"What is the problem studied in the paper, and how is it related to graph coloring?\",\"answer\":\"The paper studies the antiferromagnetic Potts model on a random graph, which reduces to coloring random graphs at zero temperature.\"},{\"question\":\"What overall conclusion does the paper reach about machine-learning-assisted Monte Carlo methods?\",\"answer\":\"Testing several approaches shows that they all fail on the chosen computationally hard sampling problems.\"}]","Machine-learning-assisted Monte Carlo 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does local Monte Carlo sampling become extremely hard for large systems?","Question",{"text":75,"@type":76},"As the number of degrees of freedom grows, MCMC convergence time can scale exponentially due to long-range correlations that prevent efficient local decorrelation.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the problem studied in the paper, and how is it related to graph coloring?",{"text":80,"@type":76},"The paper studies the antiferromagnetic Potts model on a random graph, which reduces to coloring random graphs at zero temperature.",{"name":82,"@type":73,"acceptedAnswer":83},"What overall conclusion does the paper reach about machine-learning-assisted Monte Carlo methods?",{"text":84,"@type":76},"Testing several approaches shows that they all fail on the chosen computationally hard sampling 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