{"title": "A Recurrent Model of the Interaction Between Prefrontal and Inferotemporal Cortex in Delay Tasks", "book": "Advances in Neural Information Processing Systems", "page_first": 171, "page_last": 177, "abstract": null, "full_text": "A recurrent model of the interaction between \nPrefrontal and Inferotemporal cortex in delay \n\ntasks \n\nALFONSO RENART, NESTOR PARGA \n\nDepartamento de F{sica Te6rica \nUniversidad Aut6noma de Madrid \nCanto Blanco, 28049 Madrid, Spain \n\nhttp://www.ft.uam.es/neurociencialGRUPO/grup0.1!nglish.html \n\nand \n\nEDMUND T. ROLLS \nOxford University \n\nDepartment of Experimental Psychology \n\nSouth Parks Road, Oxford OX] 3UD, England \n\nAbstract \n\nA very simple model of two reciprocally connected attractor neural net(cid:173)\nworks is studied analytically in situations similar to those encountered \nin delay match-to-sample tasks with intervening stimuli and in tasks of \nmemory guided attention. The model qualitatively reproduces many of \nthe experimental data on these types of tasks and provides a framework \nfor the understanding of the experimental observations in the context of \nthe attractor neural network scenario. \n\n1 Introduction \n\nWorking memory is usually defined as the capability to actively hold information in mem(cid:173)\nory for short periods of time. In primates, visual working memory is usually studied in \nexperiments in which, after the presentation of a given visual stimulus, the monkey has \nto withhold its response during a certain delay period in which no specific visual stimulus \nis shown. After the delay, another stimulus is presented and the monkey has to make a \nresponse which depends on the interaction between the two stimuli. In order to bridge the \ntemporal gap between the stimuli, the first one has to be held in memory during the delay. \nElectrophysiological recordings in primates during the performance of this type of tasks \nhas revealed that some populations of neurons in different brain areas such as prefrontal \n(PF), inferotemporal (IT) or posterior parietal (PP) cortex, maintain approximately con(cid:173)\nstant firing rates during the delay periods (for a review see [1]) and this delay activity states \nhave been postulated as the internal representations of the stimuli provoking them [2]. Al(cid:173)\nthough up to now most of the modeling effort regarding the operation of networks able to \nsupport stable delay activity states has been put in the study of un i-modular (homogeneous) \nnetworks, there is evidence that in order for the monkey to solve the tasks satisfactorily, the \ninteraction of several different neural structures is needed. A number of studies of delay \nmatch-to-sample tasks with intervening stimuli in primates performed by Desimone and \n\n\f172 \n\nA. Renart, N Parga and E. TRolls \n\ncolleagues has revealed that although IT cortex supports delay activity states and shows \nmemory related effects (differential responses to the same, fixed stimulus depending on its \nstatus on the trial, e.g. whether it matches or not the sample), it cannot, by itself, provide \nthe information necessary to solve the task, as the delay activity states elicited by each of \nthe stimuli in a sequence are disrupted by the input information associated with each new \nstimulus presented [3, 4, 5]. Another structure is therefore needed to store the information \nfor the whole duration of the trial. PF cortex is a candidate, since it shows selective delay \nactivity maintained through entire trials even with intervening stimuli [6]. A series of par(cid:173)\nallel experiments by the same group on memory guided attention [7, 8] have also shown \ndifferential firing of IT neurons in response to the same visual stimulus shown after a delay \n(an array of figures), depending on previous information shown before the delay (one of \nthe figures in the array working as a target stimulus). This evidence suggests a distributed \nmemory system as the proper scenario to study working memory tasks as those described \nabove. Taking into account that both IT and PF cortex are known to be able to support \ndelay activity states, and that they are bi-directionally connected, in this paper we propose \na simple model consisting of two reciprocally connected attractor neural networks to be \nidentified with IT and PF cortex. Despite its simplicity, the model is able to qualitatively \nreproduce the behavior of IT and PF cortex during delay match-to-sample tasks with in(cid:173)\ntervening stimuli, the behavior of IT cells during memory guided attention tasks, and to \nprovide an unified picture of these experimental data in the context of associative memory \nand attractor neural networks. \n\n2 Model and dynamics \n\nThe model network consists of a large number of (excitatory) neurons arranged in two \nmodules. Following [9, 10], each neuron is assumed to be a dynamical element which \ntransforms an incoming afferent current into an output spike rate according to a given \ntransduction function. A given afferent current Iai to neuron i (i = 1, ... ,N) in module a \n(a = IT, PF) decays with a characteristic time constant T but increases proportionally to \nthe spike rates Vbj of the rest of the neurons in the network (both from inside and outside \nits module) connected to it, the contribution of each presynaptic neuron, e.g. neuron j from \nmodule b, being proportional to the synaptic efficacy Jt/ between the two. This can be \nexpressed through the following equation \n\nd1ai(t) = _ Iai(t) + '\" J~~,b) \n\n. + h(~xt) \n\nT ~ ~J \n\nVbJ \n\ndt \n\na~ \n\n. \n\n(1) \n\nbj \n\nAn external current h~~xt) from outside the network, representing the stimuli, can also \nbe imposed on every neuron. Selective stimuli are modeled as proportional to the stored \npatterns, i.e. h~~ezt) = haTJ~i' where ha is the intensity of the external current to module a. \n\nThe transduction function of the neurons transforming currents into rates has been chosen \nas a threshold hyperbolic tangent of gain G and threshold O. \n\nThe synaptic efficacies between the neurons of each module and between the neurons in \ndifferent modules are respectively [11, 12] \n\nJ(a,a) -\nij \n\n- 1(1 _ J)Nt ~ TJai -\n\nJo \n\np \n\"'( I-' \n\nI) (I-' \n\nTJaj -\n\nI) \n\ni.../- J' \n\nr \n\na = IT,PF \n\n(2) \n\nj (a,b) -\nij \n\n9 \n\n- 1(1 _ J)Nt ~ TJai -\n\np \n\"'( I-' \n\nI) (I-' \n\nTJbj -\n\nI) \n\n\\.J\" \nv ~,J \n\n.../- b \n\na r \n\n. \n\n(3) \n\n\fRecurrent Model of IT-PF Interactions in Delay Tasks \n\n173 \n\nThe intra-modular connections express the learning of P binary patterns {17~i = 0,1, f.L = \n1, ... , P} by each module, each of them signaling which neurons are active in each of \nthe sustained activity configurations. Each variable Tl~i is supposed to take the values 1 \nand 0 with probabilities f and (1 -\nf) respectively, independently across neurons and \nacross patterns. The inter-modular connections reflect the temporal associations between \nthe sustained activity states of each module. In this way, every stored pattern f.L in the IT \nmodule has an associated pattern in the PF module which is labelled by the same index. \nThe normalization constant Nt = N(Jo + g) has been chosen so that the sum of the \nmagnitudes of the inter- and the intra-modular connections remains constant and equal to \n1 while their relative values are varied. When this constraint is imposed the strength of \nthe connections can be expressed in terms of a single independent parameter 9 measuring \nthe relative intensity of the inter- vs. the intra-modular connections (Jo can be set equal \nto 1 everywhere). We will limit our study to the case where the number of stored patterns \nper module P does not increase proportionally to the size of the modules N since a large \nnumber of stored patterns does not seem necessary to describe the phenomenology of the \ndelay match-to-sample experiments. \n\nSince the number of neurons in a typical network one may be interested in is very large, \ne.g. '\" 105 - 106 , the analytical treatment of the set of coupled differential equations (1) \nbecomes intractable. On the other hand, when the number of neurons is large, a reliable de(cid:173)\nscription of the asymptotic solutions of these equations can be found using the techniques \nof statistical mechanics [13, 9]. In this framework, instead of characterizing the states \nof the system by the state of every neuron, this characterization is performed in terms of \nmacroscopic quantities called order parameters which measure and quantify some global \nproperties of the network as a whole. The relevant order parameters appearing in the de(cid:173)\nscription of our system are the overlaps of the state of each module with each of the stored \npatterns m~, defined as: \n\nm~ = N\u00ab 2)17~i - f)Vai \u00bb1/ , \n\n(4) \n\n1 \nX \n\ni \n\nwhere the symbol \u00ab ... \u00bb1/ stands for an average over the stored patterns. \nUsing the free energy per neuron of the system at zero temperature :F (which we do not \nwrite explicitly to reduce the technicalities to a minimum) we have modeled the experi(cid:173)\nments by giving the order parameters the following dynamics: \n\n(5) \n\nThis dynamics ensures that the stationary solutions, corresponding to the values of the \norder parameters at the attractors, correspond also to minima of the free energy, and that, \nas the system evolves, the free energy is always minimized through its gradient. The time \nconstant of the macroscopic dynamics is a free parameter which has been chosen equal to \nthe time constant of the individual neurons, reflecting the assumption that neurons operate \nin parallel. Its value has been set to T = 10 ms. Equations (5) have been solved by a \nsimple discretizing procedure (first order Runge-Kutta method). \n\nSince not all neurons in the network receive the same inputs, not all of them behave in \nthe same way, i.e. have the same firing rates. In fact, the neurons in each of the module \ncan be split into different sub-populations according to their state of activity in each of \nthe stored patterns. The mean firing rate of the neurons in each SUb-population depends \non the particular state realized by the network (characterized by the values of the order \nparameters). Associated to each pattern there are two larger sub-populations, to be denoted \nas foreground (all active neurons) and background (all inactive neurons) of that pattern. \n\n\f174 \n\nA. Renart, N. Parga and E. T. Rolls \n\nThe overlap with a given pattern can be expressed as the difference between the mean firing \nrate of the neurons in its foreground and its background. The average is performed over all \nother sub-populations to which each neuron in the foreground (background) may belong \nto, where the probability of a given sub-population is equal to the fraction of neurons in \nthe module belonging to it (determined by the probability distribution of the stored patterns \nas given above). This partition of the neurons into sub-populations is appealing since, in \nexperiments, cells are usually classified in terms of their response properties to a set of \nfixed stimuli, i.e. whether each stimulus is effective or ineffective in driving their response. \n\nThe modeling of the different experiments proceeded according to the macroscopic dynam(cid:173)\nics (5), where each stimulus was implemented as an extra current for a desired period of \ntime. \n\n3 Sequence with intervening stimuli \n\nIn order to study delay match-to-sample tasks with intervening stimuli [5, 6], the module \nto be identified with IT was sequentially stimulated with external currents proportional to \nsome of the stored patterns with a delay between them. To take into account the large \nfraction of PF neurons with non-selective responses to the visual stimuli (which may be \ninvolved in other aspects of the task different from the identification of the stimuli), and \nsince the neurons in our modules are, by definition, stimulus selective (although they are \nprobably connected to the non-selective neurons) a constant, non-selective current of the \nsame intensity as the selective input to the IT module was applied (during the same time) \nequally to all sub-populations of the PF module. The external current to the IT module was \nstimulus selective because the fraction of IT neurons with non-selective responses to the \nvisual stimuli is very small [6]. The results can be seen in Figure 1 where the sequence \nABA with A as the sample stimulus and B as a non-matching stimulus has been studied. \nThe values of the model parameters are listed in the caption. In Figure 1 a, the mean firing \nrates of the foreground populations of patterns AIT and BIT of the IT module have been \nplotted as a function of time. The main result is that, as observed in the experiments, the \ndelay activity in the IT module is determined by the last stimulus presented. The delay \nactivity provoked by a given stimulus is disrupted by the next, unless it corresponds to the \nsame stimulus, in which case the effect of the stimulus is to increase the firing rate of the \nneurons in its foreground. We have checked that no noticeable effects occur if more non(cid:173)\nmatching stimuli are presented (they are all equivalent with respect to the sample) or if a \nnon-match stimulus is repeated. \n\nIf the coupling g between the modules is weak enough [12] the behavior in the PF module \nis different. This can be seen in Figure 1 b, where the time evolution of the mean firing rates \nof the foreground of the two associated patterns ApF and BpF stored in the PF module are \nshown. In agreement with the findings of Desimone and colleagues, the neurons in the \nPF module remain correlated with the sample for the whole trial, despite the non-selective \nsignal received by all PF neurons (not only those in the foreground of the sample) and the \nfact that the selective current from the IT module tends to activate the pattern associated \nwith the current stimulus. \n\nDesimone and colleagues [5, 6] report that the response of some neurons (not necessarily \nthose with sample selective delay activity or with stimulus selective responses) in both IT \nand PF cortex to some stimuli, is larger if those stimuli are matches in their trials than if \nthe same stimuli are non-matches. This has been denoted as match enhancement. In the \npresent scenario the explanation is straightforward: when a stimulus is a non-match, IT and \nPF are in different states and therefore send inconsistent signals to each other. The firing \nrate of the neurons of each module is maintained in that case solely by the contribution \nto the total current coming from the recurrent collaterals. On the other hand, when the \nstimulus is the match, both modules find themselves in states associated in the synapses \n\n\fRecurrent Model of IT-PF Interactions in Delay Tasks \n\n175 \n\n0.8 \n\n0.7 Ir-\n\n0.6 \n\n., 0.5 \na; \na: \nC> 0.4 \nc: \n.'\" Ii: 0.3 \n\n(a) \n\nr-\n\n' ''I \n! i \n! ' \n\\ \ni \n, \n! \ni \nI \nI \n\\ \n\"'---._ .. _--\n\n\\ \n\n0.2 \n\n0.1 r.~ .... .. _ .. _ .-J ~ ___ --,\u00b7L .. __ \n\no \n\nO'---'--~~-~~~-\"\"\"\"\"'-'---' \n4 56789 \nTime (s) \n\n3 \n\n2 \n\n(b) \n\n\\ \n\n0.7 \n\n0.6 \n\n0.5 \n\n0.4 \n\n0.3 \n\n., \na; \na: \nC> c: \n\u00b7c \nIi: \n\n\\. \n\n0.2 \n\n. \n\nfL... \n\n0.1 \"l .... ____ J \\. ___ . ___ ._.J l. __ ._. ___ . \n\ni\\..... \u2022\u2022 \n\nOL--'--~~-~~~-........... -,---, \n9 \n\n7 \n\n8 \n\no \n\n234 5 \nTime (s) \n\n6 \n\nFigure 1: (a) Mean rates in the foreground of patterns AIT (solid line) and BIT (dashed \nline) in the IT module as a function of time. (b) Same but for patterns ApF and BpF of the \nPF module. Model parameters are G = 1.3, () = 10-3, f = 0.2, 9 = 10-2, h = 0.13. \nStimuli are presented during 500 ms at seconds 0, 3, and 6 following the sequence ABA. \n\nbetween the neurons connecting them, PF because it has remained that way the whole trial, \nand IT because it is driven by the current stimulus. When this happens, the contribution \nto the total current from the recurrent collaterals and from the long range afferents add up \nconsistently, and the firing rate increases. In order for this explanation to hold there should \nbe a correlation between the top-down input from PF and the sensory bottom-up signal to \nIT. Indeed, experimental evidence for such a correlation has very recently been found [14]. \nThis is an important experimental finding which supports our theory. \n\nLooking at Figure 1, one sees that the effect is not evident in the model during the time \nof stimulus presentation, which is the period where it has been reported. The effect is, in \nfact, present, although its magnitude is too small to be noticeable in the figure. We would \nargue, however, that this quantitative difference is an artifact of the model. This is because \nthe enhancement effect is very noticeable on the delay periods, where essentially the same \nneurons are active as during the stimulus presentations (i.e., where the same correlations \nbetween the top-down and bottom-up signals exist) but with lower firing rates. During \nstimulus presentations the firing rates are closer to the saturation regime, and therefore the \ndynamical response range of the neurons is largely reduced. \n\n4 Memory guided attention \n\nTo test the differential response of cells as a function of the contents of memory, we have \nfollowed [7, 8] and studied a sub-population of IT cells which are simultaneously in the \nforeground of one of the patterns (AIT) and in the background of another (BIT) in the same \nconditions as the previous section (same model parameters). In Figure 2a the response \nof this sub-population as a function of time has been plotted in two different situations. \nIn the first one, the effective stimulus AIT was shown first (throughout this section non \nselective stimulation of PF proceeded as in the last section) and after a delay, a stimulus \narray equal to the sum of AIT and BIT was presented. The second situation is exactly \nequal, except for the fact that the cue stimulus shown first was the ineffective stimulus BIT. \nThe response of the same sub-population to the same stimulus array is totally different and \ndetermined by the cue stimulus: If the sub-population is in the background of the cue, its \nresponse is null during the trial except for the initial period of the presentation of the array. \nIn accordance with the experimental observations [7, 8], its response grows initially (as \none would expect, since during the array presentation time, stimulation is symmetric with \n\n\f176 \n\nA. Renart, N. Parga and E. T. Rolls \n\nrespect of A and B) but is later suppressed by the top-down signal being sent by the PF \nmodule. This suppression provides a clear example of a situation in which the contents \nof memory (in the form of an active PF activity state) are explicitly gating the access of \nsensory information to IT, implementing a non-spatial attentional mechanism. \n\n0.8 .---~~~-~-~-~---, \n0.7 r-\n\n(a) \nr \n\nQ) \n\niii cr: \n'\" c .\" u: \n\n0.6 \n\n0.5 \n\n0.4 \n\n0.3 \n\n0.2 \n\n0.1 \n\n0 \n\n_ .. _--_ .. -----_ .... _.... \"-.. _----_ .. _-\n\n! \\ \n\nr\\ \n\n2 \n\n3 \n\n4 \n\n5 \n\n6 \n\nTime (s) \n\nI \n\n(b) \nr-\u00b71 \n! \ni i \nl.-\\ l_ .. ___ .. __ ._._ .. \n\n\u2022 \n\nI \n\n0.7 \n\n0.6 \n\n0.5 \n\n0.4 \n\n0.3 \n\n* cr: \n'\" c \u00b7c u: \n0.1 r--\\ \n\n0.2 \n\n0 \n\n-0.1 \n\n0 \n\n2 \n\n3 \n\n4 \n\n5 \n\n6 \n\nTime (s) \n\nFigure 2: (a) Mean rates as a function of time in IT neurons which are both in the fore(cid:173)\nground AIT and in the background of BIT when the cue stimulus is AIT (solid line) or BIT \n(dashed line). (b) Mean rates of the same neurons when CIT is the cue stimulus and the \narray is AIT alone (long dashed line), BIT alone (short dashed line) or the sum of AIT and \nBIT (solid line). Cue present until 500 ms. Array present from 3000 ms to 3500 ms. \nModel parameters as in Figure 1 \n\nIn the model, the PF module remains in a state correlated with the cue during the whole \ntrial (to our knowledge there are no measurements of PF activity during memory guided \nattention tasks) and therefore provides a persistent signal 'in the direction' ofthe cue which \nbiases the competition between AIT and BIT established at the onset of the array. This \nis how the gating mechanism is implemented. The competitive interactions between the \nstimuli in the array are studied in Figure 2b, which is an emulation of the target-absent trials \nof [8]. In this figure, the same sub-population is studied under situations in which the cue \nstimulus is not present in the array (another one of the stored patterns, i.e. CIT) The three \ncurves correspond to different arrays: The effective stimulus alone, the ineffective stimulus \nalone, and a sum of the two as in the previous experiment. In all three, the PF module \nremains in a sustained activity state correlated with CIT the whole trial and therefore, since \nthe patterns are independent, the signal it sends to IT is symmetric with respect of A and \nB. Thus, the response of the sub-population during the array is in this case unbiased, and \nthe effect of the competitive interactions can be isolated. The result is that, as observed \nexperimentally, the response to the complex array is intermediate between the one to the \neffective stimulus alone and the one to the ineffective stimulus alone. The nature of the \ncompetition in an attractor network like the one under study here is based on the fact that \ncomplex stimulus combinations are not stored in the recurrent collaterals of each module. \nThese connections tend to stabilize the individual patterns which, being independent, tend \nto cancel each other when presented together. After the array is presented, the state of the \nIT module, which is correlated with CIT in the initial delay, becomes correlated with AIT \nor BIT if they are presented alone. When the array contains both of them in a symmetric \nfashion, since the sum of the patterns is not a stored pattern itself, the IT module remains \ncorrelated with pattern CIT due to the signal from the PF module. \n\n\fRecurrent Model of IT-PF Interactions in Delay Tasks \n\n177 \n\n5 Discussion \n\nWe have proposed a toy model consisting of two reciprocally connected attractor mod(cid:173)\nules which reproduces nicely experimental observations regarding intra-trial data in delay \nmatch-to-sample and memory guided attention experiments in which the interaction be(cid:173)\ntween IT and PF cortex is relevant. Several important issues are taken into account in the \nmodel: a complex interaction between the PF and IT modules resultant from the associa(cid:173)\ntion of frequent patterns of activity in both modules, delay activity states in each module \nwhich exert mutually modulatory influences on each other, and a common substrate (we \nemphasize that the results on Sections 3 and 4 where obtained with exactly the same model \nparameters, just by changing the type of task) for the explanation of apparently diverse \nphenomena. Perception is clearly an active process which results from the complex in(cid:173)\nteractions between past experience and incoming sensory information. The main goal of \nthis model was to show that a very simple associational (Hebbian) pattern of connectivity \nbetween a perceptual module and a 'working memory' module can provide the basic in(cid:173)\ngredients needed to explain coherently different experimentally found neural mechanisms \nrelated to this process. The model has clear limitations in terms of 'biological realism' \nwhich will have to be improved in order to use it to make quantitative predictions and com(cid:173)\nparisons, and does not provide a complete an exhaustive account of the very complex and \ndiverse phenomena in which temporo-frontal interactions are relevant (there is, for exam(cid:173)\nple, the issue of how to reset PF activity in between trials [15]). However, it is precisely the \nsimplicity of the mechanism it provides and the fact that it captures the essential features of \nthe experiments, despite being so simple, what makes it likely that it will remain relevant \nafter being refined. \n\nAcknowledgements \n\nThis work was funded by a Spanish grant PB96-0047. We acknowledge the Max Planck \nInstitute for Physics of Complex Systems in Dresden, Germany, for the hospitality received \nby A.R. and N.P. during the meeting held there from March 1 to 26, 1999. \n\nReferences \n\n[1] J. M. Fuster. 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Spin glass theory and beyond. Singapore: World Scientific \n\n(1987) \n\n[14] H. Tomita, M Ohbayashi, K. Nakahara, I. Hasegawa & Y. Miyashita. Nature 401, 699-703 \n\n(1999) \n\n[15] D. Durstewitz, M. Kelc & o. Giintiirkiin. 1. Neurosci. 19,2807-2822 (1999) \n\n\f", "award": [], "sourceid": 1705, "authors": [{"given_name": "Alfonso", "family_name": "Renart", "institution": null}, {"given_name": "N\u00e9stor", "family_name": "Parga", "institution": null}, {"given_name": "Edmund", "family_name": "Rolls", "institution": null}]}