A Tutorial On Computational Cognitive Neuroscience .

Computational Cognitive Neurosciencethe hippocampus in some behavior, then models of thisbehavior must all share some hippocampal-likeproperties. This reduction in model heterogeneity shouldcause different labs to converge on similar models andthereby facilitate rapid scientific progress.Second, attending to the neuroscience data canexpose relationships between seemingly unrelatedbehaviors. For example, cognitive neuroscience modelsof (information-integration) category learning and(implicit) sequence learning had independently identifiedsimilar cortical-striatal circuits (e.g., Ashby et al., 1998;Grafton, Hazeltine, & Ivry, 1995). This raised thepossibility that these two seemingly disparate behaviorsshared some previously unknown deep functionalsimilarity. Several studies have explored this possibility.First, Willingham, Wells, Farrell, and Stemwedel (2000)had showed that implicit motor sequence production isdisrupted when the response key locations are switched,but not when the hands used to depress the keys areswitched. Ashby, Ell, and Waldron (2003) showed thatthis same pattern of results holds for gcategorization and sequence learning through theirhypothesized underlying neural circuits, this dependenceof information-integration categorization on responselocation learning would have been much more difficultto discover. More recently, an inactivation study showedthat the basal ganglia are not required for the productionof overlearned motor sequences (Desmurget & Turner,2010), thereby suggesting that the same may be true ofinformation-integration categorization (as was predictedby the CCN model of Ashby et al., 2007). Thisprediction was recently confirmed with an fMRIexperiment (Waldschmidt & Ashby, 2011).Third, in many cases, studying the underlyingneuroscience leads to surprising and dramatic behavioralpredictions that would be difficult or impossible toderive from a purely cognitive approach. For hypothesized to depend on dopamine-mediatedreinforcement learning at cortical-striatal synapses(Ashby et al., 1998). Because the reward follows thebehavior, the dopamine must operate on a memory tracethat identifies recently active synapses. The most likelycandidate for this trace is partially phosphorylatedCaMKII, which loses its sensitivity to dopamine afterjust a few seconds (e.g., Lisman Schulman, & Cline,2002; see section 6.1 for details). Thus, attention to theunderlying neuroscience generates a novel andsurprising prediction: delaying feedback by just a fewseconds should impair information-integration categorylearning, but not other forms of category learning (e.g.,rule-based) thought to rely on executive attention andworking memory. Several studies have confirmed these3predictions (Maddox, Ashby, & Bohil, 2003; Maddox &Ing, 2005).Fourth, CCN models are especially amenable to aconverging operations approach to model testingbecause they make predictions about both behavioral andneuroscience data. Thus, rather than simply testing themagainst behavioral data, it should also be possible to testCCN models against a variety of neuroscience data,including single-unit recording data, lesion data,psychopharmacological data, fMRI data, and possiblyeven EEG data. The ability to test CCN models againstsuch a broad spectrum of data should facilitate theprocess of testing, rejecting, and refining new models.4. CCN IdealsOne thing that sets CCN apart from previousmodeling traditions is that its principles of modelbuilding and testing are unique. In traditional cognitivebased mathematical modeling of behavior, theoverriding criterion for establishing the validity of amodel is goodness-of-fit to the behavioral data (usuallypenalized for model complexity; see, e.g., Helie, 2006;Pitt, Kim, Navarro, & Myung, 2006). In general, there isa secondary goal of encapsulating existing cognitivetheory, but most cognitive theories are extremelydifficult to falsify, and as a result, if a cognitive modelfits data well then it is almost never rejected because ofthe cognitive assumptions it makes. There are manyexamples where models making very different cognitiveassumptions provide approximately equal levels ofgoodness-of-fit, so in many cognitive domains there aremany competing mathematical models that make verydifferent cognitive assumptions. For example, the resultsfrom many memory experiments can be well fit by avariety of models that make radically different cognitiveassumptions (e.g., Raaijmakers & Shiffrin, 2004), andunfortunately, appeals to cognitive theory have not donemuch to winnow down this crowded field. Many otherexamples exist in the cognitive literature, including thewell known difficulty in discriminating between serialand parallel models of visual or memory search (e.g.,Townsend & Ashby, 1983), the ability of exemplar,prototype, and decision bound models of categorizationto mimic each other (Ashby & Maddox, 1993), and thedifficulty in discriminating between single- and dualprocess models of recognition memory (e.g., Diana,Reder, Arndt, & Park, 2006; Jang, Wixted, & Huber,2009).These problems are greatly reduced in CCN becausegoodness-of-fit to behavioral data is only one of anumber of criteria that are used to assess model validity.This section describes four ideal principles used duringmodel building and testing in CCN. It should be stressed

Computational Cognitive Neurosciencethat these are ideals. Arguably, no existing models meetall these criteria. Nevertheless, these principles areuseful for helping researchers build and evaluate CCNmodels.4.1. The Neuroscience Ideal. A CCN model shouldnot make any assumptions that are known to contradictthe current neuroscience literature.In general, the Neuroscience Ideal means that whenbuilding or evaluating a CCN model, the validity of fourtypes of assumptions should be considered. First, themodel should only postulate connections among brainregions that have been verified in neuroanatomicaltracing studies. Second, the model should correctlyspecify whether each projection is excitatory orinhibitory. Third, the qualitative behavior of units ineach brain region should agree with studies of singleneurons in these regions. Finally, any learningassumptions that are made should agree with existingdata on neural plasticity [e.g., long-term potentiation(LTP) and long-term depression (LTD)]. If a modelmakes an assumption that is known to be incompatiblewith the neuroscience literature then the model should berejected, regardless of how well it accounts forbehavioral data.Note that the Neuroscience Ideal does not say that aCCN model must be compatible with all existingneuroscience data. In other words, not all errors areequal and the Neuroscience Ideal weighs errors ofcommission much more heavily than errors of omission(Meeter, Jehee, & Murre, 2007). Every model is anabstraction and thus omits some of the complexity foundin the natural world. One key to building a successfulCCN model is to identify the critical features of theexisting neuroscience literature that are mostfunctionally relevant to the behavior being modeled. Forexample, neuroanatomical tracing studies will identifymore interconnections among brain regions thantypically should be included in a CCN model becausefor the behavior under study some of theseinterconnections are likely to be more functionallyimportant than others.A related problem is that when building most CCNmodels it will be necessary to make some choices forwhich the neuroscience literature is little help – eitherbecause there are no neuroscience data or because theexisting data are equivocal. Thus, the Neuroscience Idealshould not be interpreted as suggesting that all knownneuroscience must be incorporated into a CCN model orthat every feature of a CCN model must be grounded inneuroscience, but rather only that the neuroscience thatis incorporated should not contradict the existingneuroscience literature. Finally, it is important to keep in4mind that the Neuroscience Ideal is just that: an ideal.No model is ever correct and, even if one wereeventually able to design a model fully compatible withthe Neuroscience Ideal, this would make the model socomplex that it likely would be impossible to test.1 Forthese reasons, the Neuroscience Ideal should be balancedwith the following heuristic.4.2. The Simplicity Heuristic. No extra neuroscientific detail should be added to the model unlessthere are data to test this component of the model or themodel cannot function without this detail.This is just a version of Occam’s razor. It isespecially important with CCN models however,because unlike cognitive models, there will almostalways be many extra neuroscientific details that onecould add to a CCN model. For example, one could usemulti-compartment models of each neuron or evenmodel specific ion channels. Adding untestedcomplexity, even if it is neuroscientifically valid,increases the number of free parameters in the model andthe computing time required for fitting. In addition,when untested details are added, it becomes difficult todetermine whether the success of the model is due tothese details or to the more macroscopic properties thatinspired the model in the first place.The phrase “to test this component of the model” inthe Simplicity Heuristic should be interpreted loosely.For example, if previous research shows that a behavioris dependent on the cerebellum then the cerebellumcould be included in the model, even if no cerebellardata will be fit by the model (e.g., single unit recordingsor lesion data).4.3. The Set-in-Stone Ideal. Once set, thearchitecture of the network and the models of eachindividual unit should remain fixed throughout allapplications.Connections between brain regions do not changefrom task to task, nor does the qualitative nature viawhich a neuron responds to input. Thus, the model’sanalogues of these features should also not change whenthe empirical application changes. This ideal greatlyreduces the mathematical flexibility of CCN models.Ideally, the overall architecture is constrained by knownneuroanatomy and the model of each individual unit isconstrained by existing single-unit recording data fromthe analogous brain region. Thus, although a CCN model1The reader is referred to Meeter et al. (2007) for furtherdiscussion of other common untested assumptions in CCNmodels.

Computational Cognitive Neuroscience5will initially have many unknown constants, most ofthese will be set by single-unit recording data and then,by the Set-in-Stone Ideal, they will remain invariantacross all applications of the model. If some of thedetails turn out to be incorrect after they have been ‘setin-stone’, then the incorrect details should be changedand a new model should be constructed. However, notethat such revisions do not add flexibility to the existingmodel; rather they lead to the creation of a new model.Thus, after a constant is set in stone, it should not beconsidered a free parameter in any future application ofthe model.The Set-in-Stone Ideal applies to the brain areas thatconstitute the focus of explanation of the model, andshould not be expected to apply to brain regions that areeither upstream or downstream from this hypothesizednetwork. For example, many models of learning,memory, or cognition will require visual input. In taskswhere variation in behavior depends primarily onprocessing within the hypothesized network rather thanon details of the visual processing, it is common togrossly oversimplify the model of this visual input. Forexample, a simple square wave might be used, ratherthan a spiking model. Applying such a model to adifferent task, which depends on different visual inputs,might require changing the abstract model of visualinput. Similarly, a model of working memory mightinclude a greatly oversimplified model of motorresponding that could change when the model is appliedto a new task with different motor requirements. So insummary, the Set-in-Stone Ideal is meant to apply to thebrain regions that are the focus of the model and not tothe inputs or outputs of that model.approached. For example, a CCN model might be testedagainst single-unit recording data, BOLD responsesfrom fMRI experiments, or even behavioral datacollected from animal or human participants with somespecific brain lesion, or under the influence of someparticular psychoactive drug.Because a CCN model can be tested against datafrom multiple sources, it can gain or lose support moreeasily than a cognitive model. For instance, followingthe Neuroscience Ideal (Section 4.1), the collection ofnew neuroscience data could invalidate a model byturning an error of omission into an error of commission.For example, a model might posit a direct projectionfrom the pre-supplementary motor area (preSMA) toSMA. After all, given their names, this seems a sensibleassumption. Recent neuroanatomy studies however,suggest that preSMA does not project to SMA (Dum &Strick, 2005), and therefore this discovery invalidatesany CCN model that posits such a projection, regardlessof how well it fits behavioral data. Another possibilityhowever, is that new neuroscience data could verify apreviously unsupported assumption, thereby lending newsupport to the CCN model. Of course, similar outcomescould follow the collection of behavioral data; a modelprediction could be verified or invalidated after newbehavioral data are collected. What is crucial here is thatboth types of data can be used to argue for or against theCCN model. This is different from cognitive orcomputational neuroscience models that restrict theirapplication to only one data type.4.4. The Goodness-of-Fit Ideal. A CCN modelshould provide good accounts of behavioral data and atleast some neuroscience data.The list of ideals proposed in Sections 4.1-4.4 is notthe first attempt to specify the essential characteristics ofCCN models explicitly. For instance, O’Reilly (1998)proposed six principles for computational models of thecortex: (1) biological realism, (2) distributedrepresentations, (3) inhibitory competition, (4)bidirectional activation propagation, (5) error-drivenlearning of specific tasks and, (6) Hebbian learning oftask-free statistical properties of the environment. Mostof these principles are related to the Neuroscience Idealabove in that they specify biological constraints thatshould be included in any CCN model of the cortex.Hence, they can be seen as an unpacking of theNeuroscience Ideal.A decade later, Meeter et al. (2007) proposed a listof more general criteria. Specifically, they suggested thata good CCN model (1) has few assumptions, (2) isinflexible and, (3) exhibits ontological clarity. The firstof these is similar to our Simplicity Heuristic, while thesecond is similar to the Set-in-Stone Ideal. Both sets ofA model must make predictions at both thebehavioral and neuroscience levels to classify as a CCNmodel. If it only makes behavioral predictions then itshould be classified as a cognitive model, whereas if itonly makes neuroscience predictions then it should beclassified as a computational neuroscience model. Thus,in general, CCN models are more ambitious thantraditional cognitive models because CCN models areexpected to account simultaneously for a wider range ofdata than cognitive models. Note that the only term thatmakes this statement an ideal rather than a requirementis the word “good”. Every CCN model should make bothbehavioral and neuroscience predictions, but the idealCCN model provides good accounts of both data types.There are many different types of neuroscience data,so there is wide latitude in how this ideal can be4.5. RelationcharacteristicstopreviouslistsofCCN

Computational Cognitive Neurosciencecriteria emphasize that a model should be simple andinflexible (two ideas that are mathematically related).The last criterion, ontological clarity, is similar to ourGoodness-of-Fit Ideal, in that the scope of the modelmust be clearly established in order to determine whatkind of data needs to be fit and what kind of experimentsshould be run. In other words, the rules need to be setearly on to specify what counts as evidence for oragainst the CCN model.4.6. DiscussionThe Neuroscience Ideal makes the relationshipbetween computational neuroscience and CCN explicitby ensuring that no biological detail in the CCN model isinconsistent with existing neuroscientific data (as incomputational neuroscience). However, following theSimplicity Heuristic, CCN models typically makesimplifying assumptions about the biological detailsincluded in the model. This is because the lowest levelof data usually accounted for by CCN models is singlecell recordings. Hence, although an increasing amount ofdata is now available about the molecular neurobiologyof neurons, these data are usually not accounted for byCCN models. This makes CCN models biologicallysimpler (and thus more scalable) than mostcomputational neuroscience models.The Set-in-Stone Ideal is used to control the growthof complexity in the model. Theoretically, the Set-inStone Ideal is an implementational constraint: the samebrain is used in every task. Computationally, the Set-inStone Ideal is used to fix the value of most constants inthe model, thus drastically reducing the CCN modelcomplexity. Once set-in-stone, the Goodness-of-Fit Idealstates that many different types of data should be used totest the adequacy of CCN models, at least some of whichare behavioral and some neuroscientific. In addition, theGoodness-of-Fit Ideal makes the relationship betweenconnectionism and CCN models explicit: The biologicaldetails in the CCN model should not make the modelunscalable and prevent it from explaining behavioraldata (i.e., it should scale up like a regular connectionistmodel). However, before doing any data fit, one needs toclearly define the scope of the model.These principles are used to guide modeldevelopment and evaluation. Because of theNeuroscience Ideal there are three areas where themathematical details of CCN models differ substantiallyfrom traditional connectionist models. The firstfundamental difference is in how each individual unit ismodeled and the second is in how learning is modeled.The third difference concerns the generation of behaviorfrom neurally realistic individual units. Sections 5 - 7discuss some example CCN solutions to these problems.65. Modeling Individual UnitsThere are many choices for modeling individualunits. The classic solution is still the Hodgkin-Huxleymodel (1952). This is a set of four coupled differentialequations. One describes fast changes in intracellularvoltage and three describe slow changes in various ionconcentrations (i.e., for Na , K , and Cl-). The modelcorrectly accounts for action potentials (both theupstroke and downstroke), the refractory period, andsubthreshold depolarizations that fail to produce a spike.From a computational perspective, perhaps the greatestdrawback is that four differential equations must besolved for every unit in the model. Also, for most CCNapplications the Hodgkin-Huxley model violates theSimplicity Heuristic because rarely do such applicationsattempt to account for data that depend on intracellularconcentrations of sodium, potassium, or chloride.For these reasons, there have been a number ofattempts to produce models with fewer equations thatdisplay as many of the desirable properties of theHodgkin-Huxley model as possible. Some of theseattempts are described in the following subsections.5.1 The leaky integrate-and-fire modelThe simplest cell model, and also the oldest(Lapicque, 1907), is the leaky integrate-and-fire model(e.g., Koch, 1999). Suppose neuron B receives anexcitatory projection from neuron A. Let VA(t) and VB(t)denote the intracellular voltages at time t in neurons Aand B, respectively. Then the leaky integrate-and-firemodel assumes that the rate of change of VB(t) is givenbydVB (t ) f VA (t ) VB (t ),dt(1)where α, β, and γ are constants and the function f [VA(t)]models temporal delays in the propagation of an actionpotential from the pre- to the postsynaptic neuron. Thisfunction is described in detail in Section 5.4. Theparameter α is a measure of synaptic strength becausethe larger this value the greater the effect of an actionpotential in the presynaptic cell. In many applications,learning is modeled by assuming that α changes as afunction of experience. The parameter β det

computational neuroscience, machine learning, and neural network theory (i.e., connectionism). The ideal CCN model should not make any assumptions that are known to contradict the current neuroscience literature and at the same time provide good accounts of behavior and at least some neuroscience