{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:41:04Z","timestamp":1773441664716,"version":"3.50.1"},"reference-count":35,"publisher":"MIT Press","issue":"5","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,4,18]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Hebb's learning traces its origin in Pavlov's classical conditioning; however, while the former has been extensively modeled in the past decades (e.g., by the Hopfield model and countless variations on theme), as for the latter, modeling has remained largely unaddressed so far. Furthermore, a mathematical bridge connecting these two pillars is totally lacking. The main difficulty toward this goal lies in the intrinsically different scales of the information involved: Pavlov's theory is about correlations between concepts that are (dynamically) stored in the synaptic matrix as exemplified by the celebrated experiment starring a dog and a ringing bell; conversely, Hebb's theory is about correlations between pairs of neurons as summarized by the famous statement that neurons that fire together wire together. In this letter, we rely on stochastic process theory to prove that as long as we keep neurons' and synapses' timescales largely split, Pavlov's mechanism spontaneously takes place and ultimately gives rise to synaptic weights that recover the Hebbian kernel.<\/jats:p>","DOI":"10.1162\/neco_a_01578","type":"journal-article","created":{"date-parts":[[2023,3,21]],"date-time":"2023-03-21T22:26:05Z","timestamp":1679437565000},"page":"930-957","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":14,"title":["From Pavlov Conditioning to Hebb Learning"],"prefix":"10.1162","volume":"35","author":[{"given":"Elena","family":"Agliari","sequence":"first","affiliation":[{"name":"Sapienza University of Rome, Department of Mathematics, 00185, Rome, Italy"},{"name":"Istituto Nazionale d'Alta Matematica, 00185, Rome, Italy elena.agliari@uniroma1.it"}]},{"given":"Miriam","family":"Aquaro","sequence":"additional","affiliation":[{"name":"Sapienza University of Rome, Department of Mathematics, 00185, Rome, Italy"},{"name":"Istituto Nazionale d'Alta Matematica, 00185, Rome, Italy miriam.aquaro@uniroma1.it"}]},{"given":"Adriano","family":"Barra","sequence":"additional","affiliation":[{"name":"Istituto Nazionale d'Alta Matematica, 00185, Rome, Italy"},{"name":"University of Salento, Lecce 73100, Italy adriano.barra@unisalento.it"}]},{"given":"Alberto","family":"Fachechi","sequence":"additional","affiliation":[{"name":"Sapienza University of Rome, Department of Mathematics, 00185, Rome, Italy"},{"name":"Istituto Nazionale d'Alta Matematica, 00185, Rome, Italy alberto.fachechi@uniroma1.it"}]},{"given":"Chiara","family":"Marullo","sequence":"additional","affiliation":[{"name":"Sapienza University of Rome, Department of Mathematics, 00185, Rome, Italy"},{"name":"Istituto Nazionale d'Alta Matematica, 00185, Rome, Italy chiara.marullo@uniroma1.it"}]}],"member":"281","published-online":{"date-parts":[[2023,4,18]]},"reference":[{"issue":"109","key":"2023041921575655600_B1","article-title":"Multitasking associative networks","volume":"26","author":"Agliari","year":"2012","journal-title":"Physical Review Letters"},{"issue":"114","key":"2023041921575655600_B2","article-title":"Retrieval capabilities of hierarchical networks: From Dyson to Hopfield","volume":"2","author":"Agliari","year":"2014","journal-title":"Physical Review Letters"},{"issue":"6","key":"2023041921575655600_B3","article-title":"Can persistent Epstein- Barr virus infection induce chronic fatigue syndrome as a Pavlov feature of the immune response?","volume":"2","author":"Agliari","year":"2012","journal-title":"Journal of Biological Dynamics"},{"issue":"46","key":"2023041921575655600_B4","article-title":"Immune networks: Multitasking capabilities near saturation","volume":"41","author":"Agliari","year":"2013","journal-title":"J. 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