{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T21:46:58Z","timestamp":1770328018560,"version":"3.49.0"},"reference-count":19,"publisher":"MIT Press","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[1998,7,1]]},"abstract":"<jats:p>The learning process in Boltzmann machines is computationally very expensive. The computational complexity of the exact algorithm is exponential in the number of neurons. We present a new approximate learning algorithm for Boltzmann machines, based on mean-field theory and the linear response theorem. The computational complexity of the algorithm is cubic in the number of neurons.<\/jats:p><jats:p>In the absence of hidden units, we show how the weights can be directly computed from the fixed-point equation of the learning rules. Thus, in this case we do not need to use a gradient descent procedure for the learning process. We show that the solutions of this method are close to the optimal solutions and give a significant improvement when correlations play a significant role. Finally, we apply the method to a pattern completion task and show good performance for networks up to 100 neurons.<\/jats:p>","DOI":"10.1162\/089976698300017386","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:56:30Z","timestamp":1027770990000},"page":"1137-1156","source":"Crossref","is-referenced-by-count":134,"title":["Efficient Learning in Boltzmann Machines Using Linear Response Theory"],"prefix":"10.1162","volume":"10","author":[{"given":"H. J.","family":"Kappen","sequence":"first","affiliation":[{"name":"RWCP SNN Laboratory, Department of Biophysics, University of Nijmegen, NL 6525 EZ Nijmegen, The Netherlands"}]},{"given":"F. B.","family":"Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Instituto de Ingenier\u00eda del Conocimiento y Departamento de Ingenier\u00eda Inform\u00e1 atica, Universidad Aut\u00f3noma de Madrid, 28049 Madrid, Spain"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15516709cog0901_7"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1995.7.5.889"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1038\/326689a0"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/4\/3\/007"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.50.3171"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1989.1.1.143"},{"key":"p_9","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1007\/BF00339943","volume":"52","author":"Hopfield J.","year":"1985","journal-title":"Biological Cybernetics"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(94)00112-Y"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.55.5849"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(94)90081-7"},{"key":"p_16","doi-asserted-by":"publisher","DOI":"10.1021\/ja01299a050"},{"key":"p_18","first-page":"995","volume":"1","author":"Peterson C.","year":"1987","journal-title":"Complex Systems"},{"key":"p_19","first-page":"2173","volume":"24","author":"Plefka T.","year":"1982","journal-title":"Journal of Physics A"},{"key":"p_20","doi-asserted-by":"publisher","DOI":"10.1613\/jair.251"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1994.6.6.1174"},{"key":"p_23","doi-asserted-by":"publisher","DOI":"10.1080\/14786437708235992"},{"key":"p_24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.51.1206"},{"key":"p_25","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/2\/4\/006"},{"key":"p_26","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1994.6.3.341"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976698300017386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,23]],"date-time":"2023-04-23T19:51:22Z","timestamp":1682279482000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/10\/5\/1137-1156\/6172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,7,1]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[1998,7,1]]}},"alternative-id":["10.1162\/089976698300017386"],"URL":"https:\/\/doi.org\/10.1162\/089976698300017386","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,7,1]]}}}