{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T06:22:57Z","timestamp":1698733377552},"reference-count":4,"publisher":"MIT Press - Journals","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[1991,9]]},"abstract":" Several recent papers (Gardner and Derrida 1989; Gy\u00f6rgyi 1990; Sompolinsky et al. 1990) have found, using methods of statistical physics, that a transition to perfect generalization occurs in training a simple perceptron whose weights can only take values \u00b11. We give a rigorous proof of such a phenomena. That is, we show, for \u03b1 = 2.0821, that if at least \u03b1n examples are drawn from the uniform distribution on {+1, \u22121}n<\/jats:sup> and classified according to a target perceptron wt<\/jats:sub> \u2208 {+1, \u22121}n<\/jats:sup> as positive or negative according to whether wt<\/jats:sub>\u00b7x is nonnegative or negative, then the probability is 2\u2212(\u221an)<\/jats:sup> that there is any other such perceptron consistent with the examples. Numerical results indicate further that perfect generalization holds for \u03b1 as low as 1.5. <\/jats:p>","DOI":"10.1162\/neco.1991.3.3.386","type":"journal-article","created":{"date-parts":[[2008,3,13]],"date-time":"2008-03-13T16:37:58Z","timestamp":1205426278000},"page":"386-401","source":"Crossref","is-referenced-by-count":16,"title":["The Transition to Perfect Generalization in Perceptrons"],"prefix":"10.1162","volume":"3","author":[{"given":"Eric B.","family":"Baum","sequence":"first","affiliation":[{"name":"NEC Research Institute, Princeton, NJ 08540 USA"}]},{"given":"Yuh-Dauh","family":"Lyuu","sequence":"additional","affiliation":[{"name":"NEC Research Institute, Princeton, NJ 08540 USA"}]}],"member":"281","reference":[{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1989.1.1.151"},{"key":"p_4","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/22\/12\/004"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.41.7097"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.65.1683"}],"container-title":["Neural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mitpressjournals.org\/doi\/pdf\/10.1162\/neco.1991.3.3.386","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,12]],"date-time":"2021-03-12T21:31:30Z","timestamp":1615584690000},"score":1,"resource":{"primary":{"URL":"https:\/\/direct.mit.edu\/neco\/article\/3\/3\/386-401\/5588"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991,9]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1991,9]]}},"alternative-id":["10.1162\/neco.1991.3.3.386"],"URL":"https:\/\/doi.org\/10.1162\/neco.1991.3.3.386","relation":{},"ISSN":["0899-7667","1530-888X"],"issn-type":[{"value":"0899-7667","type":"print"},{"value":"1530-888X","type":"electronic"}],"subject":[],"published":{"date-parts":[[1991,9]]}}}