The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Saturation Level of the Hopfield Model for Neural Network
Abstract
The Hopfield model of a neural network is studied for p = α N , where p is the number of memorized patterns and N the number of neurons. The averaging over the quenched randomness is performed with the replica method, with replica symmetry broken once. It is shown that the critical value of α increases from 0.138 to 0.144, in excellent agreement with simulation results. For 0.138 < α ⩽ 0.144 retrieval states exist only with replica symmetry breaking. Wherever the difference between the replica symmetric solution and the broken symmetry solution is numerically detectable, symmetry breaking improves the retrieval. At α c the number of errors decreases from 1.5% to 0.9%.
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“Using tricks-of-trade and allowing small retrieval errors, the storage capacity is about 0 . 138 d (Crisanti et al., 1986; Hertz et al., 1991; Torres et al., 2002).”
From Hopfield Networks is All You Need (2020) · cites this paper as Crisanti et al., 1986
Citations
Cites
Neural networks and physical systems with emergent collective computational abilities.
Hopfield, J. J. (1982) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.79.8.2554 · Cited by 19,270
Research works printed but not linked: 6
- 10.1103/PhysRevLett.55.1530 · DOI
- Amit D J, Ann. Phys. (NY)
- Nadal J P, 1986, Europhys. Lett., 1, 535, 10.1209/0295-5075/1/10/008 · DOI
- 10.1103/PhysRevB.17.4384 · DOI
- Parisi G, 1980, J. Phys. A: Math. Gen., 13, 1101, 10.1088/0305-4470/13/3/042 · DOI · Paper page
- 10.1063/1.1699114 · DOI · Paper page
Cited by
Hopfield Networks is All You Need
Ramsauer, H., Schäfl, B., Lehner, J., Seidl, P., Widrich, M., Adler, T., Gruber, L., Holzleitner, M., Pavlović, M., Sandve, G. K., et al. (2020) · arXiv · doi:10.48550/arxiv.2008.02217 · Cited by 236
“138d (Crisanti et al., 1986; Hertz et al., 1991; Torres et al., 2002).”
Input-driven dynamics for robust memory retrieval in Hopfield networks
Betteti, S., Baggio, G., Bullo, F., & Zampieri, S. (2025) · Science Advances · doi:10.1126/sciadv.adu6991 · Cited by 12
“…the 80s, the words “Associative Memory Network" have closely echoed with “Hopfield Network" [Hopfield, 1982, 1984], and a plethora of subsequent works have endeavored to provide a detailed picture of the properties of such networks [Amit et al., 1987a, Crisanti et al., 1986, Treves and Amit, 1988].”
Metadata
- Authors
- Crisanti, A., Amit, D. J., & Gutfreund, H.
- Affiliations
- Hebrew University of Jerusalem (IL)
- ORCID
- Crisanti, A
- Venue
- Europhysics Letters (EPL)
- Publisher
- IOP Publishing
- Published
- 1986-08-15
- Volume
- 2
- Issue
- 4
- Pages
- 337-341
- ISSN
- 0295-5075 (ISSN-L)
- 1286-4854
- OpenAlex
- W2059988607
- Cited by
- 97
- References
- 1
- Citations by year
- 2026: 2 · 2025: 8 · 2024: 3 · 2023: 3 · 2022: 5 · 2021: 2 · 2020: 2 · 2018: 2 · 2013: 1 · 2012: 1
- FWCI
- 7.87
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Europhysics Letters (EPL) (publishedVersion)
- IRIS Research product catalog (Sapienza University of Rome) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- Hopfield neural network, saturation level, memory capacity, replica symmetry breaking, quenched randomness, pattern retrieval, error rate, replica symmetric solution, spin glass
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
