{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T07:11:27Z","timestamp":1760685087435,"version":"build-2065373602"},"reference-count":56,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T00:00:00Z","timestamp":1760659200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mach. Learn.: Sci. Technol."],"published-print":{"date-parts":[[2025,12,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We propose a data-driven approach using a restricted Boltzmann machine (RBM) to solve the Schr\u00f6dinger equation in configuration space. Traditional configuration interaction (CI) methods construct the wavefunction as a linear combination of Slater determinants, but this becomes computationally expensive due to the factorial growth in the number of configurations. Our approach extends the use of a generative model such as the RBM by incorporating a taboo list strategy to enhance efficiency and convergence. The RBM is used to efficiently identify and sample the most significant determinants, thus accelerating convergence and substantially reducing computational cost. This method achieves up to 99.99% of the correlation energy while using up to four orders of magnitude fewer determinants compared to full CI calculations and up to two orders of magnitude fewer than previous state of the art methods. Beyond efficiency, our analysis reveals that the RBM learns electron distributions over molecular orbitals by capturing quantum patterns that resemble radial distribution functions linked to molecular bonding. This suggests that the learned pattern is interpretable, highlighting the potential of machine learning for explainable quantum chemistry<\/jats:p>","DOI":"10.1088\/2632-2153\/ae0fd5","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T22:51:55Z","timestamp":1759791115000},"page":"045013","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Configuration interaction guided sampling with interpretable restricted Boltzmann machine"],"prefix":"10.1088","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3985-7955","authenticated-orcid":true,"given":"Jorge I","family":"Hernandez-Martinez","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7121-8195","authenticated-orcid":true,"given":"Andres","family":"Mendez-Vazquez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5877-6715","authenticated-orcid":true,"given":"Gerardo","family":"Rodriguez-Hernandez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0003-5525-1309","authenticated-orcid":true,"given":"Sandra","family":"Leticia Juarez-Osorio","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2025,10,17]]},"reference":[{"article-title":"Filtered rayleigh-ritz is all you need","year":"2025","author":"Abbott","key":"mlstae0fd5bib1","type":"preprint"},{"key":"mlstae0fd5bib2","doi-asserted-by":"publisher","first-page":"10231","DOI":"10.1063\/1.1730074","type":"journal-article","article-title":"A molecular-dynamics study of structural and physical properties of nitromethane nanoparticles","volume":"120","author":"Alavi","year":"2004","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib3","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1103\/RevModPhys.79.291","type":"journal-article","article-title":"Coupled-cluster theory in quantum chemistry","volume":"79","author":"Bartlett","year":"2007","journal-title":"Rev. Mod. Phys."},{"key":"mlstae0fd5bib4","doi-asserted-by":"publisher","first-page":"032","DOI":"10.21468\/SciPostPhys.14.3.032","type":"journal-article","article-title":"Learning a restricted Boltzmann machine using biased Monte Carlo sampling","volume":"14","author":"B\u00e9reux","year":"2023","journal-title":"SciPost Phys."},{"key":"mlstae0fd5bib5","first-page":"pp 1","type":"book","article-title":"Chapter 1 - introduction to the Hartree-Fock method","author":"Blinder","year":"2019"},{"key":"mlstae0fd5bib6","doi-asserted-by":"publisher","DOI":"10.1063\/1.3193710","type":"journal-article","article-title":"Fermion Monte Carlo without fixed nodes: A game of life, death and annihilation in Slater determinant space","volume":"131","author":"Booth","year":"2009","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib7","doi-asserted-by":"publisher","first-page":"3171","DOI":"10.1021\/acs.jctc.5b00422","type":"journal-article","article-title":"Can single-reference coupled cluster theory describe static correlation?","volume":"11","author":"Bulik","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib8","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/s00214-009-0601-5","type":"journal-article","article-title":"Configuration interaction benchmark for Be ground state","volume":"126","author":"Bunge","year":"2010","journal-title":"Theor. Chem. Acc."},{"key":"mlstae0fd5bib9","doi-asserted-by":"publisher","DOI":"10.1063\/1.4704546","type":"journal-article","article-title":"Perspective on density functional theory","volume":"136","author":"Burke","year":"2012","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib10","doi-asserted-by":"publisher","first-page":"602","DOI":"10.1126\/science.aag2302","type":"journal-article","article-title":"Solving the quantum many-body problem with artificial neural networks","volume":"355","author":"Carleo","year":"2017","journal-title":"Science"},{"key":"mlstae0fd5bib11","doi-asserted-by":"publisher","first-page":"9889","DOI":"10.1021\/acs.jpclett.2c02576","type":"journal-article","article-title":"Electrofreezing of liquid ammonia","volume":"13","author":"Cassone","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstae0fd5bib12","first-page":"pp 3569","type":"book","article-title":"Markov chain Monte Carlo methods: computation and inference","volume":"vol 5","author":"Chib","year":"2001"},{"key":"mlstae0fd5bib13","doi-asserted-by":"publisher","first-page":"792","DOI":"10.1126\/science.1158722","type":"journal-article","article-title":"Insights into current limitations of density functional theory","volume":"321","author":"Cohen","year":"2008","journal-title":"Science"},{"key":"mlstae0fd5bib14","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1590\/S0100-40421998000600004","type":"journal-article","article-title":"Monte Carlo thermodynamic and structural properties of the tip4p water model: dependence on the computational conditions","volume":"21","author":"Cordeiro","year":"1998","journal-title":"Quimica Nova"},{"key":"mlstae0fd5bib15","doi-asserted-by":"publisher","first-page":"3426","DOI":"10.1021\/acs.jctc.1c00212","type":"journal-article","article-title":"Tailoring CIPSI expansions for QMC calculations of electronic excitations: the case study of thiophene","volume":"17","author":"Dash","year":"2021","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib16","first-page":"pp 143","type":"book","article-title":"The configuration interaction method: Advances in highly correlated approaches","volume":"vol 34","author":"David Sherrill","year":"1999"},{"year":"1996","author":"de la Pe\u00f1a","key":"mlstae0fd5bib17","type":"book"},{"key":"mlstae0fd5bib18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.99.115134","type":"journal-article","article-title":"Dynamical configuration interaction: Quantum embedding that combines wave functions and Green\u2019s functions","volume":"99","author":"Dvorak","year":"2019","journal-title":"Phys. Rev. B"},{"key":"mlstae0fd5bib19","doi-asserted-by":"publisher","first-page":"8132","DOI":"10.1063\/1.466807","type":"journal-article","article-title":"Benchmark studies of electron correlation in six-electron systems","volume":"100","author":"Fermann","year":"1994","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib20","doi-asserted-by":"publisher","first-page":"2083","DOI":"10.1007\/s10910-024-01644-2","type":"journal-article","article-title":"On the Rayleigh\u2013Ritz variational method. Non-orthogonal basis set","volume":"62","author":"Fern\u00e1ndez","year":"2024","journal-title":"J. Math. Chem."},{"key":"mlstae0fd5bib21","doi-asserted-by":"publisher","first-page":"1185","DOI":"10.1021\/acs.jctc.3c01190","type":"journal-article","article-title":"Distributed implementation of full configuration interaction for one trillion determinants","volume":"20","author":"Gao","year":"2024","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib22","doi-asserted-by":"publisher","first-page":"3591","DOI":"10.1021\/acs.jctc.9b00176","type":"journal-article","article-title":"Quantum package 2.0: an open-source determinant-driven suite of programs","volume":"15","author":"Garniron","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib23","type":"conference-proceedings","article-title":"Generative adversarial nets","volume":"vol 27","author":"Goodfellow","year":"2014"},{"key":"mlstae0fd5bib24","doi-asserted-by":"publisher","first-page":"5370","DOI":"10.1021\/acs.jctc.9b00674","type":"journal-article","article-title":"What levels of coupled cluster theory are appropriate for transition metal systems? a study using near-exact quantum chemical values for 3d transition metal binary compounds","volume":"15","author":"Hait","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib25","doi-asserted-by":"publisher","first-page":"2484","DOI":"10.1021\/acs.jctc.2c01216","type":"journal-article","article-title":"Solving the schr\u00f6dinger equation in the configuration space with generative machine learning","volume":"19","author":"Herzog","year":"2022","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib26","doi-asserted-by":"publisher","first-page":"1771","DOI":"10.1162\/089976602760128018","type":"journal-article","article-title":"Training products of experts by minimizing contrastive divergence","volume":"14","author":"Hinton","year":"2002","journal-title":"Neural Comput."},{"first-page":"pp 599","year":"2012","author":"Hinton","key":"mlstae0fd5bib27","type":"book"},{"key":"mlstae0fd5bib28","doi-asserted-by":"publisher","first-page":"268","DOI":"10.12693\/APhysPolA.128.268","type":"journal-article","article-title":"Ci calculations of the ground state ionization potential and electron affinity of aluminum","volume":"128","author":"Hussein","year":"2015","journal-title":"Acta Phys. Pol. A"},{"article-title":"Nist computational chemistry comparison and benchmark database (CCCBDB)","year":"2022","author":"Johnson","key":"mlstae0fd5bib29","type":"other"},{"key":"mlstae0fd5bib30","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.jqsrt.2013.06.003","type":"journal-article","article-title":"Average characteristics of the configuration interaction in atoms and their applications","volume":"129","author":"Karazija","year":"2013","journal-title":"J. Quantum Spectrosc. Radiat. Transfer"},{"article-title":"Auto-encoding variational bayes","year":"2013","author":"Kingma","key":"mlstae0fd5bib31","type":"preprint"},{"key":"mlstae0fd5bib32","doi-asserted-by":"publisher","first-page":"01","DOI":"10.1038\/s41598-019-57158-4","type":"journal-article","article-title":"The role of the dipole moment orientations in the crystallization tendency of the van der Waals liquids - molecular dynamics simulations","volume":"10","author":"Koperwas","year":"2020","journal-title":"Sci. Rep."},{"year":"2006","author":"Krauth","key":"mlstae0fd5bib33","type":"book"},{"key":"mlstae0fd5bib34","doi-asserted-by":"publisher","first-page":"1631","DOI":"10.1162\/neco.2008.04-07-510","type":"journal-article","article-title":"Representational power of restricted Boltzmann machines and deep belief networks","volume":"20","author":"Le Roux","year":"2008","journal-title":"Neural Comput."},{"key":"mlstae0fd5bib35","first-page":"pp 295","type":"book","article-title":"Chapter seventeen - time-dependent configuration interaction using the graphical unitary group approach: nonlinear electric properties","volume":"vol 76","author":"Lestrange","year":"2018"},{"key":"mlstae0fd5bib36","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1021\/acs.jpclett.1c03913","type":"journal-article","article-title":"Multireference density functional theory for describing ground and excited states with renormalized singles","volume":"13","author":"Li","year":"2022","journal-title":"J. Phys. Chem. Lett."},{"key":"mlstae0fd5bib37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.7.013191","type":"journal-article","article-title":"Spin coupling is all you need: encoding strong electron correlation in molecules on quantum computers","volume":"7","author":"Marti-Dafcik","year":"2025","journal-title":"Phys. Rev. Res."},{"key":"mlstae0fd5bib38","doi-asserted-by":"publisher","first-page":"15199","DOI":"10.1039\/c2cp42393f","type":"journal-article","article-title":"A study of the influence of isotopic substitution on the melting point and temperature of maximum density of water by means of path integral simulations of rigid models","volume":"14","author":"McBride","year":"2012","journal-title":"Phys. Chem. Chem. Phys."},{"key":"mlstae0fd5bib39","doi-asserted-by":"publisher","first-page":"1306","DOI":"10.1162\/NECO_a_00113","type":"journal-article","article-title":"Refinements of universal approximation results for deep belief networks and restricted Boltzmann machines","volume":"23","author":"Montufar","year":"2011","journal-title":"Neural Comput."},{"key":"mlstae0fd5bib40","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/j.ijar.2016.09.003","type":"journal-article","article-title":"Hierarchical models as marginals of hierarchical models","volume":"88","author":"Mont\u00fafar","year":"2017","journal-title":"Int. J. Approx. Reason."},{"article-title":"Restricted Boltzmann machine for modeling complex physical systems: a case study in artificial spin ice","year":"2024","author":"Popy","key":"mlstae0fd5bib41","type":"preprint"},{"year":"2003","author":"Saad","key":"mlstae0fd5bib42","type":"book"},{"year":"2011","author":"Saad","key":"mlstae0fd5bib43","type":"book"},{"key":"mlstae0fd5bib44","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1080\/00268976.2014.952696","type":"journal-article","article-title":"Q-Chem","volume":"113","author":"Shao","year":"2014","journal-title":"Mol. Phys."},{"key":"mlstae0fd5bib45","doi-asserted-by":"publisher","DOI":"10.1063\/1.4928643","type":"journal-article","article-title":"Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states","volume":"143","author":"Sharma","year":"2015","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.85.081103","type":"journal-article","article-title":"Full configuration interaction perspective on the homogeneous electron gas","volume":"85","author":"Shepherd","year":"2012","journal-title":"Phys. Rev. B"},{"article-title":"Computational scaling of the configuration interaction method with system size","year":"1996","author":"Sherrill","key":"mlstae0fd5bib47","type":"other"},{"year":"2011","author":"Sholl","key":"mlstae0fd5bib48","type":"book"},{"year":"1996a","author":"Szabo","key":"mlstae0fd5bib49","type":"book"},{"year":"1996b","author":"Szabo","key":"mlstae0fd5bib50","type":"book"},{"key":"mlstae0fd5bib51","doi-asserted-by":"publisher","first-page":"7511","DOI":"10.1063\/1.476183","type":"journal-article","article-title":"A comparison between the CISD[TQ] wave function and other highly correlated methods: Molecular geometry and harmonic vibrational frequencies of MgH2","volume":"108","author":"Tschumper","year":"1998","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib52","doi-asserted-by":"publisher","first-page":"2139","DOI":"10.1021\/acs.jctc.8b00536","type":"journal-article","article-title":"Modern approaches to exact diagonalization and selected configuration interaction with the adaptive sampling ci method","volume":"16","author":"Tubman","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"mlstae0fd5bib53","doi-asserted-by":"publisher","DOI":"10.1063\/1.4955109","type":"journal-article","article-title":"A deterministic alternative to the full configuration interaction quantum Monte Carlo method","volume":"145","author":"Tubman","year":"2016","journal-title":"J. Chem. Phys."},{"key":"mlstae0fd5bib54","type":"conference-proceedings","article-title":"Attention is all you need","volume":"vol 30","author":"Vaswani","year":"2017"},{"key":"mlstae0fd5bib55","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1214\/20-STS812","type":"journal-article","article-title":"Revisiting the Gelman\u2013Rubin Diagnostic","volume":"36","author":"Vats","year":"2021","journal-title":"Stat. Sci."},{"key":"mlstae0fd5bib56","doi-asserted-by":"publisher","first-page":"1186","DOI":"10.1016\/j.neucom.2017.09.065","type":"journal-article","article-title":"An overview on restricted Boltzmann machines","volume":"275","author":"Zhang","year":"2018","journal-title":"Neurocomputing"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T06:45:39Z","timestamp":1760683539000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ae0fd5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,17]]},"references-count":56,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,17]]},"published-print":{"date-parts":[[2025,12,30]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/ae0fd5","relation":{},"ISSN":["2632-2153"],"issn-type":[{"type":"electronic","value":"2632-2153"}],"subject":[],"published":{"date-parts":[[2025,10,17]]},"assertion":[{"value":"Configuration interaction guided sampling with interpretable restricted Boltzmann machine","name":"article_title","label":"Article Title"},{"value":"Machine Learning: Science and Technology","name":"journal_title","label":"Journal Title"},{"value":"paper","name":"article_type","label":"Article Type"},{"value":"\u00a9 2025 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2025-06-08","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-10-06","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2025-10-17","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}