The name is absent

The number of correctly memorized patterns (Vi vectors in the stationary states) in the
fully connected Hopfield autoassociative memory model is 0.14N. Deleting synaptic con-
nections will cause forgetting of some patterns and distortion of others. Assume that a cer-
tain percentage d of synaptic connections is randomly deleted (zeroed in the model). The
remaining connections may get stronger, W’ij = c(d,k)Wij, where the compensating factor
c(d,k)>1 is a multiplicative factor depending on d and a parameter k(d), called a compensa-
tion-strategy parameter, that is fitted to experimental data. Horn et al. [12] proved that tak-
ing c(d,k) = dk/(1-d) significantly slows the memory deterioration. Depending on the com-
pensation-strategy k(d) after the same evolution period various degrees of deterioration are
obtained. Thus failure of proper compensation for synaptic deletion may explain why pa-
tients with similar density of synaptic connections per unit of cortical volume show quite
different cognitive impairments.

Hopfield networks require non-local learning and thus are not plausible from the
neurobiological point of view. Ruppin and Reggia [25], Horn et al. [11], and Ruppin et al.
[24] improved this model in several ways. Similar conclusions were obtained from other
memory models (Willshaw, Hebbian, modified Hopfield networks), with over 1000 neurons
used in simulations. Activity-dependent Hebbian models allow to study memory acquisi-
tion. Even in such simple models faster forgetting of more recent memories can be ob-
served. This effect (called ‘Ribbot gradient’ in psychological literature) has been known
since a long time in retrograde amnesia [16] and has also been observed in Alzheimer's pa-
tients. Temporal gradients of memory decline and several other experimental phenomena
characterizing memory degradation in AD patients have been recreated in Hebbian models.
Local compensatory mechanisms are sufficient [11] to maintain high capacity of the mem-
ory - there is no global error function that is optimized. The way deletion and compensation
factors change in time has an influence on the final performance of the network. Cognitive
impairments are therefore history-dependent in this model, leading to a broad variability of
the AD symptoms despite similar levels of structural damage of the brain.

4. Synaptic runaway model

Hasselmo [9],[10] has focused on a different phenomenon observed in associative
memory attractor networks. Storing a new pattern the activity of such networks goes
through similar patterns and if certain memory capacity is exceeded interferes with them.
This interference creates an exponentially large number of patterns that the system tries to
store, bringing in effect pathological, exponential growth of the number and the strength of
synaptic connections. This is called the “synaptic runaway” effect. If it does exist in real
biological neural networks it should lead to very high metabolic demands of hyperactive

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