{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:16:46Z","timestamp":1772173006065,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009083","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T00:00:00Z","timestamp":1652313600000}}],"reference-count":66,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T00:00:00Z","timestamp":1651449600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NYU-ECNU Institute of Brain and Cognitive Science"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Working memory is a core component of critical cognitive functions such as planning and decision-making. Persistent activity that lasts long after the stimulus offset has been considered a neural substrate for working memory. Attractor dynamics based on network interactions can successfully reproduce such persistent activity. However, it requires a fine-tuning of network connectivity, in particular, to form continuous attractors which were suggested for encoding continuous signals in working memory. Here, we investigate whether a specific form of synaptic plasticity rules can mitigate such tuning problems in two representative working memory models, namely, rate-coded and location-coded persistent activity. We consider two prominent types of plasticity rules, differential plasticity correcting the rapid activity changes and homeostatic plasticity regularizing the long-term average of activity, both of which have been proposed to fine-tune the weights in an unsupervised manner. Consistent with the findings of previous works, differential plasticity alone was enough to recover a graded-level persistent activity after perturbations in the connectivity. For the location-coded memory, differential plasticity could also recover persistent activity. However, its pattern can be irregular for different stimulus locations under slow learning speed or large perturbation in the connectivity. On the other hand, homeostatic plasticity shows a robust recovery of smooth spatial patterns under particular types of synaptic perturbations, such as perturbations in incoming synapses onto the entire or local populations. However, homeostatic plasticity was not effective against perturbations in outgoing synapses from local populations. Instead, combining it with differential plasticity recovers location-coded persistent activity for a broader range of perturbations, suggesting compensation between two plasticity rules.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009083","type":"journal-article","created":{"date-parts":[[2022,5,2]],"date-time":"2022-05-02T13:36:05Z","timestamp":1651498565000},"page":"e1009083","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":9,"title":["Unsupervised learning for robust working 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Lim","year":"2014","journal-title":"J Neurosci"},{"key":"pcbi.1009083.ref014","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2011.00040","article-title":"Short-term facilitation may stabilize parametric working memory trace.","volume":"5","author":"V Itskov","year":"2011","journal-title":"Front Comput Neurosci."},{"key":"pcbi.1009083.ref015","doi-asserted-by":"crossref","first-page":"e1006928","DOI":"10.1371\/journal.pcbi.1006928","article-title":"Stability of working memory in continuous attractor networks under the control of shortterm plasticity.","volume":"15","author":"A Seeholzer","year":"2019","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1009083.ref016","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1098\/rstb.1992.0110","article-title":"A neural network model of the vestibulo-ocular reflex using a local synaptic learning rule","volume":"337","author":"DB Arnold","year":"1992","journal-title":"Philos Trans R Soc Lond B Biol 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Harry Klopf","year":"1988","journal-title":"Psychobiology"},{"key":"pcbi.1009083.ref026","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1162\/0899766053011555","article-title":"Temporal Sequence Learning, Prediction, and Control: A Review of Different Models and Their Relation to Biological Mechanisms.","volume":"17","author":"F W\u00f6rg\u00f6tter","year":"2005","journal-title":"Neural Comput."},{"key":"pcbi.1009083.ref027","doi-asserted-by":"crossref","first-page":"110","DOI":"10.3758\/BF03337824","article-title":"Some biological implications of a differential-Hebbian learning rule.","author":"MA Gluck","year":"1989","journal-title":"Psychobiology"},{"key":"pcbi.1009083.ref028","doi-asserted-by":"crossref","first-page":"892","DOI":"10.1038\/36103","article-title":"Activity-dependent scaling of quantal amplitude in neocortical neurons","volume":"391","author":"GG Turrigiano","year":"1998","journal-title":"Nature"},{"key":"pcbi.1009083.ref029","doi-asserted-by":"crossref","first-page":"8812","DOI":"10.1523\/JNEUROSCI.20-23-08812.2000","article-title":"Stable Hebbian learning from spike timing-dependent plasticity","volume":"20","author":"MCW Van Rossum","year":"2000","journal-title":"J Neurosci"},{"key":"pcbi.1009083.ref030","doi-asserted-by":"crossref","first-page":"473","DOI":"10.1016\/S0896-6273(03)00255-1","article-title":"Robust spatial working memory through homeostatic synaptic scaling in heterogeneous cortical networks","volume":"38","author":"A Renart","year":"2003","journal-title":"Neuron"},{"key":"pcbi.1009083.ref031","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1162\/neco.2010.07-09-1056","article-title":"Hebbian Plasticity and Homeostasis in a Model of Hypercolumn of the Visual Cortex.","volume":"1859","author":"RR Pool","year":"2010","journal-title":"Neural Comput."},{"key":"pcbi.1009083.ref032","doi-asserted-by":"crossref","first-page":"470","DOI":"10.1038\/20939","article-title":"Neuronal correlates of parametric working memory in the prefrontal cortex","volume":"399","author":"R Romo","year":"1999","journal-title":"Nature"},{"key":"pcbi.1009083.ref033","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1126\/science.1104171","article-title":"Flexible control of mutual inhibition: A neural model of two-interval discrimination","volume":"307","author":"CK Machens","year":"2005","journal-title":"Science (80-)."},{"key":"pcbi.1009083.ref034","doi-asserted-by":"crossref","first-page":"1724","DOI":"10.1126\/science.274.5293.1724","article-title":"Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity","volume":"274","author":"C van Vreeswijk","year":"1996","journal-title":"Science (80-)."},{"key":"pcbi.1009083.ref035","doi-asserted-by":"crossref","first-page":"156","DOI":"10.12688\/f1000research.7387.1","article-title":"Continuous Attractor Neural Networks: Candidate of a Canonical Model for Neural Information Representation.","volume":"5","author":"S Wu","year":"2016","journal-title":"F1000Research"},{"key":"pcbi.1009083.ref036","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1016\/j.neuron.2012.12.032","article-title":"NMDA Receptors Subserve Persistent Neuronal Firing during Working Memory in Dorsolateral Prefrontal Cortex","volume":"77","author":"M Wang","year":"2013","journal-title":"Neuron"},{"key":"pcbi.1009083.ref037","doi-asserted-by":"crossref","first-page":"6922","DOI":"10.1038\/ncomms7922","article-title":"Diverse synaptic plasticity mechanisms orchestrated to form and retrieve memories in spiking neural networks.","volume":"6","author":"F Zenke","year":"2015","journal-title":"Nat Commun"},{"key":"pcbi.1009083.ref038","doi-asserted-by":"crossref","first-page":"5319","DOI":"10.1038\/ncomms6319","article-title":"Formation and maintenance of neuronal assemblies through synaptic plasticity.","volume":"5","author":"A Litwin-Kumar","year":"2014","journal-title":"Nat Commun."},{"key":"pcbi.1009083.ref039","doi-asserted-by":"crossref","first-page":"477","DOI":"10.1016\/0896-6273(95)90304-6","article-title":"Cellular basis of working memory","volume":"14","author":"P. Goldman-Rakic","year":"1995","journal-title":"Neuron"},{"key":"pcbi.1009083.ref040","doi-asserted-by":"crossref","first-page":"1903","DOI":"10.1152\/jn.1999.81.4.1903","article-title":"Isodirectional Tuning of Adjacent Interneurons and Pyramidal Cells During Working Memory: Evidence for Microcolumnar Organization in PFC","volume":"81","author":"SG Rao","year":"1999","journal-title":"J Neurophysiol"},{"key":"pcbi.1009083.ref041","doi-asserted-by":"crossref","first-page":"3487","DOI":"10.1152\/jn.00188.2002","article-title":"Correlated Discharges Among Putative Pyramidal Neurons and Interneurons in the Primate Prefrontal Cortex","volume":"88","author":"C Constantinidis","year":"2002","journal-title":"J Neurophysiol"},{"key":"pcbi.1009083.ref042","volume-title":"Introduction to Linear Algebra","author":"G. Strang","year":"2017"},{"key":"pcbi.1009083.ref043","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1523\/JNEUROSCI.1970-10.2011","article-title":"Glutamate Receptor Subtypes Mediating Synaptic Activation of Prefrontal Cortex Neurons: Relevance for Schizophrenia","volume":"31","author":"DC Rotaru","year":"2011","journal-title":"J Neurosci"},{"key":"pcbi.1009083.ref044","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.tins.2017.12.003","article-title":"Synaptic tenacity or lack thereof: spontaneous remodeling of synapses","volume":"41","author":"NE Ziv","year":"2018","journal-title":"Trends Neurosci"},{"key":"pcbi.1009083.ref045","doi-asserted-by":"crossref","first-page":"3646","DOI":"10.1523\/JNEUROSCI.21-10-03646.2001","article-title":"Coding specificity in cortical microcircuits: A multiple-electrode analysis of primate prefrontal cortex","volume":"21","author":"C Constantinidis","year":"2001","journal-title":"J Neurosci"},{"key":"pcbi.1009083.ref046","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1146\/annurev.ne.11.030188.000425","article-title":"Excitatory amino acid neurotransmission: NMDA receptors and Hebb-type synaptic plasticity","volume":"11","author":"CW Cotman","year":"1988","journal-title":"Annu Rev Neurosci"},{"key":"pcbi.1009083.ref047","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1038\/s41583-019-0253-y","article-title":"Mechanisms underlying gain modulation in the cortex.","volume":"21","author":"KA Ferguson","year":"2020","journal-title":"Nat Rev Neurosci"},{"key":"pcbi.1009083.ref048","doi-asserted-by":"crossref","first-page":"3143","DOI":"10.1111\/j.1460-9568.2005.04087.x","article-title":"Learning in realistic networks of spiking neurons and spike-driven plastic synapses","volume":"21","author":"G Mongillo","year":"2005","journal-title":"Eur J Neurosci"},{"key":"pcbi.1009083.ref049","doi-asserted-by":"crossref","DOI":"10.3389\/fncom.2011.00047","article-title":"Synaptic scaling in combination with many generic plasticity mechanisms stabilizes circuit connectivity.","volume":"5","author":"C. Tetzlaff","year":"2011","journal-title":"Front Comput Neurosci."},{"key":"pcbi.1009083.ref050","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1016\/j.conb.2017.03.015","article-title":"The temporal paradox of Hebbian learning and homeostatic plasticity","author":"F Zenke","year":"2017","journal-title":"Current Opinion in Neurobiology"},{"key":"pcbi.1009083.ref051","article-title":"Searching for long time scales without fine tuning.","author":"X Chen","year":"2020","journal-title":"arxiv"},{"key":"pcbi.1009083.ref052","doi-asserted-by":"crossref","first-page":"350","DOI":"10.1523\/JNEUROSCI.3276-09.2010","article-title":"Functional, But Not Anatomical, Separation of \u201cWhat\u201d and \u201cWhen\u201d in Prefrontal Cortex.","volume":"30","author":"CK Machens","year":"2010","journal-title":"J Neurosci"},{"key":"pcbi.1009083.ref053","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1073\/pnas.1619449114","article-title":"Stable population coding for working memory coexists with heterogeneous neural dynamics in prefrontal cortex","volume":"114","author":"JD Murray","year":"2017","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1009083.ref054","doi-asserted-by":"crossref","first-page":"4163","DOI":"10.1523\/JNEUROSCI.3152-17.2018","article-title":"Low-Dimensional and Monotonic Preparatory Activity in Mouse Anterior Lateral Motor Cortex","volume":"38","author":"HK Inagaki","year":"2018","journal-title":"J Neurosci"},{"key":"pcbi.1009083.ref055","doi-asserted-by":"crossref","first-page":"23021","DOI":"10.1073\/pnas.1915984117","article-title":"Low-dimensional dynamics for working memory and time encoding","volume":"117","author":"CJ Cueva","year":"2020","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi.1009083.ref056","doi-asserted-by":"crossref","first-page":"2095","DOI":"10.1016\/j.cub.2012.08.058","article-title":"Neuronal circuits underlying persistent representations despite time varying activity","volume":"22","author":"S Druckmann","year":"2012","journal-title":"Curr Biol"},{"key":"pcbi.1009083.ref057","doi-asserted-by":"crossref","unstructured":"Alemi A, Den\u00e8ve S, Machens CK, Slotine JJ. Learning nonlinear dynamics in efficient, balanced spiking networks using local plasticity rules. 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