{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T19:52:50Z","timestamp":1773085970960,"version":"3.50.1"},"reference-count":46,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:00:00Z","timestamp":1750204800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006280","name":"Ministerio de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["PID2021-124047NB-I00"],"award-info":[{"award-number":["PID2021-124047NB-I00"]}],"id":[{"id":"10.13039\/501100006280","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006769","name":"Russian Science Foundation","doi-asserted-by":"publisher","award":["24-19-00433"],"award-info":[{"award-number":["24-19-00433"]}],"id":[{"id":"10.13039\/501100006769","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Appl. Math. Stat."],"abstract":"<jats:p>Spiking neural networks (SNNs) have significant potential for a power-efficient neuromorphic AI. However, their training is challenging since most of the learning principles known from artificial neural networks are hardly applicable. Recently, the concept of \u201cblessing of dimensionality\u201d has successfully been used to treat high-dimensional data and representations of reality. It exploits the fundamental trade-off between the complexity and simplicity of statistical sets in high-dimensional spaces without relying on global optimization techniques. We show that the frequency encoding of memories in SNNs can leverage this paradigm. It enables detecting and learning arbitrary information items, given that they operate in high dimensions. To illustrate the hypothesis, we develop a minimalist model of information processing in layered brain structures and study the emergence of extreme selectivity to multiple stimuli and associative memories. Our results suggest that global optimization of cost functions may be circumvented at different levels of information processing in SNNs, and replaced by chance learning, greatly simplifying the design of AI devices.<\/jats:p>","DOI":"10.3389\/fams.2025.1553779","type":"journal-article","created":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:47:28Z","timestamp":1750225648000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Blessing of dimensionality in spiking neural networks: the by-chance functional learning"],"prefix":"10.3389","volume":"11","author":[{"given":"Valeri A.","family":"Makarov","sequence":"first","affiliation":[]},{"given":"Sergey A.","family":"Lobov","sequence":"additional","affiliation":[]}],"member":"1965","published-online":{"date-parts":[[2025,6,18]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"109201","DOI":"10.1063\/5.0179424","article-title":"Roadmap to neuromorphic computing with emerging technologies","volume":"12","author":"Mehonic","year":"2024","journal-title":"APL Mater"},{"key":"B2","doi-asserted-by":"publisher","first-page":"907","DOI":"10.3945\/ajcn.2009.28512","article-title":"Brain and high metabolic rate organ mass: contributions to resting energy expenditure beyond fat-free mass","volume":"91","author":"Javed","year":"2010","journal-title":"Am J Clin Nutr"},{"key":"B3","doi-asserted-by":"publisher","first-page":"859874","DOI":"10.3389\/fncom.2022.859874","article-title":"Toward reflective spiking neural networks exploiting memristive devices","volume":"16","author":"Makarov","year":"2022","journal-title":"Front Comput Neurosci"},{"key":"B4","doi-asserted-by":"publisher","first-page":"7889","DOI":"10.1038\/s41598-020-64466-7","article-title":"Universal principles justify the existence of concept cells","volume":"10","author":"Calvo Tapia","year":"2020","journal-title":"Sci Rep"},{"key":"B5","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/0896-6273(93)90304-A","article-title":"Neural darwinism: selection and reentrant signaling in higher brain function","volume":"10","author":"Edelman","year":"1993","journal-title":"Neuron"},{"key":"B6","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1089\/brain.2011.0008","article-title":"Functional and effective connectivity: a review","volume":"1","author":"Friston","year":"2011","journal-title":"Brain Connect"},{"key":"B7","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s12065-007-0002-4","article-title":"Neuroevolution: from architectures to learning","volume":"1","author":"Floreano","year":"2008","journal-title":"Evol Intell"},{"key":"B8","doi-asserted-by":"publisher","first-page":"105065","DOI":"10.1016\/j.cnsns.2019.105065","article-title":"Basic principles drive self-organization of brain-like connectivity structure","volume":"82","author":"Calvo Tapia","year":"2020","journal-title":"Commun Nonlinear Sci Numer Simul"},{"key":"B9","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1609\/aaai.v37i1.25079","article-title":"an evolutionary structure learning strategy for spiking neural networks","volume":"37","author":"Shen","year":"2023","journal-title":"Proc AAAI Conf Artif Intell"},{"key":"B10","doi-asserted-by":"publisher","first-page":"320","DOI":"10.3390\/biomimetics8030320","article-title":"STDP-driven rewiring in spiking neural networks under stimulus-induced and spontaneous activity","volume":"8","author":"Lobov","year":"2023","journal-title":"Biomimetics"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1140\/epjs\/s11734-025-01595-y","article-title":"Network memory consolidation under adaptive rewiring","author":"Lobov","year":"2025","journal-title":"Eur Phys J Spec Top"},{"key":"B12","doi-asserted-by":"publisher","first-page":"4856","DOI":"10.1007\/s11538-018-0415-5","article-title":"High-dimensional brain: a tool for encoding and rapid learning of memories by single neurons","volume":"81","author":"Tyukin","year":"2019","journal-title":"Bull Math Biol"},{"key":"B13","doi-asserted-by":"publisher","first-page":"1332","DOI":"10.1126\/science.aab3050","article-title":"Human-level concept learning through probabilistic program induction","volume":"350","author":"Lake","year":"2015","journal-title":"Science"},{"key":"B14","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/0893-9659(93)90023-G","article-title":"Quasiorthogonal dimension of euclidean spaces","volume":"6","author":"Kainen","year":"1993","journal-title":"Appl Math Lett"},{"key":"B15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1996-5_18","author":"Kainen","year":"1997","journal-title":"Computer Intensive Methods in Control and Signal Processing"},{"key":"B16","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.neunet.2017.07.014","article-title":"Stochastic separation theorems","volume":"94","author":"Gorban","year":"2017","journal-title":"Neur Net"},{"key":"B17","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.plrev.2018.09.005","article-title":"The unreasonable effectiveness of small neural ensembles in high-dimensional brain","volume":"29","author":"Gorban","year":"2019","journal-title":"Phys Life Rev"},{"key":"B18","doi-asserted-by":"publisher","first-page":"82","DOI":"10.3390\/e22010082","article-title":"High-dimensional brain in a high-dimensional world: blessing of dimensionality","volume":"22","author":"Gorban","year":"2020","journal-title":"Entropy"},{"key":"B19","doi-asserted-by":"publisher","first-page":"501","DOI":"10.3390\/e23050501","article-title":"Limit theorems as blessing of dimensionality: neural-oriented overview","volume":"23","author":"Kreinovich","year":"2021","journal-title":"Entropy"},{"key":"B20","volume-title":"The Organization of Behavior: A Neuropsychological Theory","author":"Hebb","year":"1949"},{"key":"B21","doi-asserted-by":"publisher","first-page":"4","DOI":"10.3389\/fnsyn.2011.00004","article-title":"A history of spike-timing-dependent plasticity","volume":"3","author":"Markram","year":"2011","journal-title":"Front Synaptic Neurosci"},{"key":"B22","doi-asserted-by":"publisher","first-page":"112999","DOI":"10.1016\/j.knosys.2025.112999","article-title":"Context gating in spiking neural networks: achieving lifelong learning through integration of local and global plasticity","volume":"311","author":"Shen","year":"2025","journal-title":"Knowl-Based Syst"},{"key":"B23","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1093\/cercor\/12.8.818","article-title":"Machine psychology: autonomous behavior, perceptual categorization and conditioning in a brain-based device","volume":"12","author":"Krichmar","year":"2002","journal-title":"Cereb Cortex"},{"key":"B24","doi-asserted-by":"publisher","first-page":"6","DOI":"10.3389\/fnbot.2015.00006","article-title":"Learning touch preferences with a tactile robot using dopamine modulated STDP in a model of insular cortex","volume":"9","author":"Chou","year":"2015","journal-title":"Front Neurorobot"},{"key":"B25","doi-asserted-by":"publisher","first-page":"88","DOI":"10.3389\/fnins.2020.00088","article-title":"Spatial properties of STDP in a self-learning spiking neural network enable controlling a mobile robot","volume":"14","author":"Lobov","year":"2020","journal-title":"Front Neurosci"},{"key":"B26","doi-asserted-by":"publisher","first-page":"2678","DOI":"10.3390\/s21082678","article-title":"Spatial memory in a spiking neural network with robot embodiment","volume":"21","author":"Lobov","year":"2021","journal-title":"Sensors"},{"key":"B27","doi-asserted-by":"publisher","first-page":"234","DOI":"10.3390\/math11010234","article-title":"Spatial computing in modular spiking neural networks with a robotic embodiment","volume":"11","author":"Lobov","year":"2023","journal-title":"Mathematics"},{"key":"B28","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1113\/jphysiol.1926.sp002273","article-title":"The impulses produced by sensory nerve-endings: Part II. The response of a single end-organ","volume":"61","author":"Adrian","year":"1926","journal-title":"J Physiol"},{"key":"B29","first-page":"339","article-title":"Role of temporal spike patterns in neural codes","volume-title":"Principles of Neural Coding","author":"Petersen","year":"2013"},{"key":"B30","doi-asserted-by":"publisher","first-page":"344","DOI":"10.1038\/nn.2479","article-title":"Connectivity reflects coding: a model of voltage-based STDP with homeostasis","volume":"13","author":"Clopath","year":"2010","journal-title":"Nat Neurosci"},{"key":"B31","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1109\/DCNA59899.2023.10290361","article-title":"STRDP: a simple rule of rate dependent STDP","volume-title":"2023 7th Scientific School Dynamics of Complex Networks and their Applications (DCNA).","author":"Lobov","year":"2023"},{"key":"B32","volume-title":"Principles of Neural Science","author":"Kandel","year":"2000"},{"key":"B33","doi-asserted-by":"publisher","first-page":"5165","DOI":"10.1523\/JNEUROSCI.4499-11.2012","article-title":"Schaffer-specific local field potentials reflect discrete excitatory events at gamma-frequency that may fire postsynaptic hippocampal CA1 units","volume":"32","author":"Fernandez-Ruiz","year":"2012","journal-title":"J Neurosci"},{"key":"B34","doi-asserted-by":"publisher","first-page":"486","DOI":"10.1016\/j.neuroscience.2015.09.054","article-title":"New uses of LFPs: pathway-specific threads obtained through spatial discrimination","volume":"310","author":"Herreras","year":"2015","journal-title":"Neurosci"},{"key":"B35","doi-asserted-by":"publisher","first-page":"1738","DOI":"10.1093\/cercor\/bht022","article-title":"Spatial modules of coherent activity in pathway-specific LFPs in the hippocampus reflect topology and different modes of presynaptic synchronization","volume":"24","author":"Benito","year":"2014","journal-title":"Cereb Cortex"},{"key":"B36","doi-asserted-by":"publisher","first-page":"500","DOI":"10.3390\/s20020500","article-title":"Competitive learning in a spiking neural network: towards an intelligent pattern classifier","volume":"20","author":"Lobov","year":"2020","journal-title":"Sensors"},{"key":"B37","doi-asserted-by":"publisher","first-page":"1569","DOI":"10.1109\/TNN.2003.820440","article-title":"Simple model of spiking neurons","volume":"14","author":"Izhikevich","year":"2003","journal-title":"IEEE Trans Neur Net"},{"key":"B38","volume-title":"Methods in Neuronal Modeling: From Ions to Networks","author":"Koch","year":"1998"},{"key":"B39","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BF00275687","article-title":"Simplified neuron model as a principal component analyzer","volume":"15","author":"Oja","year":"1982","journal-title":"J Math Biol"},{"key":"B40","author":"Krizhevsky","year":"2009","journal-title":"Learning Multiple Layers of Features From Tiny Images."},{"key":"B41","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1016\/S0896-6273(02)01050-4","article-title":"Fast and slow contrast adaptation in retinal circuitry","volume":"36","author":"Baccus","year":"2002","journal-title":"Neuron"},{"key":"B42","first-page":"3867","article-title":"A unifying contrast maximization framework for event cameras, with applications to motion, depth, and optical flow estimation","volume-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition","author":"Gallego","year":"2018"},{"key":"B43","doi-asserted-by":"publisher","first-page":"1102","DOI":"10.1038\/nature03687","article-title":"Invariant visual representation by single neurons in the human brain","volume":"435","author":"Quian Quiroga","year":"2005","journal-title":"Nature"},{"key":"B44","doi-asserted-by":"publisher","first-page":"2446","DOI":"10.1152\/jn.01045.2009","article-title":"Generation of sustained field potentials by gradients of polarization within single neurons: a macroscopic model of spreading depression","volume":"103","author":"Makarova","year":"2010","journal-title":"J Neurophysiol"},{"key":"B45","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1002\/1521-1878(200008)22:8<753::AID-BIES9>3.0.CO;2-Z","article-title":"Pattern formation by local self-activation and lateral inhibition","volume":"22","author":"Meinhardt","year":"2000","journal-title":"Bioessays"},{"key":"B46","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1016\/j.tins.2016.08.004","article-title":"Homeostatic plasticity of subcellular neuronal structures: from inputs to outputs","volume":"39","author":"Wefelmeyer","year":"2016","journal-title":"Trends Neurosci"}],"container-title":["Frontiers in Applied Mathematics and Statistics"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2025.1553779\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:47:31Z","timestamp":1750225651000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fams.2025.1553779\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,18]]},"references-count":46,"alternative-id":["10.3389\/fams.2025.1553779"],"URL":"https:\/\/doi.org\/10.3389\/fams.2025.1553779","relation":{},"ISSN":["2297-4687"],"issn-type":[{"value":"2297-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,18]]},"article-number":"1553779"}}