The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
A theoretical investigation into the performance of the Hopfield model
Abstract
An analysis is made of the behavior of the Hopfield model as a content-addressable memory (CAM) and as a method of solving the traveling salesman problem (TSP). The analysis is based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix. The dynamic equation is shown to be equivalent to a projection of the input vector onto this subspace. In the case of content-addressable memory, it is shown that spurious fixed points can occur at any corner of the hypercube that is on or near the subspace spanned by the memory vectors. Analysed is why the network can frequently converge to an invalid solution when applied to the traveling salesman problem energy function. With these expressions, the network can be made robust and can reliably solve the traveling salesman problem with tour sizes of 50 cities or more.
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Citations
Cites
Self-Organization and Associative Memory
Kohonen, T. (1989) · Springer Series in Information Sciences · doi:10.1007/978-3-642-88163-3 · Cited by 8,740
Hopfield, J. J. (1984) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.81.10.3088 · Cited by 6,918
Introduction to automata theory, languages, and computation
(1980) · Computer Languages · doi:10.1016/0096-0551(80)90011-9 · Cited by 6,824
“Neural” computation of decisions in optimization problems
Hopfield, J. J., & Tank, D. W. (1985) · Biological Cybernetics · doi:10.1007/bf00339943 · Cited by 6,031
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
Lau, H. T. (1986) · Lecture Notes in Economics and Mathematical Systems · doi:10.1007/978-3-642-61649-5_4 · Cited by 796
On the stability of the Travelling Salesman Problem algorithm of Hopfield and Tank
Wilson, G. V., & Pawley, G. S. (1988) · Biological Cybernetics · doi:10.1007/bf00363956 · Cited by 546
‘Unlearning’ has a stabilizing effect in collective memories
Hopfield, J. J., Feinstein, D. I., & Palmer, R. G. (1983) · Nature · doi:10.1038/304158a0 · Cited by 422
Information capacity of the Hopfield model
Abu-Mostafa, Y., & St. Jacques, J. (1985) · IEEE Transactions on Information Theory · doi:10.1109/tit.1985.1057069 · Cited by 267
Theories on the Hopfield neural networks
Abe, S. (1989) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.1989.118633 · Cited by 90
Cited by
Elements of Artificial Neural Networks
Mehrotra, K., Mohan, C., & Ranka, S. (1996) · The MIT Press eBooks · doi:10.7551/mitpress/2687.001.0001 · Cited by 912
Neural Networks for Combinatorial Optimization: A Review of More Than a Decade of Research
Smith, K. A. (1999) · INFORMS Journal on Computing · doi:10.1287/ijoc.11.1.15 · Cited by 401
Super-resolution target identification from remotely sensed images using a Hopfield neural network
Tatem, A. J., Lewis, H. G., Atkinson, P. M., & Nixon, M. S. (2001) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/36.917895 · Cited by 310
Metadata
- Authors
- Aiyer, S. V. B., Niranjan, M., & Fallside, F.
- Venue
- IEEE Transactions on Neural Networks
- Published
- 1990-06
- Volume
- 1
- Issue
- 2
- Pages
- 204-215
- ISSN
- 1045-9227 (ISSN-L)
- OpenAlex
- W1990566849
- Cited by
- 381
- References
- 13
- FWCI
- 13.45
- Type
- journal article
- Language
- en
- Open access
- closed
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