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It has been recently shown that a learning transition happens when a Hopfield Network stores examples generated as superpositions of random features, where new attractors corresponding to such features appear in the model.
Neural networks and physical systems with emergent collective computational abilities
John J Hopfield · 1982
Earlier work this paper cites.
Multiconnected neural network models
E Gardner · 1987
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Statistical mechanics of neural networks near saturation
Daniel J Amit, Hanoch Gutfreund, and Haim Sompolinsky · 1987
Earlier work this paper cites.
Information storage in neural networks with low levels of activity
Daniel J Amit, Hanoch Gutfreund, and Haim Sompolinsky · 1987
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Spin glass theory and beyond: An Introduction to the Replica Method and Its Applications
Marc Mézard, Giorgio Parisi, and Miguel Angel Virasoro · 1987
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Random features for large-scale kernel machines
Ali Rahimi and Benjamin Recht · 2007
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Dense associative memory for pattern recognition
Dmitry Krotov and John J Hopfield · 2016
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Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton · 2016
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On a model of associative memory with huge storage capacity
Mete Demircigil, Judith Heusel, Matthias Löwe, Sven Upgang, and Franck Vermet · 2017
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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
Cited alongside, same era.
Hopfield networks is all you need
Hubert Ramsauer, Bernhard Schäfl, Johannes Lehner, Philipp Seidl, Michael Widrich, Thomas Adler, Lukas Gruber, Markus Holzleitner, Milena Pavlović, Geir Kjetil Sandve, et al · 2020
Cited alongside, same era.
Modeling the influence of data structure on learning in neural networks: The hidden manifold model
Sebastian Goldt, Marc Mézard, Florent Krzakala, and Lenka Zdeborová · 2020
Cited alongside, same era.
Generalisation error in learning with random features and the hidden manifold model
Federica Gerace, Bruno Loureiro, Florent Krzakala, Marc Mézard, and Lenka Zdeborová · 2020
Cited alongside, same era.
The gaussian equivalence of generative models for learning with shallow neural networks
Sebastian Goldt, Bruno Loureiro, Galen Reeves, Florent Krzakala, Marc Mézard, and Lenka Zdeborová · 2022
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Universality laws for high-dimensional learning with random features
Hong Hu and Yue M Lu · 2022
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Dense hebbian neural networks: a replica symmetric picture of supervised learning
Elena Agliari, Linda Albanese, Francesco Alemanno, Andrea Alessandrelli, Adriano Barra, Fosca Giannotti, Daniele Lotito, and Dino Pedreschi · 2023
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The exponential capacity of dense associative memories
Carlo Lucibello and Marc Mézard · 2023
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A new frontier for hopfield networks
Dmitry Krotov · 2023
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Dmitry Krotov and John J. Hopfield · 2021
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Song Mei and Andrea Montanari · 2022
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Learning through atypical phase transitions in overparameterized neural networks
Carlo Baldassi, Clarissa Lauditi, Enrico M. Malatesta, Rosalba Pacelli, Gabriele Perugini, and Riccardo Zecchina · 2022
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Manuscript in preparation
Silvio Kalaj and Matteo Negri
Cited in the paper.
Matteo Negri, Clarissa Lauditi, Gabriele Perugini, Carlo Lucibello, and Enrico Malatesta · 2023
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In search of dispersed memories: Generative diffusion models are associative memory networks
Luca Ambrogioni · 2023
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Dynamical regimes of diffusion models
Giulio Biroli, Tony Bonnaire, Valentin De Bortoli, and Marc Mézard · 2024
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