An associative network with spatially organized connectivity

We investigate the properties of an autoassociative network of threshold-linear units whose synaptic connectivity is spatially structured and asymmetric. Since the methods of equilibrium statistical mechanics cannot be applied to such a network due to the lack of a Hamiltonian, we approach the problem through a signal-to-noise analysis, that we adapt to spatially organized networks. The conditions are analyzed for the appearance of stable, spatially non-uniform profiles of activity with large overlaps with one of the stored patterns. It is also shown, with simulations and analytic results, that the storage capacity does not decrease much when the connectivity of the network becomes short range. In addition, the method used here enables us to calculate exactly the storage capacity of a randomly connected network with arbitrary degree of dilution.Comment: 27 pages, 6 figures; Accepted for publication in JSTA

How informative are spatial CA3 representations established by the dentate gyrus?

In the mammalian hippocampus, the dentate gyrus (DG) is characterized by sparse and powerful unidirectional projections to CA3 pyramidal cells, the so-called mossy fibers. Mossy fiber synapses appear to duplicate, in terms of the information they convey, what CA3 cells already receive from entorhinal cortex layer II cells, which project both to the dentate gyrus and to CA3. Computational models of episodic memory have hypothesized that the function of the mossy fibers is to enforce a new, well separated pattern of activity onto CA3 cells, to represent a new memory, prevailing over the interference produced by the traces of older memories already stored on CA3 recurrent collateral connections. Can this hypothesis apply also to spatial representations, as described by recent neurophysiological recordings in rats? To address this issue quantitatively, we estimate the amount of information DG can impart on a new CA3 pattern of spatial activity, using both mathematical analysis and computer simulations of a simplified model. We confirm that, also in the spatial case, the observed sparse connectivity and level of activity are most appropriate for driving memory storage and not to initiate retrieval. Surprisingly, the model also indicates that even when DG codes just for space, much of the information it passes on to CA3 acquires a non-spatial and episodic character, akin to that of a random number generator. It is suggested that further hippocampal processing is required to make full spatial use of DG inputs.Comment: 19 pages, 11 figures, 1 table, submitte

Noise-enhanced computation in a model of a cortical column

Varied sensory systems use noise in order to enhance detection of weak signals. It has been conjectured in the literature that this effect, known as stochastic resonance, may take place in central cognitive processes such as the memory retrieval of arithmetical multiplication. We show in a simplified model of cortical tissue, that complex arithmetical calculations can be carried out and are enhanced in the presence of a stochastic background. The performance is shown to be positively correlated to the susceptibility of the network, defined as its sensitivity to a variation of the mean of its inputs. For nontrivial arithmetic tasks such as multiplication, stochastic resonance is an emergent property of the microcircuitry of the model network