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An anti-Hebbian model of familiarity discrimination in the

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					                                                            An anti-Hebbian model of familiarity discrimination in the perirhinal cortex
                                                                                                             Malcolm W. Brown                                                             Rafal Bogacz
                                                                                                             University of Bristol                                                     Princeton University



Perirhinal cortex                                                                                            Storage capacity                                                                                                 Reason for capacity difference
Work in monkeys has established that discrimination of the relative familiarity or novelty of visual         When it is assumed that responses of neurons providing input to the familiarity discrimination network           The difference in capacities of the models based on Hebbian and anti-Hebbian learning may be
stimuli is dependent on the perirhinal cortex, and this finding is consistent with studies of amnesic        are uncorrelated, models based on either Hebbian or anti-Hebbian learning achieve very high storage              explained intuitively by the fact that the Hebbian models have a natural tendency to extract features;
patients [5,6]. Within the monkey’s perirhinal cortex, ~25% of neurons respond strongly to the sight of      capacity, which capacity is much greater than that of associative memories for recall. The former is             hence they focus on elements common to all the input patterns (i.e. features). By contrast, the anti-
novel objects but respond only weakly or briefly when these objects are seen again [6,14].                   proportional to the number of synapses in the network, the latter to that number divided by the number           Hebbian model focuses on elements characteristic to individual patterns rather than their common
                                                                                                             of neurons [9]. This difference may be intuitively explained by comparing the two tasks: recall – for            features
                                                                                              30 spikes/s    example, you see a person and you want to recall his/her name and the episode of the previous
Monkey brain                                                                                                 meeting with the person – and familiarity discrimination – you see a person and you want to determine             • Hebbian: learns features common to all stimuli
                                                                                   Stimulus          s       whether or not you have seen him/her previously. In the first case, the network has to recall the whole
ventral view
                                                                                                             representation of the name and the episode, which is encoded in the activity of a number of neurons –
                                                             Novel
                                                                                                             let us denote this number by N. By contrast, for familiarity discrimination, there is just a binary output:
                                                                                                             the stimulus is novel or familiar. The number of outputs in the case of familiarity discrimination is N
                                                                                                             times smaller (so, in this sense, familiarity discrimination is N times easier than recall). Therefore,
                                                                                                             intuitively, the capacity for familiarity discrimination is of order N times higher.


                                                                                                              • Retrieval                                          • Familiarity discrimination                                • Anti-Hebbian: ignores features common to all stimuli

                                                             Familiar                                                                                    J
                                                                                                                                                         u                                                    Novel
                                                                                                                                                          l                                                     ?
                                                                                                                                                          i                                                  Familiar
                                                                                                                                                         a
                                                                                                              • Capacity ~ number of synapses per                  • Capacity = 0.023 x number of                             Estimation of the capacity of human perirhinal net
                                                                                                                neuron [12]                                          synapses
Models of familiarity discrimination                                                                          • CA3:                                               • Perirhinal cortex:                                       We also estimate the capacity of putative networks of novelty neurons in the human perirhinal cortex:
                                                                                                                 – 2.3*106 pyramidal neurons                          – 4*106 novelty neurons
All previously published models of familiarity discrimination in the perirhinal cortex [1,10,11] are based                                                                                                                                       • Assumptions:
on Hebbian learning. Here we present a model based on anti-Hebbian learning.
                                                                                                                 – 4*104 synapses per neuron                          – 104 synapses per neuron
                                                                                                                                                                                                                                                    – 4,000,000 novelty neurons
The Figure below shows the synaptic plastic changes of a single perirhinal novelty neuron for the anti-          – 105 stimuli                                        – 109 stimuli
Hebbian model after presentation of a novel stimulus.                                                                                                                                                                                               – No noise
                                                                                                                                                                                                                                                    – 10,000 synapses per neuron                                                              1,000 synapses per neuron
                                                                                                             Under the assumption of uncorrelated firing rates of the input neurons, if the perirhinal cortex worked
                                                                                                                                                                                                                                           10,000,000,000                                                                        10,000,000,000
                                                                                                             akin to these models, it alone could discriminate the familiarity of many more stimuli than current                            1,000,000,000                                                                         1,000,000,000
                                                                                                             neural network models indicate could be recalled (recollected) by all the remaining areas of the                                   100,000,000                                                                          100,000,000
novel
                                                                                                             cerebral cortex. [1].                                                                                                               10,000,000                                                                           10,000,000




                                                                                                                                                                                                                                            P




                                                                                                                                                                                                                                                                                                                                 P
                                                                                                                                                                                                                                                  1,000,000                                                                            1,000,000
                                                                                                                                                                                                                                                   100,000                                                                              100,000
                                                                                                                                                                                                                                                                                                                       Hebbian
                                                                                                             Neuronal recordings indicate that the perirhinal neurons have correlated firing rates [8] (i.e. two                                    10,000
                                                                                                                                                                                                                                                                                                                       Anti-Hebbian
                                                                                                                                                                                                                                                                                                                                         10,000
                                                                                                                                                                                                                                                      1,000
                                             Homosynaptic LTD – known to exist in the perirhinal
                                                                                                                                                                                                                                                                                                                                           1,000
                                                                                                             neurons may selectively respond to similar groups of stimuli). Correlation between responses                                              100                                                                                  100
                                             cortex [7]                                                      decreases the capacity of different familiarity discrimination models differently.                                                         10                                                                                   10
                                                                                                                                                                                                                                                         1
                                                                                                             The left side of the Figure below shows that the capacity of a model [1] based on Hebbian learning (the                                     0.000001 0.00001   0.0001      0.001      0.01      0.1   1
                                                                                                                                                                                                                                                                                                                                              1
                                                                                                                                                                                                                                                                                                                                              0.000001 0.00001   0.0001     0.001       0.01   0.1   1
familiar                                                                                                     simulations are described in [2]) decreases very markedly even when the correlation is very small. The                                                                  correlation                                                                          correlation
                                                                                                             right side of the Figure shows that correlation reduces the capacity of the anti-Hebbian model far less
                                                                                                             than the network based on Hebbian learning.                                                                                                                                                  correlation between responses of distant perirhinal
                                             To maintain the neuron’s overall excitability, the synaptic
                                                                                                             Furthermore, for familiarity discrimination networks based on Hebbian learning the influence on                                                                                              neurons measured in [8]
                                             weights of connections from inactive input neurons must
                                                                                                             capacity of correlation between responses of input neurons increases when the size of the network
                                             be increased. This increase may be mediated by
                                                                                                             grows. By contrast, for the anti-Hebbian model the effect of correlation on capacity decreases with
                                             homeostatic mechanisms that act to maintain average
                                             neuronal activity and thus promote network stability (they
                                                                                                             increasing network size. Hence for large networks, the anti-Hebbian model achieves a capacity much               Conclusion
                                                                                                             greater than any of the networks based on Hebbian learning when there are even very small
                                             have been reported in cultures and slices of cortical
                                                                                                             correlations between the responses of the input neurons.
                                             neurons; for review see [13]).                                                                                                                                                   If perirhinal cortex worked akin to the anti-Hebbian model, it could discriminate familiarity for up to
                                                                                                                                                                                                                              thousands of times more stimuli than if it worked according to the models based on Hebbian learning.
                                                                                                              2500                                                     1400
Note that when the same stimulus is presented again, the membrane potential of the novelty neuron                                             N=100 simulation                                                  N=100 sim.
                                                                                                                                                                                                                              The consistency of the anti-Hebbian and other models with the results of experimental observations is
will be lower (because the weights of synapses of inputs that were active for this stimulus have been                                         N=100 prediction         1200                                     N=200 sim.
                                                                                                              2000                                                                                                            compared in [3].
reduced) and the novelty neuron will be inactive (or, more generally, less active). Thus the neuron                                           N=200 simulation                                                  N=300 sim.
                                                                                                                                                                       1000                                     N=100 pred.
responds more strongly to novel than familiar stimuli.                                                                                        N=200 prediction
The anti-Hebbian model includes a single layer of novelty neurons receiving projections from the input        1500                            N=300 simulation                                                  N=200 pred.
                                                                                                                                                                       800
                                                                                                                                                                                                                              References
                                                                                                             P




neurons. If each novelty neuron makes its own decision about stimulus familiarity, the overall response                                       N=300 prediction                                                  N=300 pred.
                                                                                                                                                                   P




(“answer”) of the network is encoded in the population activity of the novelty neurons. It is necessary to                                                             600
                                                                                                              1000
ensure that individual novelty neurons remain independent assessors of familiarity if the information                                                                                                                         [1] R. Bogacz, M.W. Brown and C. Giraud-Carrier, Model of familiarity discrimination in the perirhinal cortex, J. Comp. Neurosci. 10 (2001) 5-23.
                                                                                                                                                                                                                              [2] R. Bogacz, Computational models of familiarity discrimination in the perirhinal cortex, Ph.D. thesis, University of Bristol, 2001. (also available at:
storage capacity of the network is to be maximised [1]. Otherwise, should all the novelty neurons be                                                                   400                                                    http://www.math.princeton.edu/~rbogacz).
                                                                                                                                                                                                                              [3] R. Bogacz and M.W. Brown, Comparison of computational models of familiarity discrimination in the perirhinal cortex, Hippocampus (in press). (also available at:
active after the presentation of each of a series of novel stimuli, then the synaptic weights of each of         500                                                                                                          http://www.math.princeton.edu/~rbogacz).
the novelty neurons would be modified in the same way, and hence all the novelty neurons would                                                                         200                                                    [4] R. Bogacz and M.W. Brown, The restricted influence of the sparseness of coding on the capacity of the familiarity discrimination networks, submitted.
                                                                                                                                                                                                                              [5] M.W. Brown and J.P. Aggleton, Recognition memory: what are the roles of the perirhinal cortex and hippocampus? Nat. Rev. Neurosci. 2 (2001) 51-62.
come to have highly correlated weights. Thus, eventually, they would all be active or inactive together                                                                  0                                                    [6] M.W. Brown and J.Z. Xiang, Recognition memory: Neuronal substrates of the judgement of prior occurrence, Prog. Neurobiol. 55 (1998) 149-189.
                                                                                                                  0                                                                                                           [7] K. Cho, N. Kemp, J. Noel, J.P. Aggleton, M.W. Brown, Z.I. Bashir, A new form of long-term depression in the perirhinal cortex, Nat. Neurosci. 3 (2000) 150-156.
and the whole network would have the same capacity as a single novelty neuron. To avoid this
                                                                                                                       0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1                0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1         [8] C.A. Erickson, B. Jagadeesh, R. Desimone, Clustering of perirhinal neurons with similar properties following visual experience in adult monkey, Nat. Neurosci. 3 (2000)
problem, the number of novelty neurons active for any one stimulus must be limited, i.e. only a subset                                                                                                                        1143-1148.

of novelty neurons must respond to any given stimulus. This limitation of the number of active novelty                                sqrt(|rij |)                                            sqrt(|rij |)                    [9] J.J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Nat. Acad. Sci. 79 (1982) 2554-2558.
                                                                                                                                                                                                                              [10] K.A. Norman and R.C. O’Reilly, Modelling hippocampal and neocortical contributions to recognition memory: a complementary learning systems approach, Technical
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neurons is achieved in the model by inhibitory competition: only the fraction of neurons with the highest                                                                                                                     [11] V.S. Sohal and M.E. Hasselmo, A model for experience-dependent changes in the responses of infero-temporal neurons, Network 11 (2000) 169-190.
membrane potentials are selected to be active, the activity of the remainder being suppressed by                                  1  1  0.185 N 3r 3                                                             3         [12] A. Treves and E.T. Rolls A computational analysis of the role of the hippocampus in memory. Hippocampus 4 (1994) 374-391.

inhibition, and only these most active neurons have their weights modified [10].                                         Pm ax                                                   Pmax  0.013N  0.31N 2 r
                                                                                                                                                                                                     2                        [13] G.G. Turrigiano and S.B. Nelson, Hebb and homeostasis in neuronal plasticity, Cur. Opin. Neurobiol. 10 (2000) 358-364.
                                                                                                                                                                                                                              [14] J.Z. Xiang and M.W. Brown, Differential neuronal encoding of novelty, familiarity and recency in regions of the anterior temporal lobe, Neuropharmacology 37 (1998)
                                                                                                                                        4 Nr 3                                                                                657-676.

				
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