{"title": "The Effect of Catecholamines on Performance: From Unit to System Behavior", "book": "Advances in Neural Information Processing Systems", "page_first": 100, "page_last": 108, "abstract": null, "full_text": "100 \n\nServan-Schreiber, Printz and Cohen \n\nThe Effect of Catecholamines on Performance: \n\nFrom Unit to System Behavior \n\nDavid Servan-Schreiber, Harry Printz and Jonathan D. Cohen \n\nSchool of Computer Science and Department of Psychology \n\nCarnegie Mellon University \n\nPittsburgh. PA 15213 \n\nABSTRACT \n\nAt the level of individual neurons. catecholamine release increases the \nresponsivity of cells to excitatory and inhibitory inputs. We present a \nmodel of catecholamine effects in a network of neural-like elements. \nWe argue that changes in the responsivity of individual elements do \nnot affect their ability to detect a signal and ignore noise. However. \nthe same changes in cell responsivity in a network of such elements do \nimprove the signal detection performance of the network as a whole. We \nshow how this result can be used in a computer simulation of behavior \nto account for the effect of eNS stimulants on the signal detection \nperformance of human subjects. \n\nIntroduction \n\n1 \nThe catecholamines-norepinephrine and dopamine-are neuroactive substances that are \npresumed to modulate information processing in the brain, rather than to convey discrete \nsensory or motor signals. Release of norepinephrine and dopamine occurs over wide \nareas of the central nervous system. and their post-synaptic effects are long lasting. \nThese effects consist primarily of an enhancement of the response of target cells to other \nafferent inputs, inhibitory as well as excitatory (see [4] for a review). \n\nIncreases or decreases in catecholaminergic tone have many behavioral consequences \nincluding effects on motivated behaviors. attention, learning and memory. and motor \n\n\fThe Effect of Catecholamines on Performance: From Unit to System Behavior \n\n101 \n\nbehavior. At the information processing level, catecholamines appear to affect the ability \nto detect a signal when it is imbedded in noise (see review in [3]). \nIn terms of signal detection theory, this is described as a change in the performance of the \nsystem. However, there is no adequate account of how these changes at the system level \nrelate to the effect of catecholamines on individual cells. Several investigators [5,12,2] \nhave suggested that catecholamine-mediated increases in a cell's responsivity can be \ninterpreted as a change in the cell's signal-to-noise ratio. By analogy, they proposed that \nthis change at the unit level may account for changes in signal detection performance at \nthe behavioral level. \nIn the first part of this paper we analyze the relation between unit responsivity, signal-to(cid:173)\nnoise ratio and signal detection performance in a network of neural elements. We start \nby showing that the changes in unit responsivity induced by catecholamines do not result \nin changes in signal detection performance of a single unit. We then explain how, in \nspite of this fact, the aggregrate effect of such changes in a chain of units can lead to \nimprovements in the signal detection performance of the entire network. \nIn the second part, we show how changes in gain - which lead to an increase in the \nsignal detection performance of the network - can account for a behavioral phenomenon. \nWe describe a computer simulation of a network performing a signal detection task that \nhas been applied extensively to behavioral research: the continuous performance test. \nIn this simulation, increasing the responsivity of individual units leads to improvements \nin performance that closely approximate the improvement observed in human subjects \nunder conditions of increased catecholaminergic tone. \n\n2 Effect of Gain on a Single Element \nWe assume that the response of a typical neuron can be described by a strictly increasing \nfunction !G(x) from real-valued inputs to the interval (0, 1). This function relates the \nstrength of a neuron's net afferent input x to its probability of firing, or activation. We \ndo not require that!G is either continuous or differentiable. \nFor instance, the family of logistics, given by \n\n!G(x) = 1 + e-(G%+B) \n\n1 \n\nhas been proposed as a model of neural activation functions [7,1]. These functions are \nall strictly increasing, for each value of the gain G> 0, and all values of the bias B. \n\nThe potentiating effect of catecholamines on responsivity can be modelled as a change \nin the shape of its activation function. In the case of the logistic, this is achieved by \nincreasing the value of G, as illustrated in Figure 1. However, our analysis applies to \nany suitable family of functions, {fG}. We require only that each member function!G \nis strictly increasing, and that as G -;. 00, the family {fG} converges monotonically to \n\n\f102 \n\nServan-Schreiber, Printz and Cohen \n\n0.0 b==::::L::==-._:::::::::=-----I'---__ ....L...-______ ---' \n\n-6.0 \n\n- 0 \n\n-\n\nThis means that as G increases. the value !G(x) gets steadily closer to 1 if x > O. and \nsteadily closer to 0 if x < O. \n\n2.1 Gain Does Not Affect Signal Detection Performance \n\nConsider the signal detection performance of a network in which the response of a single \nunit is compared with a threshold to determine the presence or absence of a signal. We \nassume that in the presence of the signal. this unit receives a positive (excitatory) net \nafferent input Xs. and in the absence of the signal it receives a null or negative (inhibitory) \ninput XA. When zero-mean noise is added to this quantity. in the presence as well as the \nabsent:e of the signal, the unit's net input in each case is distributed around Xs or XA \nrespectively. Therefore its response is distributed around !G(xs) or !G(XA) respectively \n(see Figure 2). \n\nIn other words, the input in the case where the signal is present is a random variable \nXs\u2022 with probability density function (pdt) PXs and mean Xs, and in the absence of the \nsignal it is the random variable XA\u2022 with pdf PXA and mean XA. These then determine \nthe random variables YGS =!G(Xs) and YGA =!G(XA). with pdfs PYas and PYGA' which \nrepresent the response in the presence or absence of the signal for a given value of the \ngain. Figure 2 shows examples of PYas and PYGA for two different values of G. in the case \nwhere!G is the biased logistic. \nIf the input pdfs PXs and PXA overlap. the output pdfs PYas and PYGA will also overlap. \nThus for any given threshold () on the y-axis used to categorize the output as \"signal \npresent\" or \"signal absent,\" there will be some misses and some false alarms. The best \n\n1 A sequence of functions {gil} converges almost everywhere to the function g if the set of points where it \n\ndiverges, or converges to the wrong value, is of measure zero. \n\n\fThe Effect of Catecholamines on Performance: From Unit to System Behavior \n\n103 \n\n\u00b721) \n\n01) \n\n21) \n\n41) \n\n61) \n\n% (Nelb'plll) \n\n\u00b721) \n\n01) \n\n21) \n\n41) \n\n61) \n\n% (Nelillplll) \n\n---------p-~----\n\n----~p~----------\n\nFigure 2: Input and Output Probability Density Functions. The curves at the bottom are the pdfs \nof the net input in the signal absent (left) and signal present (right) cases. The curves along the \ny-axis are the response pdfs for each case; they are functions of the activation y, and represent the \ndistribution of outputs. The top graph shows the logistic and response pdfs for G = 0.5, B = -1; \nthe bottom graph shows them for G = 1. 0, B = -1. \n\nthe system can do is to select a threshold that optimizes performance. More precisely, \nthe expected payoff or performance of the unit is given by \n\nE(O) = A + a:. Pr(YGS ~ 0) -\n\n(3. Pr(YGA ~ 0) \n\nwhere A, a:, and (3 are constants that together reflect the prior probability of the signal, \nand the payoffs associated with correct detections or hits, correct ignores, false alarms \nand misses. Note that Pr(Y GS ~ 0) and Pr(Y GA ~ 0) are the probabilities of a hit and a \nfalse alarm, respectively. \nBy solving the equation dE/dB = 0 we can determine the value 0* that maximizes E. We \ncall 0* the optimal threshold. Our first result is that for any activation function f that \nsatisfies our assumptions, and any fixed input pdfs PXs and PXA the unit's performance at \noptimal threshold is the same. We call this the Constant Optimal Performance Theorem, \nwhich is stated and proved in [10]. In particular, for the logistic, increasing the gain \nG does not induce better performance. It may change the value of the threshold that \nyields optimal performance, but it does not change the actual performance at optimum. \nThis is because a strictly increasing activation function produces a point-to-point mapping \nbetween the distributions of input and output values. Since the amount of overlap between \n\n\f104 \n\nServan-Schreiber, Printz and Cohen \n\nthe two input pdfs PXs and PXA does not change as the gain varies, the amount of overlap \nin the response pdfs does not change either, even though the shape of the response pdfs \ndoes change when gain increases (see Figure 2). 2 \n\n3 Effect of Gain on a Chain of Elements \nAlthough increasing the gain does not affect the signal detection performance of a single \nelement, it does improve the perfonnance of a chain of such elements. By a chain, we \nmean an arrangement in which the output of the firs t unit provides the input to another \nunit (see Figure 3). Let us call this second element the response unit We monitor the \noutput of this second unit to detennine the presence or absence of a signal. \n\nInput Unit \n\nResponse Unit \n\nx \n\ny \n\nz \n\nv \n\nFigure 3: A Chain of Units. The output of the unit receiving the signal is combined with noise \nto provide input to a second unit, called the response unit. The activation of the response unit is \ncompared to a threshold to determine the presence or absence of the signal. \n\nAs in the previous discussion. noise is added to the net input to each unit in the chain \nin the presence as well as in the absence of a signal. We represent noise as a random \nvariable V. with pdf PV that we assume to be independent of gain. As in the single-unit \ncase, the input to the first unit is a random variable Xs. with pdf PXs in the presence \nof the signal and a random variable XA \u2022 with pdf PXA in the absence of the signal. The \noutput of the first unit is described by the random variables Y GS and Y GA with pdfs PYas \nand PYGA \u2022 Now. because noise is added to the net input of the response unit as well. the \ninput of the response unit is the random variable Zas = Y GS + V or ZGA = Y GA + V. again \ndepending on whetber the signal is present or absent We write PZas and pz.ru for the \npdfs of these random variables. fJZos is the convolution of py os and PV, and pz.ru is the \nconvolution of PYGA and Pv. The effect of convolving the output pdfs of the input unit \nwith the noise distribution is to increase the overlap between the resulting distributions \n(PZas and pz.ru). and therefore decrease the discriminability of the input to the response \nunit. \nHow are these distributions affected by an increase in gain on the input unit? By the \nConstant Optimal Perfonnance Theorem. we already know that the overlap between PYGS \nand PY GA remains constant as gain increases. Furthermore. as stated above, we have \nassumed that the noise distribution is independent of gain. It would therefore seem that \na change in gain should not affect the overlap between PZos and pz.ru. However. it is \n\n2We present the intuitions underlying our results in tenns of the overlap between the pdfs. However, the \n\nproofs themselves are analytical. \n\n\fThe Effect of Catecholamines on Performance: From Unit to System Behavior \n\n105 \n\npossible to show that. under very general conditions, the overlap between PZos and pz.a.. \ndecreases when the gain of the input unit increases, thereby improving perfonnance of the \ntwo-layered system. We call this the chain effect; the Chain Performance Theorem [10] \ngives sufficient conditions for its appearance. 3 \nParadoxically. the chain effect arises because the noise added to the net input of the \nresponse unit is not affected by variations in the gain. As we mentioned before, increasing \nthe gain separates the means of the output pdfs of the input unit. I-'(Y GS) and I-'(Y GA) \n(eventhough this does not affect the performance of the first unit). Suppose all the \nprobability mass were concentrated at these means. Then PZos would be a copy of Pv \ncentered at I-'(Y GS). and pz.a.. would be a copy of pv centered at I-'(Y GS). Thus in this case, \nincreasing the gain does correspond to rigidly translating PZos and PZat. apart, thereby \nreducing their overlap and improving performance. \n\n0 \n.\n\n11\n] \n~ .. \n\n-4/J \n\n\u00b72/J \n\nO/J \n\n2/J \n\n4/J \n\n6/J \n\nx(Ne' rnplll) \n\n-4/J \n\n\u00b72/J \n\nO/J \n\n2/J \n\n4/J \n\n6/J \n\nx (Nell\"\"Ul) \n\n---------p-~-------\n\n-------p~------------\n\nFigure 4: Dependence of Chain Output Pdfs Upon Gain. These graphs use the same conventions \nand input pdfs as Figure 2. They depict the output pdfs, in the presence of additive Gaussian noise, \nfor G = 0.5 (top) and G = 1.0 (bottom), \n\nA similar effect arises in more general circumstances, when PYas and PY(JA are not con(cid:173)\ncentrated at their means. Figure 4 provides an example. illustrating PZas and PZat. for \nthree different values of the gain. The first unit outputs are the same as in Figure 2, but \n\n3In this discussion, we have assumed that the same noise was added to the net input into each unit of a \nchain. However, the improvement in performance of a chain of units with increasing gain does not depend on \nthis particular assumption. \n\n\f106 \n\nServan-Schreiber, Printz and Cohen \n\nthese have been convolved with the pdf PV of a Gaussian random variable to obtain the \ncurves shown. Careful inspection of the figure will reveal that the overlap between PZa \nand PZaA decreases as the gain rises. \n\n4 Simulation of the Continuous Performance Test \nThe above analysis has shown that increasing the gain of the response function of in(cid:173)\ndividual units in a very simple network can improve signal detection performance. We \nnow present computer simulation results showing that this phenomenon may account for \nimprovements of performance with catecholamine agonists in a common behavioral test \nof signal detection. \nThe continous performance test (CPT) has been used extensively to study attention and \nvigilance in behavioral and clinical research. Performance on this task has been shown to \nbe sensitive to drugs or pathological conditions affecting catecholamine systems [11.8.9]. \nIn this task, individual letters are displayed tachystoscopically in a sequence on a computer \nmonitor. In one common version of the task, a target event is to be reported when two \nconsecutive letters are identical. During baseline performance. subjects typically fail to \nreport 10 to 20% of targets (\"misses\") and inappropriately report a target during 0.5 to \n1 % of the remaining events (\"false alarms\"). Following the administration of agents \nthat directly release catecholamines from synaptic terminals and block re-uptake from \nthe synaptic cleft (i.e., CNS stimulants such as amphetamines or methylphenidate) the \nnumber of misses decreases. while the number of false alarms remains approximately the \nsame. Using standard signal detection theory measures, investigators have claimed that \nthis pattern of results reflects an improvement in the discrimination between signal and \nnon-signal events (d'), while the response criterion (f3) does not vary significantly [11.8,9]. \nWe used the backpropagation learning algorithm to train a recurrent three layer network \nto perform the CPT (see Figure 5). In this model, several simplifyng assumptions made \nin the preceding section are removed: in contrast to the simple two-unit assembly. the \nnetwork contains three layers of units (input layer, intermediate - or hidden - layer, and \noutput layer) with some recurrent connections; connection weights between these layers \nare developed entirely by the training procedure; as a result, the activation patterns on \nthe intermediate layer that are evoked by the presence or absence of a signal are also \ndetermined solely by the training procedure; finally. the representation of the signal is \ndistributed over an ensemble of units rather than determined by a single unit \n\nFollowing training, Gaussian noise with zero mean was added to the net input of each unit \nin the intermediate and output layers as each letter was presented. The overall standard \ndeviation of the noise distribution and the threshold of the response unit were adjusted \nto produce a performance equivalent to that of subjects under baseline conditions (13.0% \nmisses and 0.75% false alarms). We then increased the gain of all the intermediate \nand output units from 1.0 to 1.1 to simulate the effect of catecholamine release in the \nnetwork. This manipulation resulted in rates of 6.6% misses and 0.78% false alarms. \nThe correspondence between the network's behavior and empirical data is illustrated in \nFigure 5. \n\n\fThe EfTect of Catecholamines on Performance: From Unit to System Behavior \n\n107 \n\n16 ...... - __________ ......, _ ...... \n\n~F . . ........ \n--0- Sim. ... _ \n_ \n\n6om.F._ \n\nLetter Identification Module \n\nc~5 ~~~ \n\" \nr. .\u2022\u2022 ~J \n; \nJ \n~ .y \n\nI \n\n\\ \n\nt \n\nFeature Input Module \n\nol-____ ~O::::::::::~I~ __ --J \n\n......... \n\na.s &lmoAonI \n\nFigure 5: Simulation of the Continuous Performance Task. Len panel: The recurrent three-layer \nnetwork (12 input units, 30 intermediate units, 10 output units and 1 response unit). Each unit \nprojects to all units in the subsequent layer. In addition, each output unit also projects to each unit \nin the intermediate layer. The gain parameter G is the same for all intermediate and output units. \nIn the simulation of the placebo condition, G = 1; in the simulation of the drug condition, G = 1.1. \nThe bias B = -1 in both conditions. Right panel: Performance of human subjects [9], and of the \nsimulation, on the CPT. With methylphenidate misses dropped from 11.7% to 5.5%, false alarms \ndecreased from 0.6% to 0.5% (non-significant). \n\nThe enhancement of signal detection performance in the simulation is a robust effect. It \nappears when gain is increased in the intermediate layer only, in the output layer only, \nor in both layers. Because of the recurrent connections between the output layer and \nthe intermediate layer, a chain effect occurs between these two layers when the gain is \nincreased over anyone of them, or both of them. The impact of the chain effect is to \nreduce the distortion, due to internal noise, of the distributed representation on the layer \nreceiving inputs from the layer where gain is increased. Note also that the improvement \ntakes place even though there is no noise added to the input of the response unit. The \nresponse unit in this network acts only as an indicator of the strength of the signal in \nthe intermediate layer. Finally, as the Constant Optimal Performance Theorem predicts, \nincreasing the gain only on the response unit does not affect the performance of the \nnetwork. \n\n5 Conclusion \nFluctuations in catecholaminergic tone accompany psychological states such as arousal, \nmotivation and stress. Furthermore, dysfunctions of catecholamine systems are implicated \nin several of the major psychiatric disorders. However, in the absence of models relating \nchanges in cell function to changes in system performance, the relation of catecholamines \nto behavior has remained obscure. The findings reported in this paper suggest that the \nbehavioral impact of catecholamines depend on their effects on an ensemble of units \noperating in the presence of noise, and not just on changes in individual unit responses. \n\n\f108 \n\nServan-Schreiber, Printz and Cohen \n\nFurthermore. they indicate how neuromodulatory effects can be incorporated in parallel \ndistributed processing models of behavior. \n\nReferences \n[1] Y. Burnod and H. Korn. Consequences of stochastic release of neurotransmitters \nfor network computation in the central nervous system. Proceedings of the National \nAcademy of Science. 86:352-356. 1988. \n\n[2] L. A. Chiodo and T. W. Berger. Interactions between dopamine and amino acid~ \ninduced excitation and inhibition in the striatum. Brain Research. 375:198-203. \n1986. \n\n[3] C. 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Physiological Psy(cid:173)\n\nchology, 13:172-178, 1985. \n\n\f", "award": [], "sourceid": 210, "authors": [{"given_name": "David", "family_name": "Servan-Schreiber", "institution": null}, {"given_name": "Harry", "family_name": "Printz", "institution": null}, {"given_name": "Jonathan", "family_name": "Cohen", "institution": null}]}