Lattice physics approaches for neural networks
Open accessAbstract
Modern neuroscience has evolved into a frontier field that draws on numerous disciplines, resulting in the flourishing of novel conceptual frames primarily inspired by physics and complex systems science. Contributing in this direction, we recently introduced a mathematical framework to describe the spatiotemporal interactions of systems of neurons using lattice field theory, the reference paradigm for theoretical particle physics. In this note, we provide a concise summary of the basics of the theory, aiming to be intuitive to the interdisciplinary neuroscience community. We contextualize our methods, illustrating how to readily connect the parameters of our formulation to experimental variables using well-known renormalization procedures. This synopsis yields the key concepts needed to describe neural networks using lattice physics. Such classes of methods are attention-worthy in an era of blistering improvements in numerical computations, as they can facilitate relating the observation of neural activity to generative models underpinned by physical principles.
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Lattice field theory has been adapted to model spatiotemporal neural dynamics by discretizing neural activity on a spacetime lattice.
“In particular, lattice field theory, originally developed in quantum field theory and particle physics, has been adapted to model spatiotemporal neural dynamics by discretizing neural activity on a spacetime lattice [44].”
From Quantum-Inspired and Non-Classical Approaches to Consciousness: Models, Evidence and Constraints (2026) · cites this paper as [44]
Lattice field theory-based approaches remain primarily theoretical and computational, providing a principled formalism rather than demonstrating biologically instantiated quantum processes.
“Despite these promising features, it is important to emphasize that lattice field theory-based approaches remain primarily theoretical and computational. Their current contribution lies in providing a principled formalism for describing emergent spatiotemporal structure in neural activity, rather than in demonstrating biologically instantiated quantum processes.”
From Quantum-Inspired and Non-Classical Approaches to Consciousness: Models, Evidence and Constraints (2026) · cites this paper as [44]
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Flagged first, then by citations
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- [163]Hoover B. Liang Y. Pham B. Panda R. Strobelt H. Chau D.H. Zaki M.J. Krotov D. Energy transformer arXiv 2023 2302.07253
Cited by
Sorted by citations
Quantum-Inspired and Non-Classical Approaches to Consciousness: Models, Evidence and Constraints
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“This representation allows the construction of effective theories through coarse-graining procedures, in which macroscopic neural dynamics emerge from underlying discrete interactions, conceptually paralleling renormalisation approaches in statistical and quantum field theory [44].”
Influential
- Authors
- Bardella, G., Franchini, S., Pani, P., & Ferraina, S.
- Affiliations
- Sapienza University of Rome (IT)
- Corresponding author
- Bardella, Giampiero
- Franchini, Simone
- Venue
- iScience
- Publisher
- Elsevier BV
- Published
- 2024-12
- Volume
- 27
- Issue
- 12
- Pages
- 111390
- ISSN
- 2589-0042 (ISSN-L)
- PMC
- PMC11638618
- OpenAlex
- W4404397493
- Cited by
- 17
- References
- 190
- Citations by year
- 2026: 2 · 2025: 14 · 2024: 1
- FWCI
- 1.10
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- iScience (publishedVersion, cc-by-nc-nd)
- PubMed Central (publishedVersion, cc-by-nc-nd)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion, cc-by-nc-nd)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion, cc-by-nc-nd)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- arXiv (Cornell University)
- Funders
- University of Rome La Sapienza (PH11715C823A9528, RM12117A8AD27DB1)
- Università degli Studi di Pavia
- European Commission (CUP B51E22000150006, IR0000011)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Keywords
- lattice field theory, artificial neural networks, renormalization, complex systems
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