{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T06:26:39Z","timestamp":1767853599242,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T00:00:00Z","timestamp":1652313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"GenoMed4All n. 101017549 Horizon 2020 (EU) Project"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Purpose: In this work, we propose an implementation of the Bienenstock\u2013Cooper\u2013Munro (BCM) model, obtained by a combination of the classical framework and modern deep learning methodologies. The BCM model remains one of the most promising approaches to modeling the synaptic plasticity of neurons, but its application has remained mainly confined to neuroscience simulations and few applications in data science. Methods: To improve the convergence efficiency of the BCM model, we combine the original plasticity rule with the optimization tools of modern deep learning. By numerical simulation on standard benchmark datasets, we prove the efficiency of the BCM model in learning, memorization capacity, and feature extraction. Results: In all the numerical simulations, the visualization of neuronal synaptic weights confirms the memorization of human-interpretable subsets of patterns. We numerically prove that the selectivity obtained by BCM neurons is indicative of an internal feature extraction procedure, useful for patterns clustering and classification. The introduction of competitiveness between neurons in the same BCM network allows the network to modulate the memorization capacity of the model and the consequent model selectivity. Conclusions: The proposed improvements make the BCM model a suitable alternative to standard machine learning techniques for both feature selection and classification tasks.<\/jats:p>","DOI":"10.3390\/e24050682","type":"journal-article","created":{"date-parts":[[2022,5,12]],"date-time":"2022-05-12T21:46:53Z","timestamp":1652392013000},"page":"682","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Effectiveness of Biologically Inspired Neural Network Models in Learning and Patterns Memorization"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9758-6906","authenticated-orcid":false,"given":"Lorenzo","family":"Squadrani","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy, University of Bologna, 40126 Bologna, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5802-1195","authenticated-orcid":false,"given":"Nico","family":"Curti","sequence":"additional","affiliation":[{"name":"Department of Experimental, Diagnostic and Specialty Medicine, University of Bologna, 40126 Bologna, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2269-2338","authenticated-orcid":false,"given":"Enrico","family":"Giampieri","sequence":"additional","affiliation":[{"name":"Department of Experimental, Diagnostic and Specialty Medicine, University of Bologna, 40126 Bologna, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3185-7456","authenticated-orcid":false,"given":"Daniel","family":"Remondini","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy, University of Bologna, 40126 Bologna, Italy"},{"name":"INFN, 40127 Bologna, Italy"}]},{"given":"Brian","family":"Blais","sequence":"additional","affiliation":[{"name":"Department of Science, Bryant University, Smithfield, RI 02917, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4892-925X","authenticated-orcid":false,"given":"Gastone","family":"Castellani","sequence":"additional","affiliation":[{"name":"Department of Experimental, Diagnostic and Specialty Medicine, University of Bologna, 40126 Bologna, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,12]]},"reference":[{"key":"ref_1","unstructured":"Commission, E. (2020). White Paper on Artificial Intelligence\u2014A European Approach to Excellence and Trust, European Commission. COM(2020) 65 Final."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Linardatos, P., Papastefanopoulos, V., and Kotsiantis, S. (2021). Explainable AI: A Review of Machine Learning Interpretability Methods. Entropy, 23.","DOI":"10.3390\/e23010018"},{"key":"ref_3","first-page":"147","article-title":"A learning algorithm for boltzmann machines","volume":"9","author":"Ackley","year":"1985","journal-title":"Cognit. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"E7655","DOI":"10.1073\/pnas.1608103113","article-title":"Unreasonable effectiveness of learning neural networks: From accessible states and robust ensembles to basic algorithmic schemes","volume":"113","author":"Baldassi","year":"2016","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"030201","DOI":"10.1103\/PhysRevLett.96.030201","article-title":"Learning by Message Passing in Networks of Discrete Synapses","volume":"96","author":"Braunstein","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1113\/jphysiol.1952.sp004764","article-title":"A quantitative description of membrane current and its application to conduction and excitation in nerve","volume":"117","author":"Hodgkin","year":"1952","journal-title":"J. Physiol."},{"key":"ref_7","unstructured":"Rosenblatt, F. (1957). The Perceptron\u2014A Perceiving and Recognizing Automaton, Cornell Aeronautical Laboratory. Report 85-460-1."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1038\/s41583-018-0038-8","article-title":"On the nature and use of models in network neuroscience","volume":"19","author":"Bassett","year":"2018","journal-title":"Nat. Rev. Neurosci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1038\/nn.4502","article-title":"Network models in neuroscience","volume":"20","author":"Bassett","year":"2017","journal-title":"Nat. Neurosci."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"20170623","DOI":"10.1098\/rsif.2017.0623","article-title":"Generative models for network neuroscience: Prospects and promise","volume":"14","author":"Betzel","year":"2017","journal-title":"J. R. Soc. Interface"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1038\/nn.3690","article-title":"Contributions and challenges for network models in cognitive neuroscience","volume":"17","author":"Sporns","year":"2014","journal-title":"Nat. Neurosci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1523\/JNEUROSCI.02-01-00032.1982","article-title":"Theory for the development of neuron selectivity: Orientation specificity and binocular interaction in visual cortex","volume":"2","author":"Bienenstock","year":"1982","journal-title":"J. Neurosci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1162\/neco.1992.4.1.98","article-title":"Feature Extraction Using an Unsupervised Neural Network","volume":"4","author":"Intrator","year":"1992","journal-title":"Neural Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"7797","DOI":"10.1073\/pnas.91.16.7797","article-title":"Formation of receptive fields in realistic visual environments according to the Bienenstock, Cooper, and Munro (BCM) theory","volume":"91","author":"Law","year":"1994","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1083","DOI":"10.1073\/pnas.96.3.1083","article-title":"The Role of Presynaptic Activity in Monocular Deprivation: Comparison of Homosynaptic and Heterosynaptic Mechanisms","volume":"96","author":"Blais","year":"1999","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1088\/0954-898X_10_2_001","article-title":"Solutions of the BCM learning rule in a network of lateral interacting nonlinear neurons","volume":"10","author":"Castellani","year":"1999","journal-title":"Network"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Blais, B., Shouval, H., and Cooper, L. (1996). Time Dependence of Visual Deprivation: A Comparison between Models of Plasticity and Experimental Results, The Institute for Brain & Neural Systems\u2014Brown University.","DOI":"10.21236\/ADA316967"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0893-6080(05)80003-6","article-title":"Objective function formulation of the BCM theory of visual cortical plasticity: Statistical connections, stability conditions","volume":"5","author":"Intrator","year":"1992","journal-title":"Neural Netw."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"7723","DOI":"10.1073\/pnas.1820458116","article-title":"Unsupervised learning by competing hidden units","volume":"116","author":"Krotov","year":"2019","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_20","unstructured":"Squadrani, L., Gasperini, S., Ceccarelli, M., and Curti, N. (2022, May 11). Plasticity\u2014Unsupervised Neural Networks with Biological-Inspired Learning Rules. Available online: https:\/\/github.com\/Nico-Curti\/plasticity."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1038\/381526a0","article-title":"Experience-dependent modification of synaptic plasticity in visual cortex","volume":"381","author":"Kirkwood","year":"1996","journal-title":"Nature"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1162\/neco.1996.8.5.1021","article-title":"Effect of Binocular Cortical Misalignment on Ocular Dominance and Orientation Selectivity","volume":"8","author":"Shouval","year":"1996","journal-title":"Neural Comput."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1570","DOI":"10.4249\/scholarpedia.1570","article-title":"BCM theory","volume":"3","author":"Blais","year":"2008","journal-title":"Scholarpedia"},{"key":"ref_24","unstructured":"Bower, J.M. (1997). Dynamics of Synaptic Plasticity: A Comparison between Models and Experimental Results in Visual Cortex. Computational Neuroscience: Trends in Research, 1997, Springer."},{"key":"ref_25","unstructured":"Kingma, D.P., and Ba, J. (2017). Adam: A Method for Stochastic Optimization. arXiv."},{"key":"ref_26","unstructured":"Leen, T., Dietterich, T., and Tresp, V. (2001). Permitted and Forbidden Sets in Symmetric Threshold-Linear Networks. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_27","unstructured":"Ramachandran, P., Zoph, B., and Le, Q.V. (2017). Searching for Activation Functions. arXiv."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1038\/35016072","article-title":"Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit","volume":"405","author":"Hahnloser","year":"2000","journal-title":"Nature"},{"key":"ref_29","unstructured":"Nair, V., and Hinton, G.E. (2020, January 21\u201324). Rectified Linear Units Improve Restricted Boltzmann Machines. Proceedings of the 27th International Conference on International Conference on Machine Learning, Haifa, Israel."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.neunet.2017.12.012","article-title":"Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning","volume":"107","author":"Elfwing","year":"2018","journal-title":"Neural Netw."},{"key":"ref_31","unstructured":"Gao, F., and Zhang, B. (2020). A Use of Even Activation Functions in Neural Networks. arXiv."},{"key":"ref_32","unstructured":"Agarap, A.F. (2018). Deep Learning using Rectified Linear Units (ReLU). arXiv."},{"key":"ref_33","first-page":"315","article-title":"Deep Sparse Rectifier Neural Networks","volume":"Volume 15","author":"Gordon","year":"2011","journal-title":"Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Cooper, L.N., Intrator, N., Blais, B.S., and Shouval, H.Z. (2004). Theory of Cortical Plasticity, World Scientific.","DOI":"10.1142\/9789812562555"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"16529","DOI":"10.1523\/JNEUROSCI.1306-11.2011","article-title":"Selectivity for Spectral Motion as a Neural Computation for Encoding Natural Communication Signals in Bat Inferior Colliculus","volume":"31","author":"Andoni","year":"2011","journal-title":"J. Neurosci."},{"key":"ref_36","first-page":"2825","article-title":"Scikit-learn: Machine Learning in Python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/682\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:09:44Z","timestamp":1760137784000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/5\/682"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,12]]},"references-count":36,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["e24050682"],"URL":"https:\/\/doi.org\/10.3390\/e24050682","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,12]]}}}