Associative recall of memory without errors
Abstract
A neural network which is capable of recalling without errors any set of linearly independent patterns is studied. The network is based on a Hamiltonian version of the model of Personnaz et al. The energy of a state of N (\ifmmode\pm\else\textpm\fi{}1) neurons is the square of the Euclidean distance---in phase space---between the state and the linear subspace spanned by the patterns. This energy corresponds to nonlocal updatings of the synapses in the learning mode. Results of the mean-field theory (MFT) of the system as well as computer simulations are presented. The stable and metastable states of the network are studied as a function of ``temperature'' T and \ensuremath{\alpha}=p/N, where p is the number of embedded patterns. The maximum capacity of the network is \ensuremath{\alpha}=1. For all \ensuremath{\alpha} (0\ensuremath{\le}\ensuremath{\alpha}<1) the embedded patterns are not only locally stable but are global minima of the energy. The patterns appear, as metastable states, below a temperature T=${T}_{M}$(\ensuremath{\alpha}). The temperature ${T}_{M}$(\ensuremath{\alpha}) decreases to zero as \ensuremath{\alpha}\ensuremath{\rightarrow}1. The spurious states of the network are studied in detail in the case of random uncorrelated patterns. At finite p, they are identical to the mixture states of Hopfield's model. At finite \ensuremath{\alpha}, a spin-glass phase exists as a metastable state. According to the replica symmetric MFT the spin-glass state becomes degenerate with the patterns at \ensuremath{\alpha}=${\ensuremath{\alpha}}_{g}$=1-2/\ensuremath{\pi} and disappears above it. Possible interpretations of this unusual result are discussed. The average radius of attraction R of the patterns has been determined by computer simulations, for sizes up to N=400. The value of R for 0<\ensuremath{\alpha}<1 depends on the details of the dynamics. Results for both parallel and serial dynamics are presented. In both cases R is unity (the largest distance in phase space by definition) at \ensuremath{\alpha}\ensuremath{\rightarrow}0 and decreases monotonically to zero as \ensuremath{\alpha}\ensuremath{\rightarrow}1. Contrary to the MFT, simulations have not revealed, so far, any singularity in the properties of the spurious states at an intermediate value of \ensuremath{\alpha}.
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The approaches explored lately include systems for automatic analysis and synthesis of facial expressions.
“The approaches that have been explored lately also include systems for automatic analysis and synthesis of facial expressions [86], [56], [39], [47], [89], [88], [53], [14], [19]”
From Automatic analysis of facial expressions: the state of the art (2000) · cites this paper as [39]
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- Authors
- Kanter, I., & Sompolinsky, H.
- Affiliations
- Bar-Ilan University (IL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1987-01-01
- Volume
- 35
- Issue
- 1
- Pages
- 380-392
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2029182425
- Cited by
- 379
- References
- 13
- Citations by year
- 2026: 9 · 2025: 11 · 2024: 13 · 2023: 6 · 2022: 10 · 2021: 9 · 2020: 6 · 2019: 6 · 2018: 1 · 2017: 4 · 2016: 4 · 2015: 2 · 2014: 7 · 2013: 6 · 2012: 6
- FWCI
- 30.30
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Keywords
- associative memory, mean-field theory, metastable states, spin glass phase, spurious states, Hopfield neural network, capacity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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