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On a Model of Associative Memory with Huge Storage Capacity
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“Interaction functions of the form F ( x ) = exp( x ) lead to exponential storage capacity of 2 d/ 2 where all stored patterns are fixed points but the radius of attraction vanishes (Demircigil et al., 2017).”
From Hopfield Networks is All You Need (2020) · cites this paper as Demircigil et al., 2017
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“Modern binary Hopfield networks with energy functions based on interaction functions of the form F ( x ) = exp( x ) even lead to storage capacity of 2 d/ 2 , where all stored binary patterns are fixed points but the radius of attraction vanishes (Demircigil et al., 2017).”
From Hopfield Networks is All You Need (2020) · cites this paper as Demircigil et al., 2017
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In the citing paper
“This energy leads to an exponential storage capacity of N = 2 d/ 2 for binary patterns.”
From Hopfield Networks is All You Need (2020) · cites this paper as Demircigil et al., 2017
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“This model was generalized by Demircigil et al. (Demircigil et al., 2017) to exponential interaction functions F ( x ) = exp( x ) , which gives the energy E = -exp(lse(1 , X T ξ )) .”
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“Furthermore, with a single update the fixed point is recovered with high probability.”
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“It has been shown that the network converges with high probability after one update (Demircigil et al., 2017).”
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Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Interaction functions of the form F ( x ) = x n lead to storage capacity of α n d n -1 , where α n depends on the allowed error probability (Krotov & Hopfield, 2016; 2018; Demircigil et al., 2017) (see (Krotov & Hopfield, 2018) for the non-binary case).”
From Hopfield Networks is All You Need (2020) · cites this paper as Demircigil et al., 2017
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
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“Theorem A10 (Storage Capacity for Binary Modern Hopfield Nets (Demircigil et al. 2017)) . Consider the generalized Hopfield model with the dynamics described in Eq. (545) and interaction function F given by F ( x ) = e x . For a fixed 0 < α < ln(2) / 2 let N = exp( αd ) + 1 and let x 1 , . . . , x N be N patterns chosen uniformly at random from {-1 , +1 } d .”
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Metadata
- Authors
- Demircigil, M., Heusel, J., Löwe, M., Upgang, S., & Vermet, F.
- Affiliations
- École Normale Supérieure - PSL (FR)
- University of Münster (DE)
- Centre National de la Recherche Scientifique (FR)
- Corresponding author
- Vermet, Franck
- Venue
- Journal of Statistical Physics
- Published
- 2017-05-19
- Volume
- 168
- Issue
- 2
- Pages
- 288-299
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W2587333550
- Cited by
- 136
- References
- 13
- Citations by year
- 2026: 17 · 2025: 35 · 2024: 31 · 2023: 19 · 2022: 7 · 2021: 12 · 2020: 6 · 2019: 2 · 2018: 4 · 2017: 3
- FWCI
- 2.45
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Statistical Physics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- associative memory, Hopfield neural network, storage capacity, basins of attraction, artificial neural networks
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