Abstract
Theoretical models of associative memory generally assume most of their parameters to be homogeneous across the network. Conversely, biological neural networks exhibit high variability of structural as well as activity parameters. In this paper, we extend the classical clipped learning rule by Willshaw to networks with inhomogeneous sparseness, i.e., the number of active neurons may vary across memory items. We evaluate this learning rule for sequence memory networks with instantaneous feedback inhibition and show that little surprisingly, memory capacity degrades with increased variability in sparseness. The loss of capacity, however, is very small for short sequences of less than about 10 associations. Most interestingly, we further show that, due to feedback inhibition, too large patterns are much less detrimental for memory capacity than too small patterns.
Highlights
Many brain areas exhibit extensive recurrent connectivity
We extend a particular class of such auto-association networks, viz., sequence memory networks, to include variable sparseness and thereby add one aspect of variability that is to be expected in biological neural networks
In order to tackle this question about the mechanisms of sequence termination, we investigate the effect of skewness in the pattern size distribution, i.e., Fig. 7 Inhomogeneity reduces memory capacity. a The maximum retrievable sequence length T is shown as a function of the number P of associations stored in the network and the corresponding mean connectivity c
Summary
Many brain areas exhibit extensive recurrent connectivity. Over decades such neuronal feedback attracted a huge amount of theoretical modeling [1,2,3] and one of the most prominent functions that is proposed for the recurrent synaptic connections is that of associative memory. Willshaw’s [10] clipped Hebbian rule is used to set the synaptic states sij such that the network is able to recall the memory sequences: a synapse is in the potentiated state only if it connects two neurons that are activated in sequence at least once. In the case of homogeneous sparseness, where all patterns have the same number M of active neurons, Willshaw’s rule connects the fraction c/cm of potentiated synapses in the network with the number P of stored associations by. In the framework of this model and following [7, 12], inhibition is introduced as instantaneous negative feedback proportional to the total number mt + nt of active neurons at time t This is achieved by substituting θ → θ + ht in (10) and (11), where ht = b(mt + nt ).
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