The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.
Neural network capacity using delta rule
Abstract
It is shown that modifying the Hopfield neural network model to use the delta rule rather than the Hebbian rule substantially increases the capacity. The number of patterns one can store in a neural network of N neurons is actually greater than N (unless N is very small). For example, for N = 30, one can store 40 patterns with a success rate of close to 90%.
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“This update is based on delta-rule (Prados et al. 1989)”
From Nested Learning: The Illusion of Deep Learning Architectures (2025) · cites this paper as Prados et al. 1989
In the citing paper
“This new algorithm, which based on Delta rule (Prados et al. 1989) we refer to as Delta Gradient Descent (DGD), updates the weights not only with respect to the current elements, but it also incorporates the previous state of weights, resulting in an adaptive decay term based on the current data sample.”
From Nested Learning: The Illusion of Deep Learning Architectures (2025) · cites this paper as Prados et al. 1989
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
The capacity of the Hopfield associative memory
McEliece, R., Posner, E., Rodemich, E., & Venkatesh, S. (1987) · IEEE Transactions on Information Theory · doi:10.1109/tit.1987.1057328 · Cited by 910
Information capacity of the Hopfield model
Abu‐Mostafa, Y. S., & Jacques, J. S. (1985) · IEEE Transactions on Information Theory · doi:10.1109/tit.1985.1057069 · Cited by 266
Prados, D. L. (1988) · Electronics Letters · doi:10.1049/el:19880307 · Cited by 10
Self-citation
Research works printed but not linked: 2
- Hopfield, 1982, 79, 2554
- Prados, 1988, 24, 454
Cited by
Sorted by citations
Self indexing of neural memories
Kak, S. C. (1990) · Physics Letters A · doi:10.1016/0375-9601(90)90340-t · Cited by 24
Self-citationNumber of Autonomous Cognitive Agents in a Neural Network
Kak, S. C. (2022) · Journal of Artificial Intelligence and Consciousness · doi:10.1142/s2705078522500023 · Cited by 23
Self-citationA neural network to design neural networks
Perfetti, R. (1991) · IEEE Transactions on Circuits and Systems · doi:10.1109/31.83884 · Cited by 20
Titans: Learning to Memorize at Test Time
Behrouz, A., Zhong, P., & Mirrokni, V. (2025) · arXiv · doi:10.48550/arxiv.2501.00663 · Cited by 24
“The two learning rules of Hebbian [78] and delta [79] are the most popular learning rules for fast weight programs, which have been extensively explored in various studies [80, 76, 81, 71, 82, 38, 35].”
Neuromodulated multiobjective evolutionary neurocontrollers without speciation
Showalter, I., & Schwartz, H. M. (2020) · Evolutionary Intelligence · doi:10.1007/s12065-020-00394-9 · Cited by 12
Metadata
- Authors
- Prados, D. L., & Kak, S. C.
- Affiliations
- Louisiana State University (US)
- ORCID
- Kak, S.C.
- Venue
- Electronics Letters
- Published
- 1989-02-02
- Volume
- 25
- Issue
- 3
- Pages
- 197-199
- ISSN
- 0013-5194 (ISSN-L)
- 1350-911X
- OpenAlex
- W2013399716
- Cited by
- 19
- References
- 4
- Citations by year
- 2022: 2 · 2021: 3 · 2020: 2 · 2014: 1
- FWCI
- 2.28
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Electronics Letters (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Memory and Neural Computing
- Keywords
- Hopfield neural network, delta rule, Hebbian rule, associative memory, pattern storage capacity, pattern retrieval, neural network capacity
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- CoChat. (2026). Citation check: Neural network capacity using delta rule. https://app.cochat.ai/papers/10.1049/el:19890142
- The paper
- Prados, D. L., & Kak, S. C. (1989). Neural network capacity using delta rule. Electronics Letters. https://doi.org/10.1049/el%3A19890142
