An Exactly Solvable Asymmetric Neural Network Model

Derrida, Bernard; Gardner, E.; Zippelius, Annette

doi:10.1209/0295-5075/4/2/007

Cited by 540 publications

(348 citation statements)

References 20 publications

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“…One would expect (Sompolinsky, 1986;Derrida et al, 1987) the constraint f Ͼ lnN/N to be replaced by ln(cN )/(cN ), where c is the fraction of neurons synapting on a given neuron (anatomically ϳ10%). Hence, to allow for f ϳ 1%, one would need cN ϳ 9000, or 90,000 cells, a rather realistic number.…”

Section: Modelingmentioning

confidence: 99%

Universal Memory Mechanism for Familiarity Recognition and Identification

Yakovlev¹,

Amit²,

Romani³

et al. 2008

J. Neurosci.

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Macaque monkeys were tested on a delayed-match-to-multiple-sample task, with either a limited set of well trained images (in randomized sequence) or with never-before-seen images. They performed much better with novel images. False positives were mostly limited to catch-trial image repetitions from the preceding trial. This result implies extremely effective one-shot learning, resembling Standing's finding that people detect familiarity for 10,000 once-seen pictures (with 80% accuracy) (Standing, 1973). Familiarity memory may differ essentially from identification, which embeds and generates contextual information. When encountering another person, we can say immediately whether his or her face is familiar. However, it may be difficult for us to identify the same person. To accompany the psychophysical findings, we present a generic neural network model reproducing these behaviors, based on the same conservative Hebbian synaptic plasticity that generates delay activity identification memory. Familiarity becomes the first step toward establishing identification. Adding an inter-trial reset mechanism limits false positives for previous-trial images. The model, unlike previous proposals, relates repetition-recognition with enhanced neural activity, as recently observed experimentally in 92% of differential cells in prefrontal cortex, an area directly involved in familiarity recognition. There may be an essential functional difference between enhanced responses to novel versus to familiar images: The maximal signal from temporal cortex is for novel stimuli, facilitating additional sensory processing of newly acquired stimuli. The maximal signal for familiar stimuli arising in prefrontal cortex facilitates the formation of selective delay activity, as well as additional consolidation of the memory of the image in an upstream cortical module.

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Section: Modelingmentioning

confidence: 99%

Universal Memory Mechanism for Familiarity Recognition and Identification

Yakovlev¹,

Amit²,

Romani³

et al. 2008

J. Neurosci.

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“…Incorporating more than two patterns into the analysis is straightforward but does not lead to additional insights into the issues considered here. The statistical behavior of randomly diluted (exponential) attractor networks has been studied (17).…”

Section: A Dynamic Network Modelmentioning

confidence: 99%

Response of complex networks to stimuli

Bar‐Yam

Epstein

2004

Proc. Natl. Acad. Sci. U.S.A.

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We consider the response of complex systems to stimuli and argue for the importance of both sensitivity, the possibility of large response to small stimuli, and robustness, the possibility of small response to large stimuli. Using a dynamic attractor network model for switching of patterns of behavior, we show that the scale-free topologies often found in nature enable more sensitive response to specific changes than do random networks. This property may be essential in networks where appropriate response to environmental change is critical and may, in such systems, be more important than features, such as connectivity, often used to characterize network topologies. Phenomenologically observed exponents for functional scale-free networks fall in a range corresponding to the onset of particularly high sensitivities, while still retaining robustness.

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“…[1]- [4] and the references cited therein). This has been possible because in these types of networks one knows that there are no feedback correlations as time progresses.…”

Section: Introductionmentioning

confidence: 99%

Untitled

Bollé

Jongen

Shim

1999

Journal of Statistical Physics

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The parallel dynamics of extremely diluted symmetric Q-Ising neural networks is studied for arbitrary Q using a probabilistic approach. In spite of the extremely diluted architecture the feedback correlations arising from the symmetry prevent a closed-form solution in contrast with the extremely diluted asymmetric model. A recursive scheme is found determining the complete time evolution of the order parameters taking into account all feedback. It is based upon the evolution of the distribution of the local field, as in the fully connected model. As an illustrative example an explicit analysis is carried out for the Q = 2 and Q = 3 model. These results agree with and extend the partial results existing for Q = 2. For Q > 2 the analysis is entirely new. Finally, equilibrium fixed-point equations are derived and a capacity-gain function diagram is obtained.

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An Exactly Solvable Asymmetric Neural Network Model

Cited by 540 publications

References 20 publications

Universal Memory Mechanism for Familiarity Recognition and Identification

Universal Memory Mechanism for Familiarity Recognition and Identification

Response of complex networks to stimuli

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