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It is characteristic for the underlying recurrent connectivity in the cortex that neurons with similar tuning predominantly excite each other. The reason for such an architecture is not clear. Using an analytically tractable model as well as spiking neural networks, we show that it can naturally arise from a cooperative coding scheme. In this scheme neurons with similar responses specifically support each other by sharing their computations to obtain the desired population code. This sharing allows each neuron to effectively respond to a broad variety of inputs, while only receiving few feedforward and recurrent connections. Few strong, specific recurrent connections then replace many feedforward and less specific recurrent connections, such that the resulting connectivity optimizes the number of required synapses. This suggests that the number of required synapses may be a crucial constraining factor in biological neural networks. Synaptic savings increase with the dimensionality of the encoded variables. We find a trade-off between saving synapses and response speed. The response speed improves by orders of magnitude when utilizing the window of opportunity between excitatory and delayed inhibitory currents that arises if, as found in experiments, spike frequency adaptation is present or strong recurrent excitation is balanced by strong, shortly-lagged inhibition.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1012156","type":"journal-article","created":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T13:51:52Z","timestamp":1751550712000},"page":"e1012156","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Cooperative coding of continuous variables in networks with sparsity constraint"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0022-7542","authenticated-orcid":true,"given":"Paul","family":"Z\u00fcge","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Natalie","family":"Schieferstein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4273-2731","authenticated-orcid":true,"given":"Raoul-Martin","family":"Memmesheimer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2025,7,3]]},"reference":[{"key":"pcbi.1012156.ref001","volume-title":"Theoretical neuroscience: computational and mathematical modeling of neural systems","author":"P Dayan","year":"2001"},{"key":"pcbi.1012156.ref002","volume-title":"Fundamentals of Computational Neuroscience","author":"T Trappenberg","year":"2010"},{"issue":"1","key":"pcbi.1012156.ref003","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1113\/jphysiol.1962.sp006837","article-title":"Receptive fields, binocular interaction and functional architecture in the cat\u2019s visual cortex","volume":"160","author":"DH HUBEL","year":"1962","journal-title":"J Physiol"},{"issue":"4","key":"pcbi.1012156.ref004","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1016\/j.neuron.2016.07.015","article-title":"Efficient receptive field tiling in primate V1","volume":"91","author":"I Nauhaus","year":"2016","journal-title":"Neuron"},{"key":"pcbi.1012156.ref005","article-title":"Head direction cells recorded in the anterior thalamic nuclei of freely moving rats","author":"S Taube","year":"1995","journal-title":"J Neurosci"},{"issue":"7","key":"pcbi.1012156.ref006","doi-asserted-by":"crossref","first-page":"2626","DOI":"10.1523\/JNEUROSCI.18-07-02626.1998","article-title":"Structure of receptive fields in area 3b of primary somatosensory cortex in the alert monkey","volume":"18","author":"JJ DiCarlo","year":"1998","journal-title":"J Neurosci"},{"issue":"1","key":"pcbi.1012156.ref007","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0006-8993(71)90358-1","article-title":"The hippocampus as a spatial map. 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