Journal article
Explosive neural networks via higher-order interactions in curved statistical manifolds
- Abstract:
- Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the maximum entropy principle, we introduce curved neural networks as a class of models with a limited number of parameters that are particularly well-suited for studying higher-order phenomena. Through exact mean-field descriptions, we show that these curved neural networks implement a self-regulating annealing process that can accelerate memory retrieval, leading to explosive order-disorder phase transitions with multi-stability and hysteresis effects. Moreover, by analytically exploring their memory-retrieval capacity using the replica trick, we demonstrate that these networks can enhance memory capacity and robustness of retrieval over classical associative-memory networks. Overall, the proposed framework provides parsimonious models amenable to analytical study, revealing higher-order phenomena in complex networks.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 1.3MB, Terms of use)
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(Supplementary materials, zip, 1023.1KB, Terms of use)
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- Publisher copy:
- 10.1038/s41467-025-61475-w
Authors
+ John Templeton Foundation
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- Funder identifier:
- https://ror.org/035tnyy05
- Grant:
- 62828
- Publisher:
- Springer Nature
- Journal:
- Nature Communications More from this journal
- Volume:
- 16
- Issue:
- 1
- Article number:
- 6511
- Publication date:
- 2025-07-24
- Acceptance date:
- 2025-06-23
- DOI:
- EISSN:
-
2041-1723
- ISSN:
-
2041-1723
- Language:
-
English
- Pubs id:
-
2268936
- Local pid:
-
pubs:2268936
- Source identifiers:
-
3144428
- Deposit date:
-
2025-07-24
Terms of use
- Copyright holder:
- Aguilera et al.
- Copyright date:
- 2025
- Rights statement:
- © The Author(s) 2025. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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