Mean-field analysis of hierarchical associative networks with 'magnetisation'
- 7 May 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (9) , 2211-2224
- https://doi.org/10.1088/0305-4470/21/9/033
Abstract
A Hopfield-type neural network that can store ultrametrically organised patterns with a finite magnetisation, or bias, is studied. Both the patterns and their ancestors are remembered in one network. A homogeneous field (or threshold) is included in the model. In zero field the (replica symmetric) mean-field equations map onto those of the Hopfield model, implying that transition temperatures, storage capacity, etc. are the same. By varying appropriately the field and/or a constant added to all the synaptic strengths, it is possible to climb up and down the hierarchical tree or to focus on a certain level in the hierarchy and thereby increase the capacity slightly.Keywords
This publication has 12 references indexed in Scilit:
- Statistical mechanics of neural networks near saturationPublished by Elsevier ,2004
- Optimal storage properties of neural network modelsJournal of Physics A: General Physics, 1988
- Neural networks with hierarchically correlated patternsPhysical Review A, 1988
- Hierarchical associative networksJournal of Physics A: General Physics, 1987
- Maximum Storage Capacity in Neural NetworksEurophysics Letters, 1987
- Information storage in neural networks with low levels of activityPhysical Review A, 1987
- Associative recall of memory without errorsPhysical Review A, 1987
- The ultrametric organization of memories in a neural networkJournal de Physique, 1986
- Information storage and retrieval in spin-glass like neural networksJournal de Physique Lettres, 1985
- Neural networks and physical systems with emergent collective computational abilities.Proceedings of the National Academy of Sciences, 1982