ASSOCIATIVE MEMORY - ON THE (PUZZLING) SPARSE CODING LIMIT

Recent studies of the information capacity in a sparsely coded memory net has led to some contradictory results. In the Willshaw model, where the couplings are binary (0 or 1), the maximal quantity of information that can be stored is 1n 2 almost-equal-to 0.69 bits per synapse. On the other hand a calculation a la Gardner for (0, 1) couplings gives an upper bound for the maximal capacity of about 0.29 bits per synapse. In this paper I consider two possible sources for this discrepancy. The first one is that the criterions for defining the maximal capacity are different (with or without a constraint of perfect errorless storage). The second one is a difference in the choice of the probability distribution of the random patterns used to compute this capacity. This analysis shows in particular that for the Willshaw model the maximal information capacity is much larger when the number of active neurons is exactly the same in every stored pattern, than when it is given only in average. In addition I give an argument showing that this result may be generic, e.g., valid for any activity level and independent of the learning rule.