{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T12:02:27Z","timestamp":1767960147026,"version":"3.49.0"},"reference-count":13,"publisher":"MIT Press - Journals","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2003,7,1]]},"abstract":"<jats:p> We study the selectivity properties of neurons based on BCM and kurtosis energy functions in a general case of noisy high-dimensional input space. The proposed approach, which is used for characterization of the stable states, can be generalized to a whole class of energy functions. We characterize the critical noise levels beyond which the selectivity is destroyed. We also perform a quantitative analysis of such transitions, which shows interesting dependency on data set size. We observe that the robustness to noise of the BCM neuron (Bienenstock, Cooper, &amp; Munro, 1982; Intrator &amp; Cooper, 1992) increases as a function of dimensionality. We explicitly compute the separability limit of BCM and kurtosis learning rules in the case of a bimodal input distribution. Numerical simulations show a stronger robustness of the BCM rule for practical data set size when compared with kurtosis. <\/jats:p>","DOI":"10.1162\/089976603321891837","type":"journal-article","created":{"date-parts":[[2003,6,3]],"date-time":"2003-06-03T21:41:41Z","timestamp":1054676501000},"page":"1621-1640","source":"Crossref","is-referenced-by-count":5,"title":["The Effect of Noise on a Class of Energy-Based Learning Rules"],"prefix":"10.1162","volume":"15","author":[{"given":"A.","family":"Bazzani","sequence":"first","affiliation":[{"name":"Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy,"}]},{"given":"D.","family":"Remondini","sequence":"additional","affiliation":[{"name":"Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy,"}]},{"given":"N.","family":"Intrator","sequence":"additional","affiliation":[{"name":"Institute for Brain and Neural Systems, Brown University, Providence, RI 02912, U.S.A."}]},{"given":"G. C.","family":"Castellani","sequence":"additional","affiliation":[{"name":"Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy,"}]}],"member":"281","reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/0959-4388(94)90101-5"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.02-01-00032.1982"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1162\/089976698300017142"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1088\/0954-898X\/10\/2\/001"},{"key":"p_5","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.89.10.4363"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.2307\/2289161"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80003-6"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1137\/1111018"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.14-03-01634.1994"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1038\/375328a0"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/BF00275687"},{"key":"p_13","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1996.8.5.1021"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1016\/S0042-6989(97)00087-4"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/089976603321891837","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:50:04Z","timestamp":1615585804000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/15\/7\/1621-1640\/6750"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,7,1]]},"references-count":13,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2003,7,1]]}},"alternative-id":["10.1162\/089976603321891837"],"URL":"https:\/\/doi.org\/10.1162\/089976603321891837","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,7,1]]}}}