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The Hopfield model is a paradigmatic model of neural networks that has been analyzed for many decades in the statistical physics, neuroscience, and machine learning communities.
J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities., Proceedings of the national academy of sciences 79
1982
Earlier work this paper cites.
E. Gardner, Multiconnected neural network models, Journal of Physics A: Mathematical and General 20
1987
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C. Cortes, A. Krogh, and J. Hertz, Hierarchical associative networks, Journal of Physics A: Mathematical and General 20
1987
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M. Mézard, G. Parisi, and M. A. Virasoro, Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications , Vol. 9 (World Scientific Publishing Company, 1987)
1987
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H. Gutfreund, Neural networks with hierarchically correlated patterns, Physical Review A 37
1988
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A. Krogh and J. Hertz, Mean-field analysis of hierarchical associative networks with’magnetisation’, Journal of Physics A: Mathematical and General 21
1988
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J. F. Fontanari and W. Theumann, On the storage of correlated patterns in hopfield’s model, Journal de Physique 51
1990
Earlier work this paper cites.
R. Der, V. Dotsenko, and B. Tirozzi, Modified pseudo-inverse neural networks storing correlated patterns, Journal of Physics A: Mathematical and General 25
1992
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J. Van Hemmen, Hebbian learning, its correlation catastrophe, and unlearning, Network: Computation in Neural Systems 8
1997
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M. Löwe, On the storage capacity of hopfield models with correlated patterns, The Annals of Applied Probability 8
1998
Cited alongside, same era.
G. E. Hinton, S. Osindero, and Y.-W. Teh, A fast learning algorithm for deep belief nets, Neural computation 18
2006
Cited alongside, same era.
G. E. Hinton and R. R. Salakhutdinov, Reducing the dimensionality of data with neural networks, science 313
2006
Cited alongside, same era.
E. Agliari, A. Barra, A. De Antoni, and A. Galluzzi, Parallel retrieval of correlated patterns: From hopfield networks to boltzmann machines, Neural Networks 38
2013
Cited alongside, same era.
D. Krotov and J. J. Hopfield, Dense associative memory for pattern recognition, Advances in neural information processing systems 29
2016
Cited alongside, same era.
2020
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S. Goldt, M. Mézard, F. Krzakala, and L. Zdeborová, Modeling the influence of data structure on learning in neural networks: The hidden manifold model, Physical Review X 10
2020
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F. Gerace, B. Loureiro, F. Krzakala, M. Mézard, and L. Zdeborová, Generalisation error in learning with random features and the hidden manifold model, in International Conference on Machine Learning (PMLR, 2020) pp. 3452–3462
2020
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2021
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M. Demircigil, J. Heusel, M. Löwe, S. Upgang, and F. Vermet, On a model of associative memory with huge storage capacity, Journal of Statistical Physics 168
2017
Cited alongside, same era.
A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, Attention is all you need, Advances in neural information processing systems 30
2017
Cited alongside, same era.
M. Mézard, Mean-field message-passing equations in the hopfield model and its generalizations, Physical Review E 95
2017
Cited alongside, same era.
2017
Cited alongside, same era.
D. J. Amit, H. Gutfreund, and H. Sompolinsky, Statistical mechanics of neural networks near saturation, Annals of physics 173
Cited in the paper.
D. J. Amit, H. Gutfreund, and H. Sompolinsky, Information storage in neural networks with low levels of activity, Physical Review A 35
Cited in the paper.
J. Steinberg and H. Sompolinsky, Associative memory of structured knowledge, Scientific Reports 12
2022
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S. Mei and A. Montanari, The generalization error of random features regression: Precise asymptotics and the double descent curve, Communications on Pure and Applied Mathematics 75
2022
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S. Goldt, B. Loureiro, G. Reeves, F. Krzakala, M. Mézard, and L. Zdeborová, The gaussian equivalence of generative models for learning with shallow neural networks, in Mathematical and Scientific Machine Learning (PMLR, 2022) pp. 426–471
2022
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H. Hu and Y. M. Lu, Universality laws for high-dimensional learning with random features, IEEE Transactions on Information Theory (2022)
2022
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C. Baldassi, C. Lauditi, E. M. Malatesta, R. Pacelli, G. Perugini, and R. Zecchina, Learning through atypical phase transitions in overparameterized neural networks, Phys. Rev. E 106
2022
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