An attractor network in the hippocampus: Theory and neurophysiology
Abstract
A quantitative computational theory of the operation of the CA3 system as an attractor or autoassociation network is described. Based on the proposal that CA3–CA3 autoassociative networks are important for episodic or event memory in which space is a component (place in rodents and spatial view in primates), it has been shown behaviorally that the CA3 supports spatial rapid one-trial learning and learning of arbitrary associations and pattern completion where space is a component. Consistent with the theory, single neurons in the primate CA3 respond to combinations of spatial view and object, and spatial view and reward. Furthermore, single CA3 neurons reflect the recall of a place from an object in a one-trial object-place event memory task. CA3 neurons also reflect in their firing a memory of spatial view that is retained and updated by idiothetic information to implement path integration when the spatial view is obscured. Based on the computational proposal that the dentate gyrus produces sparse representations by competitive learning and via the mossy fiber pathway forces new representations on the CA3 during learning (encoding), it has been shown behaviorally that the dentate gyrus supports spatial pattern separation during learning, and that the mossy fiber system to CA3 connections are involved in learning but not in recall. The perforant path input to CA3 is quantitatively appropriate to provide the cue for recall in CA3. The concept that the CA1 recodes information from CA3 and sets up associatively learned back-projections to neocortex to allow subsequent retrieval of information to neocortex provides a quantitative account of the large number of hippocampo–neocortical back-projections.
Footnotes
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↵1 Corresponding author.
↵1 E-mail Edmund.Rolls{at}psy.ox.ac.uk; fax 44-1865-310447.
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Article is online at http://www.learnmem.org/cgi/doi/10.1101/lm.631207
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2 Each memory is precisely defined in the theory: it is a set of firing rates of the population of neurons (which represent a memory) that can be stored and later retrieved, with retrieval being possible from a fraction of the originally stored set of neuronal firing rates.
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3 The sparseness a in Equation 3 is strictly the population sparseness (Treves and Rolls 1991; Franco et al. 2007). The population sparseness ap would be measured by measuring the distribution of firing rates of all neurons to a single stimulus at a single time. The single neuron sparseness or selectivity as would be measured by the distribution of firing rates to a set of stimuli, which would take a long time. The selectivity or sparseness as of a single neuron measured across a set of stimuli often takes a similar value to the population sparseness a in the brain, and does so if the tuning profiles of the neurons to the set of stimuli are uncorrelated (Franco et al. 2007). These concepts are elucidated by Franco et al. (2007).
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4 For example, if only one granule cell in 100 were active in the dentate gyrus, and each CA3 cell received a connection from 50 randomly placed granule cells, then the number of active mossy fiber inputs received by CA3 cells would follow a Poisson distribution of average 50/100 = 1/2, that is, 60% of the cells would not receive any active input, 30% would receive only one, 7.5% two, little more than 1% would receive three, and so on. (It is easy to show from the properties of the Poisson distribution and our definition of sparseness, that the sparseness of the mossy fiber signal as seen by a CA3 cell would be x/(1 + x), with x = CMFaDG, assuming equal strengths for all mossy fiber synapses.) If three mossy fiber inputs were required to fire a CA3 cell and these were the only inputs available, we see that the activity in CA3 would be roughly as sparse, in the example, as in the dentate gyrus. CMF is the number of mossy fiber connections to a CA3 neuron, and aDG is the sparseness of the representation in the dentate granule cells.
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- Received May 17, 2007.
- Accepted July 18, 2007.
- Copyright © 2007, Cold Spring Harbor Laboratory Press
