The calcitron: A simple neuron model that implements many learning rules via the calcium control hypothesis

Toviah Moldwin, Li Shay Azran and Idan Segev

PLOS Computational Biology, 2025, vol. 21, issue 1, 1-30

Abstract: Theoretical neuroscientists and machine learning researchers have proposed a variety of learning rules to enable artificial neural networks to effectively perform both supervised and unsupervised learning tasks. It is not always clear, however, how these theoretically-derived rules relate to biological mechanisms of plasticity in the brain, or how these different rules might be mechanistically implemented in different contexts and brain regions. This study shows that the calcium control hypothesis, which relates synaptic plasticity in the brain to the calcium concentration ([Ca2+]) in dendritic spines, can produce a diverse array of learning rules. We propose a simple, perceptron-like neuron model, the calcitron, that has four sources of [Ca2+]: local (following the activation of an excitatory synapse and confined to that synapse), heterosynaptic (resulting from the activity of other synapses), postsynaptic spike-dependent, and supervisor-dependent. We demonstrate that by modulating the plasticity thresholds and calcium influx from each calcium source, we can reproduce a wide range of learning and plasticity protocols, such as Hebbian and anti-Hebbian learning, frequency-dependent plasticity, and unsupervised recognition of frequently repeating input patterns. Moreover, by devising simple neural circuits to provide supervisory signals, we show how the calcitron can implement homeostatic plasticity, perceptron learning, and BTSP-inspired one-shot learning. Our study bridges the gap between theoretical learning algorithms and their biological counterparts, not only replicating established learning paradigms but also introducing novel rules.Author summary: Researchers have developed various learning rules for artificial neural networks, but it is unclear how these rules relate to the brain’s natural processes. This study focuses on the calcium control hypothesis, which links changes in brain connections to calcium levels in neurons. The researchers created a simple neuron model that includes four sources of calcium and showed that by adjusting these, the model can mimic different types of learning, like recognizing patterns or learning from single events. This study helps connect theoretical learning models with how the brain might actually work, offering insights into both established and new learning mechanisms.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1012754

DOI: 10.1371/journal.pcbi.1012754

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