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However, learning as optimisation fails to account for a time-varying environment during the learning process and the resulting point estimate in parameter space does not account for uncertainty. Here, we frame learning as filtering, i.e., a principled method for including time and parameter uncertainty. We derive the filtering-based learning rule for a spiking neuronal network\u2014the Synaptic Filter\u2014and show its computational and biological relevance. For the computational relevance, we show that filtering improves the weight estimation performance compared to a gradient learning rule with optimal learning rate. The dynamics of the mean of the Synaptic Filter is consistent with spike-timing dependent plasticity (STDP) while the dynamics of the variance makes novel predictions regarding spike-timing dependent changes of EPSP variability. Moreover, the Synaptic Filter explains experimentally observed negative correlations between homo- and heterosynaptic plasticity.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009721","type":"journal-article","created":{"date-parts":[[2022,2,23]],"date-time":"2022-02-23T18:31:04Z","timestamp":1645641064000},"page":"e1009721","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":10,"title":["Learning as filtering: Implications for spike-based plasticity"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8245-2366","authenticated-orcid":true,"given":"Jannes","family":"Jegminat","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9321-6481","authenticated-orcid":true,"given":"Simone Carlo","family":"Surace","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1847-3389","authenticated-orcid":true,"given":"Jean-Pascal","family":"Pfister","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,2,23]]},"reference":[{"issue":"6","key":"pcbi.1009721.ref001","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1038\/9173","article-title":"How voltage-dependent conductances can adapt to maximize the information encoded by neuronal firing rate","volume":"2","author":"M Stemmler","year":"1999","journal-title":"Nature neuroscience"},{"issue":"6","key":"pcbi.1009721.ref002","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/S0896-6273(03)00761-X","article-title":"Learning in spiking neural networks by reinforcement of stochastic synaptic transmission","volume":"40","author":"HS Seung","year":"2003","journal-title":"Neuron"},{"issue":"12","key":"pcbi.1009721.ref003","doi-asserted-by":"crossref","first-page":"1677","DOI":"10.1038\/nn1561","article-title":"Matching storage and recall: hippocampal spike timing\u2013dependent plasticity and phase response curves","volume":"8","author":"M Lengyel","year":"2005","journal-title":"Nature neuroscience"},{"issue":"6","key":"pcbi.1009721.ref004","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1016\/j.ipl.2005.05.023","article-title":"A gradient descent rule for spiking neurons emitting multiple spikes","volume":"95","author":"O Booij","year":"2005","journal-title":"Information Processing Letters"},{"issue":"3","key":"pcbi.1009721.ref005","doi-asserted-by":"crossref","first-page":"420","DOI":"10.1038\/nn1643","article-title":"The tempotron: a neuron that learns spike timing\u2013based decisions","volume":"9","author":"R G\u00fctig","year":"2006","journal-title":"Nature neuroscience"},{"key":"pcbi.1009721.ref006","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.neunet.2013.02.003","article-title":"A supervised multi-spike learning algorithm based on gradient descent for spiking neural networks","volume":"43","author":"Y Xu","year":"2013","journal-title":"Neural Networks"},{"issue":"3","key":"pcbi.1009721.ref007","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1016\/j.neuron.2013.11.030","article-title":"Learning by the dendritic prediction of somatic spiking","volume":"81","author":"R Urbanczik","year":"2014","journal-title":"Neuron"},{"issue":"1-4","key":"pcbi.1009721.ref008","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/S0925-2312(01)00658-0","article-title":"Error-backpropagation in temporally encoded networks of spiking neurons","volume":"48","author":"SM Bohte","year":"2002","journal-title":"Neurocomputing"},{"key":"pcbi.1009721.ref009","unstructured":"Bohte SM, Mozer MC. 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