Quantum spin models for numerosity perception
Open accessAbstract
Humans share with animals, both vertebrates and invertebrates, the capacity to sense the number of items in their environment already at birth. The pervasiveness of this skill across the animal kingdom suggests that it should emerge in very simple populations of neurons. Current modelling literature, however, has struggled to provide a simple architecture carrying out this task, with most proposals suggesting the emergence of number sense in multi-layered complex neural networks, and typically requiring supervised learning; while simple accumulator models fail to predict Weber’s Law, a common trait of human and animal numerosity processing. We present a simple quantum spin model with all-to-all connectivity, where numerosity is encoded in the spectrum after stimulation with a number of transient signals occurring in a random or orderly temporal sequence. We use a paradigmatic simulational approach borrowed from the theory and methods of open quantum systems out of equilibrium, as a possible way to describe information processing in neural systems. Our method is able to capture many of the perceptual characteristics of numerosity in such systems. The frequency components of the magnetization spectra at harmonics of the system’s tunneling frequency increase with the number of stimuli presented. The amplitude decoding of each spectrum, performed with an ideal-observer model, reveals that the system follows Weber’s law. This contrasts with the well-known failure to reproduce Weber’s law with linear system or accumulators models.
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Each existing quantum model of brain activity focuses on a specific dimension of neural processes, such as consciousness, cognition, or perception.
“Each existing model focuses on a specific dimension of neural processes, such as consciousness, cognition, or perception (including numerosity perception; see, for instance, the spin model in [14]), with the overarching goal of understanding the brain.”
From Quantum Models of Consciousness from a Quantum Information Science Perspective (2025) · cites this paper as [14]
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Self-citation
- Authors
- Yago Malo, J., Cicchini, G. M., Morrone, M. C., & Chiofalo, M. L.
- Affiliations
- Neuroscience Institute (IT)
- University of Pisa (IT)
- Venue
- PLOS ONE
- Publisher
- Public Library of Science (PLoS)
- Published
- 2023-04-25
- Volume
- 18
- Issue
- 4
- Pages
- e0284610
- ISSN
- 1932-6203 (ISSN-L)
- PMC
- PMC10128973
- OpenAlex
- W4366981651
- Cited by
- 5
- References
- 51
- Citations by year
- 2025: 3 · 2024: 1 · 2023: 1
- FWCI
- 1.02
- Type
- journal article
- Language
- en
- Update notices
- correction (2025-08-26)
- Open access
- gold
- doi.org
- Licence
- Locations
- PLoS ONE (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CINECA IRIS Institutial research information system (University of Pisa) (submittedVersion, cc-by)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Funders
- H2020 European Research Council (Advanced Grant GenPercept No. 832813)
- Ministero dell’Istruzione, dell’Università e della Ricerca (PRIN2017 Grant No. 2017SBCPZY, Italian 376 national program PON 2014-2020, DM MUR 1062/2021, PRIN2017)
- FLAG-ERA Joint Transnational Call 2019 Grant DOMINO
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Cognitive and developmental aspects of mathematical skills
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- numerosity perception, number sense, quantum spin systems, open quantum systems, all-to-all connectivity, Weber's law, ideal observer, neural information processing, accumulator model
- MeSH terms
- Animals, Cognition, Humans, Infant, Newborn, Neurons, Perception, Visual Perception, Neural Networks, Computer
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