We study analytically the effect of metrically structured connectivity on the behavior of autoassociative networks. We focus on three simple rate-based model neurons: threshold-linear, binary or smoothly saturating units. For a connectivity which is short range enough the threshold-linear network shows localized retrieval states. The saturating and binary models also exhibit spatially modulated retrieval states if the highest activity level that they can achieve is above the maximum activity of the units in the stored patterns. In the zero quenched noise limit, we derive an analytical formula for the critical value of the connectivity width below which one observes spatially non-uniform retrieval states. Localization reduces storage capacity, but only by a factor of 2~3. The approach that we present here is generic in the sense that there are no specific assumptions on the single unit input-output function nor on the exact connectivity structure.

Localized activity profiles and storage capacity of rate-based autoassociative networks / Roudi, Y.; Treves, A.. - In: PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS. - ISSN 1539-3755. - 73:6(2006), pp. 1-9. [10.1103/PhysRevE.73.061904]

Localized activity profiles and storage capacity of rate-based autoassociative networks

Treves, A.
2006-01-01

Abstract

We study analytically the effect of metrically structured connectivity on the behavior of autoassociative networks. We focus on three simple rate-based model neurons: threshold-linear, binary or smoothly saturating units. For a connectivity which is short range enough the threshold-linear network shows localized retrieval states. The saturating and binary models also exhibit spatially modulated retrieval states if the highest activity level that they can achieve is above the maximum activity of the units in the stored patterns. In the zero quenched noise limit, we derive an analytical formula for the critical value of the connectivity width below which one observes spatially non-uniform retrieval states. Localization reduces storage capacity, but only by a factor of 2~3. The approach that we present here is generic in the sense that there are no specific assumptions on the single unit input-output function nor on the exact connectivity structure.
2006
73
6
1
9
061904
https://doi.org/10.1103/PhysRevE.73.061904
https://arxiv.org/abs/cond-mat/0505349
Roudi, Y.; Treves, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/12796
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