{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T18:27:15Z","timestamp":1779301635891,"version":"3.51.4"},"reference-count":96,"publisher":"IOP Publishing","issue":"3","license":[{"start":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T00:00:00Z","timestamp":1720051200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T00:00:00Z","timestamp":1720051200000},"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":[[2024,9,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We provide a novel neural network architecture that can: i) output R-matrix for a given quantum integrable spin chain, ii) search for an integrable Hamiltonian and the corresponding R-matrix under assumptions of certain symmetries or other restrictions, iii) explore the space of Hamiltonians around already learned models and reconstruct the family of integrable spin chains which they belong to. The neural network training is done by minimizing loss functions encoding Yang\u2013Baxter equation, regularity and other model-specific restrictions such as hermiticity. Holomorphy is implemented via the choice of activation functions. We demonstrate the work of our neural network on the spin chains of difference form with two-dimensional local space. In particular, we reconstruct the R-matrices for all 14 classes. We also demonstrate its utility as an <jats:italic>Explorer<\/jats:italic>, scanning a certain subspace of Hamiltonians and identifying integrable classes after clusterisation. The last strategy can be used in future to carve out the map of integrable spin chains with higher dimensional local space and in more general settings where no analytical methods are available.<\/jats:p>","DOI":"10.1088\/2632-2153\/ad56f9","type":"journal-article","created":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T22:46:40Z","timestamp":1718146000000},"page":"035003","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["The R-mAtrIx Net"],"prefix":"10.1088","volume":"5","author":[{"given":"Shailesh","family":"Lal","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suvajit","family":"Majumder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1906-1359","authenticated-orcid":true,"given":"Evgeny","family":"Sobko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,7,4]]},"reference":[{"key":"mlstad56f9bib1","doi-asserted-by":"publisher","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"mlstad56f9bib2","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1016\/j.physletb.2017.10.024","article-title":"Machine-learning the string landscape","volume":"774","author":"He","year":"2017","journal-title":"Phys. Lett. B"},{"key":"mlstad56f9bib3","doi-asserted-by":"publisher","first-page":"JHEP09(2017)157","DOI":"10.1007\/JHEP09(2017)157","article-title":"Machine learning in the string landscape","author":"Carifio","year":"2017","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.96.066014","article-title":"Machine learning of Calabi-Yau volumes","volume":"96","author":"Krefl","year":"2017","journal-title":"Phys. Rev. D"},{"key":"mlstad56f9bib5","doi-asserted-by":"publisher","first-page":"JHEP08(2017)038","DOI":"10.1007\/JHEP08(2017)038","article-title":"Evolving neural networks with genetic algorithms to study the String Landscape","author":"Ruehle","year":"2017","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib6","doi-asserted-by":"publisher","DOI":"10.1002\/prop.201900087","article-title":"Machine learning line bundle cohomology","volume":"68","author":"Brodie","year":"2020","journal-title":"Fortsch. Phys."},{"key":"mlstad56f9bib7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.046001","article-title":"Machine learning string standard models","volume":"105","author":"Deen","year":"2022","journal-title":"Phys. Rev. D"},{"key":"mlstad56f9bib8","doi-asserted-by":"publisher","DOI":"10.1016\/j.physletb.2021.136139","article-title":"Machine learning Calabi-Yau four-folds","volume":"815","author":"He","year":"2021","journal-title":"Phys. Lett. B"},{"key":"mlstad56f9bib9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.103.126014","article-title":"Machine learning for complete intersection Calabi-Yau manifolds: a methodological study","volume":"103","author":"Erbin","year":"2021","journal-title":"Phys. Rev. D"},{"key":"mlstad56f9bib10","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ac37f7","article-title":"Deep multi-task mining Calabi\u2013Yau four-folds","volume":"3","author":"Erbin","year":"2022","journal-title":"Mach. Learn. Sci. Tech."},{"key":"mlstad56f9bib11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.046017","article-title":"Applying machine learning to the Calabi-Yau orientifolds with string vacua","volume":"105","author":"Gao","year":"2022","journal-title":"Phys. Rev. D"},{"key":"mlstad56f9bib12","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1142\/S2810939222500034","article-title":"Calabi-Yau metrics, energy functionals and machine-learning","volume":"1","author":"Ashmore","year":"2023","journal-title":"Int. J. Data Sci. Math. Sci."},{"key":"mlstad56f9bib13","doi-asserted-by":"publisher","first-page":"jhep04(2021)001","DOI":"10.1007\/jhep04(2021)001","article-title":"Moduli-dependent Calabi-Yau and SU (3)-structure metrics from Machine Learning","author":"Anderson","year":"2021","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib14","first-page":"pp 223","article-title":"Numerical Calabi-Yau metrics from holomorphic networks","author":"Douglas","year":"2022"},{"key":"mlstad56f9bib15","doi-asserted-by":"publisher","DOI":"10.1088\/2632-2153\/ac8e4e","article-title":"Numerical metrics for complete intersection and Kreuzer-Skarke Calabi-Yau manifolds","volume":"3","author":"Larfors","year":"2022","journal-title":"Mach. Learn. Sci. Tech."},{"key":"mlstad56f9bib16","article-title":"The world in a grain of sand: condensing the string vacuum degeneracy","author":"He","year":"2021"},{"key":"mlstad56f9bib17","article-title":"Deep learning the ising model near criticality","author":"Morningstar","year":"2017"},{"key":"mlstad56f9bib18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.96.245119","article-title":"Machine learning Z 2 quantum spin liquids with quasiparticle statistics","volume":"96","author":"Zhang","year":"2017","journal-title":"Phys. Rev. B"},{"key":"mlstad56f9bib19","article-title":"Machine learning etudes in conformal field theories","author":"Chen","year":"2020"},{"key":"mlstad56f9bib20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.105.025018","article-title":"Conformal bootstrap with reinforcement learning","volume":"105","author":"K\u00e1ntor","year":"2022","journal-title":"Phys. Rev. D"},{"key":"mlstad56f9bib21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.041601","article-title":"Solving conformal field theories with artificial intelligence","volume":"128","author":"K\u00e1ntor","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"mlstad56f9bib22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevD.107.025005","article-title":"6D (2,0) bootstrap with the soft-actor-critic algorithm","volume":"107","author":"K\u00e1ntor","year":"2023","journal-title":"Phys. Rev. D"},{"key":"mlstad56f9bib23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.4.043031","article-title":"Decoding conformal field theories: from supervised to unsupervised learning","volume":"4","author":"Kuo","year":"2022","journal-title":"Phys. Rev. Res."},{"key":"mlstad56f9bib24","article-title":"Machine learning of Ising criticality with spin-shuffling","author":"Basu","year":"2022"},{"key":"mlstad56f9bib25","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.1038\/s41598-020-58263-5","article-title":"Machine-learning studies on spin models","volume":"10","author":"Shiina","year":"2020","journal-title":"Sci. Rep."},{"key":"mlstad56f9bib26","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.10.011069","article-title":"Deep quantum geometry of matrices","volume":"10","author":"Han","year":"2020","journal-title":"Phys. Rev. X"},{"key":"mlstad56f9bib27","article-title":"The deep Ritz method: a deep learning-based numerical algorithm for solving variational problems","author":"Weinan","year":"2017"},{"key":"mlstad56f9bib28","article-title":"Physics informed deep learning (part I): data-driven solutions of nonlinear partial differential equations","author":"Raissi","year":"2017"},{"key":"mlstad56f9bib29","article-title":"Deep learning for symbolic mathematics","author":"Lample","year":"2019"},{"key":"mlstad56f9bib30","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1038\/s41586-021-04086-x","article-title":"Advancing mathematics by guiding human intuition with AI","volume":"600","author":"Davies","year":"2021","journal-title":"Nature"},{"key":"mlstad56f9bib31","article-title":"Machine-learning mathematical structures","author":"He","year":"2021"},{"key":"mlstad56f9bib32","doi-asserted-by":"publisher","first-page":"eaay2631","DOI":"10.1126\/sciadv.aay2631","article-title":"AI Feynman: a physics-inspired method for symbolic regression","volume":"6","author":"Udrescu","year":"2020","journal-title":"Sci. Adv."},{"key":"mlstad56f9bib33","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1007\/BF02551274","article-title":"Approximation by superpositions of a sigmoidal function","volume":"2","author":"Cybenko","year":"1989","journal-title":"Math. Control Signals Syst."},{"key":"mlstad56f9bib34","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1016\/0893-6080(89)90020-8","article-title":"Multilayer feedforward networks are universal approximators","volume":"2","author":"Hornik","year":"1989","journal-title":"Neural Netw."},{"key":"mlstad56f9bib35","first-page":"p 30","article-title":"The expressive power of neural networks: a view from the width","author":"Lu","year":"2017"},{"key":"mlstad56f9bib36","article-title":"Representation benefits of deep feedforward networks","author":"Telgarsky","year":"2015"},{"key":"mlstad56f9bib37","first-page":"p 249","article-title":"Understanding the difficulty of training deep feedforward neural networks","author":"Glorot","year":"2010"},{"key":"mlstad56f9bib38","article-title":"Improving neural networks by preventing co-adaptation of feature detectors","author":"Hinton","year":"2012"},{"key":"mlstad56f9bib39","first-page":"1929","article-title":"Dropout: a simple way to prevent neural networks from overfitting","volume":"15","author":"Srivastava","year":"2014","journal-title":"J. Mach. Learn. Res."},{"key":"mlstad56f9bib40","first-page":"pp 448","article-title":"Batch normalization: accelerating deep network training by reducing internal covariate shift","author":"Ioffe","year":"2015"},{"key":"mlstad56f9bib41","article-title":"A disciplined approach to neural network hyper-parameters: Part 1\u2013learning rate, batch size, momentum, and weight decay","author":"Smith","year":"2018"},{"key":"mlstad56f9bib42","article-title":"Fixup initialization: residual learning without normalization","author":"Zhang","year":"2019"},{"key":"mlstad56f9bib43","article-title":"Keras: the python deep learning library","volume":"ascl","author":"Chollet","year":"2018","journal-title":"Astrophysics Source Code Library"},{"key":"mlstad56f9bib44","article-title":"TensorFlow: large-scale machine learning on heterogeneous systems","author":"Abadi"},{"key":"mlstad56f9bib45","first-page":"pp 8024","article-title":"PyTorch: an imperative style, high-performance deep learning library","volume":"vol 32","author":"Paszke","year":"2019"},{"key":"mlstad56f9bib46","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.180201","article-title":"Machine learning hidden symmetries","volume":"128","author":"Liu","year":"2022","journal-title":"Phys. Rev. Lett."},{"key":"mlstad56f9bib47","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.126.180604","article-title":"Machine learning conservation laws from trajectories","volume":"126","author":"Liu","year":"2021","journal-title":"Phys. Rev. Lett."},{"key":"mlstad56f9bib48","article-title":"Learning symmetries of classical integrable systems","author":"Bondesan","year":"2019"},{"key":"mlstad56f9bib49","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.033499","article-title":"Discovering symmetry invariants and conserved quantities by interpreting siamese neural networks","volume":"2","author":"Wetzel","year":"2020","journal-title":"Phys. Rev. Res."},{"key":"mlstad56f9bib50","doi-asserted-by":"crossref","DOI":"10.1088\/2632-2153\/acd989","article-title":"Deep learning symmetries and their lie groups, algebras, and subalgebras from first principles","author":"Forestano","year":"2023"},{"key":"mlstad56f9bib51","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1103\/RevModPhys.34.394","article-title":"S-matrix theory of strong interactions without elementary particles","volume":"34","author":"Chew","year":"1962","journal-title":"Rev. Mod. Phys."},{"key":"mlstad56f9bib52","author":"Eden","year":"1966"},{"key":"mlstad56f9bib53","article-title":"Snowmass white paper: S-matrix bootstrap","author":"Kruczenski","year":"2022"},{"key":"mlstad56f9bib54","doi-asserted-by":"publisher","first-page":"JHEP11(2017)143","DOI":"10.1007\/JHEP11(2017)143","article-title":"The S-matrix bootstrap II: two dimensional amplitudes","author":"Paulos","year":"2017","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib55","doi-asserted-by":"publisher","first-page":"JHEP12(2019)040","DOI":"10.1007\/JHEP12(2019)040","article-title":"The S-matrix bootstrap. Part III: higher dimensional amplitudes","author":"Paulos","year":"2019","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib56","doi-asserted-by":"publisher","first-page":"JHEP11(2018)093","DOI":"10.1007\/JHEP11(2018)093","article-title":"A note on the S-matrix bootstrap for the 2d O(N) bosonic model","author":"He","year":"2018","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib57","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1016\/0550-3213(78)90239-0","article-title":"Relativistic factorized S matrix in two-dimensions having O(N) isotopic symmetry","volume":"26","author":"Zamolodchikov","year":"1977","journal-title":"JETP Lett."},{"key":"mlstad56f9bib58","first-page":"pp 149","article-title":"How algebraic Bethe ansatz works for integrable model","author":"Faddeev","year":"1996"},{"key":"mlstad56f9bib59","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/B0-12-512666-2\/00191-7","article-title":"Yang-Baxter equations","volume":"5","author":"Perk","year":"2006","journal-title":"Encycl. Math. Phys."},{"key":"mlstad56f9bib60","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1007\/BF02285311","article-title":"Yang-Baxter equation and representation theory: I","volume":"5","author":"Kulish","year":"1981","journal-title":"Lett. Math. Phys."},{"key":"mlstad56f9bib61","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1007\/BF01221646","article-title":"Quantum R matrix for the generalized toda system","volume":"102","author":"Jimbo","year":"1986","journal-title":"Commun. Math. Phys."},{"key":"mlstad56f9bib62","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0370-2693(85)90259-X","article-title":"Trigonometric solution of triangle equations and classical lie algebras","volume":"159","author":"Bazhanov","year":"1985","journal-title":"Phys. Lett. B"},{"key":"mlstad56f9bib63","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/BF01221256","article-title":"Integrable quantum systems and classical lie algebras","volume":"113","author":"Bazhanov","year":"1987","journal-title":"Commun. Math. Phys."},{"key":"mlstad56f9bib64","doi-asserted-by":"publisher","first-page":"508","DOI":"10.1143\/PTP.68.508","article-title":"Classification of exactly solvable two-component models","volume":"68","author":"Sogo","year":"1982","journal-title":"Prog. Theor. Phys."},{"key":"mlstad56f9bib65","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1016\/0375-9601(81)90994-4","article-title":"New families of commuting transfer matrices in q state vertex models","volume":"84","author":"Perk","year":"1981","journal-title":"Phys. Lett. A"},{"key":"mlstad56f9bib66","doi-asserted-by":"publisher","first-page":"2035","DOI":"10.1142\/S0217751X91001027","article-title":"Baxterization","volume":"6","author":"Jones","year":"1991","journal-title":"Int. J. Mod. Phys. A"},{"key":"mlstad56f9bib67","doi-asserted-by":"publisher","first-page":"JHEP10(2018)110","DOI":"10.1007\/JHEP10(2018)110","article-title":"Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems","author":"Vieira","year":"2018","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib68","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ab529f","article-title":"Classifying integrable spin-1\/2 chains with nearest neighbour interactions","volume":"52","author":"De Leeuw","year":"2019","journal-title":"J. Phys. A: Math. Theor."},{"key":"mlstad56f9bib69","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.125.031604","article-title":"Classifying nearest-neighbor interactions and deformations of AdS","volume":"125","author":"de Leeuw","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"mlstad56f9bib70","doi-asserted-by":"publisher","first-page":"069","DOI":"10.21468\/SciPostPhys.11.3.069","article-title":"Yang-Baxter and the boost: splitting the difference","volume":"11","author":"de Leeuw","year":"2021","journal-title":"SciPost Phys."},{"key":"mlstad56f9bib71","doi-asserted-by":"publisher","DOI":"10.1002\/prop.202100057","article-title":"Integrability Ex Machina","volume":"69","author":"Krippendorf","year":"2021","journal-title":"Fortsch. Phys."},{"key":"mlstad56f9bib72","article-title":"Searching for activation functions","author":"Ramachandran","year":"2017"},{"key":"mlstad56f9bib73","article-title":"Adam: a method for stochastic optimization","author":"Kingma","year":"2014"},{"key":"mlstad56f9bib74","first-page":"pp 770","article-title":"Deep residual learning for image recognition","author":"He","year":"2016"},{"key":"mlstad56f9bib75","first-page":"306","article-title":"Lorentz group for two-dimensional integrable lattice systems","volume":"55","author":"Tetel\u2019man","year":"1982","journal-title":"Soviet Journal of Experimental and Theoretical Physics"},{"key":"mlstad56f9bib76","article-title":"Robust learning with Jacobian regularization","author":"Hoffman","year":"2019"},{"key":"mlstad56f9bib77","article-title":"Minimum width for universal approximation","author":"Park","year":"2020"},{"key":"mlstad56f9bib78","first-page":"pp 192","article-title":"The loss surfaces of multilayer networks","author":"Choromanska","year":"2015"},{"key":"mlstad56f9bib79","first-page":"p 27","article-title":"Identifying and attacking the saddle point problem in high-dimensional non-convex optimization","author":"Dauphin","year":"2014"},{"key":"mlstad56f9bib80","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1070\/RM1979v034n05ABEH003909","article-title":"The quantum method of the inverse problem and the Heisenberg XYZ model","volume":"34","author":"Takhtadzhan","year":"1979","journal-title":"Russ. Math. Surv."},{"key":"mlstad56f9bib81","article-title":"Drawing the map of integrable spin chains","author":"Lal"},{"key":"mlstad56f9bib82","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1016\/j.nuclphysb.2003.08.015","article-title":"The N = 4 SYM integrable super spin chain","volume":"670","author":"Beisert","year":"2003","journal-title":"Nucl. Phys. B"},{"key":"mlstad56f9bib83","doi-asserted-by":"publisher","first-page":"JHEP08(2013)043","DOI":"10.1007\/JHEP08(2013)043","article-title":"The all-loop integrable spin-chain for strings on AdS3\u00d7 S 3\u00d7 T 4: the massive sector","author":"Borsato","year":"2013","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib84","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8121\/ac21e5","article-title":"Protected states in AdS3 backgrounds from integrability","volume":"54","author":"Majumder","year":"2021","journal-title":"J. Phys. A: Math. Theor."},{"key":"mlstad56f9bib85","doi-asserted-by":"publisher","first-page":"JHEP03(2022)138","DOI":"10.1007\/JHEP03(2022)138","article-title":"Mirror thermodynamic Bethe ansatz for AdS3\/CFT2","author":"Frolov","year":"2022","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib86","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1126\/science.1165893","article-title":"Distilling free-form natural laws from experimental data","volume":"324","author":"Schmidt","year":"2009","journal-title":"Science"},{"key":"mlstad56f9bib87","article-title":"Learning disentangled representations and group structure of dynamical environments","volume":"vol 33","author":"Quessard","year":"2020"},{"key":"mlstad56f9bib88","doi-asserted-by":"publisher","first-page":"JHEP05(2020)145","DOI":"10.1007\/JHEP05(2020)145","article-title":"Bounding scattering of charged particles in 1+1 dimensions","author":"Paulos","year":"2020","journal-title":"J. High Energy Phys."},{"key":"mlstad56f9bib89","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/s11128-005-7655-7","article-title":"Yang-Baxterizations, universal quantum gates and Hamiltonians","volume":"4","author":"Zhang","year":"2005","journal-title":"Quantum Inf. Proc."},{"key":"mlstad56f9bib90","doi-asserted-by":"publisher","first-page":"0685","DOI":"10.26421\/QIC10.7-8-8","article-title":"Extraspecial two-Groups, generalized Yang-Baxter equations and braiding quantum gates","volume":"10","author":"Rowell","year":"2010","journal-title":"Quantum Inf. Comput."},{"key":"mlstad56f9bib91","doi-asserted-by":"publisher","first-page":"37","DOI":"10.26421\/QIC20.1-2-3","article-title":"Quantum entanglement, supersymmetry and the generalized Yang-Baxter equation","volume":"20","author":"Padmanabhan","year":"2020","journal-title":"Quantum Inf. Comput."},{"key":"mlstad56f9bib92","doi-asserted-by":"publisher","first-page":"311","DOI":"10.22331\/q-2020-08-27-311","article-title":"Braiding quantum gates from partition algebras","volume":"4","author":"Padmanabhan","year":"2020","journal-title":"Quantum"},{"key":"mlstad56f9bib93","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1142\/S0218001493000339","article-title":"Signature verification using a \u201csiamese\u201d time delay neural network","volume":"7","author":"Bromley","year":"1993","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"mlstad56f9bib94","first-page":"pp 1735","article-title":"Dimensionality reduction by learning an invariant mapping","author":"Hadsell","year":"2006"},{"key":"mlstad56f9bib95","first-page":"1109","article-title":"Large scale online learning of image similarity through ranking","volume":"11","author":"Chechik","year":"2010","journal-title":"J. Mach. Learn. Res."},{"key":"mlstad56f9bib96","first-page":"pp 815","article-title":"Facenet: a unified embedding for face recognition and clustering","author":"Schroff","year":"2015"}],"container-title":["Machine Learning: Science and Technology"],"original-title":[],"link":[{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9","content-type":"text\/html","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9\/pdf","content-type":"application\/pdf","content-version":"am","intended-application":"similarity-checking"},{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,4]],"date-time":"2024-07-04T07:22:22Z","timestamp":1720077742000},"score":1,"resource":{"primary":{"URL":"https:\/\/iopscience.iop.org\/article\/10.1088\/2632-2153\/ad56f9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,4]]},"references-count":96,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,7,4]]},"published-print":{"date-parts":[[2024,9,1]]}},"URL":"https:\/\/doi.org\/10.1088\/2632-2153\/ad56f9","relation":{},"ISSN":["2632-2153"],"issn-type":[{"value":"2632-2153","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,4]]},"assertion":[{"value":"The R-mAtrIx Net","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 2024 The Author(s). Published by IOP Publishing Ltd","name":"copyright_information","label":"Copyright Information"},{"value":"2023-11-06","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-06-11","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2024-07-04","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}