On the need for computer modeling: The case of language processing

Computational modeling constitutes a fundamental extension to the psychological scientific toolkit. The present contribution aims to clarify the pros and cons of modeling techniques, using examples from language processing. We present some strategies that may help avoid potential pitfalls of the computational modeling approach. The traditional relationship' between theory and experimentation in psycholinguistic research is also considered as well as some limitations associated with the standard experimental approach. Finally, we insist upon the complementarity between theory, experimentation and modeling.


Introduction
A few years ago, during a lunch discussion, Paul Bertelson came up, in his usual perceptive and provocative manner, with something like \what is all this fuss about computational psychology? Isn't that what we h a ve been doing all the time since cognitive psychology was launched? Then what is the di erence?" This paper is an attempt to answer Bertelson's questions. We argue that the de ning feature of the computational approach is the use of computer simulation techniques to develop models of processing systems, and we suggest that, within an information-processing framework, such tools constitute a natural complement to experimental procedures.
Correspondence should be addressed to Alain Content needs the address here. The writing of this paper has bene ted from support from the Swiss National Fund for Scienti c Research (grant 11-39553.93)and Belgian National Fund for Scienti c Research ( g r a n t 9.4565.92). We thank Daniel Holender, Guy Lories, and Dominic Massaro for their comments on a previous version, and Axel Cleeremans for stimulating discussions and encouragements.
Most psychologists interested in the study of human perception and cognition share the fundamental assumption that mental activity can be described and analyzed as the functioning of a particular kind of physical machine. Most authors would also argue that descriptions of information processing mechanisms provide explanations of perception, cognition and human behavior. On the other hand, the de ning feature of the computational approach is the recourse to computer techniques as tools to model or simulate information processing systems through numerical or symbolic computation. Thus, in that context, we believe that Bertelson was right i n p o i n ting out the natural liation between the basic assumptions of cognitive psychology and the recourse to computer modeling. As far as cognitive psychology's agenda is to explain mental life through descriptions in terms of information processing mechanisms, there may n o t b e a n y principled disagreement between that programme and the computational approach. In fact, as often noted, the information-processing framework is largely derived from the application of the computer metaphor to mental activity. So, within the information processing approach to psychology, whether one appeals to computational modeling or not may be more a matter of research strategy than a matter of principle.
Still, not all current metatheories in psychology seem to stick to the principle of mechanistic explanation, and several well-known scholars have expressed concerns about the potential and limitations of the information-processing approach a s a n answer to psychological inquiry (e.g., Neisser, 1976Norman, 1980. For instance, in a recent paper entitled \Has psychology a Future?", Eleanor Gibson (1994, p.70) claims When someone asks me (as they quite often do), \But what is the mechanism?" my answer is that I am not a mechanist and I do not believe in separation of mental processes and action.
We believe that such disagreements may be more apparent than real and may result from an unduly restricted notion of mechanism. In our view, the question \what is the mechanism?" entails little more than a prompt to provide explanations framed as answers to \How?" questions. While we agree in principle that some psychologically relevant explanations may not need to take the form of responses to \How?" questions, we assume that mechanistic descriptions of information processing provide valuable explanations for several aspects of human cognition. Massaro and Cowan (1993) similarly argue that ecological realism, the physical symbol system hypothesis, connectionism, and the modularity h ypothesis constitute four variants of a more general information processing framework, and we tend to agree with this analysis. We w ould add the dynamic system modeling approach ( P ort & van Gelder, 1995b) as one further variant. As a consequence, \computational" is used in this paper as a cover term including all frameworks using automatic computation devices to simulate mental activity. T h us, our acception diverges from others', who use the term to refer more speci cally to the metaphor of the Von Neumann computer, excluding other approaches based on connectionist or dynamical systems.
Even within the circle of psychologists who adhere to the information processing framework, there is no clear agreement on the role of the computational modeling enterprise in cognitive p s y c hology. Some (Loftus, 1993) warn of the dangers of superpowerful tools leading to supercomplex models. Others seem to remain skeptical or agnostic (MacKay, 1993) others still put great hopes in the contribution of computational modeling or even consider that computational models are a requisite of psychological theories (Broadbent, 1987Estes, 1993Johnson-Laird, 1983Johnson-Laird, 1988Parisi & Burani, 1988. Our own feeling is that the relevance and the contribution of the computational approach in current cognitive research is often misunderstood. We believe that the modeling endeavor is a fundamental improvement to the psychological scienti c toolkit. So, one aim of the present c o ntribution is to clarify the pros and cons of modeling techniques, with a particular focus on aspects of language processing. Another aim, without any i n tention of being prescriptive, is to suggest some strategies that may help avoid potential pitfalls of the computational modeling approach.
In the rst section of the paper, we o er some general de nitions of the nature and function of theories and models within psychological science. In the second section, we reconsider the traditional relationship between theory and experimentation in psycholinguistic research, and we discuss limitations associated with the standard experimental approach. The nal section examines the contribution of computational modeling to psychological inquiry, and underscores the complementarities between theory, experimentation and modeling.

Theories and Models as Information Processing Explanations
Psychology, a s a n y other science, aims at producing theories. To articulate in some detail the nature of the modeling endeavor and its relation to psychological theorizing, it is necessary to clarify the relationship between theories and models.

Theories
A theory is a structured set of mental constructs (concepts, propositions, de nitions) that provides an explanation for some set of phenomena. According to the Encyclop dia Britannica, a scienti c theory is a systematic ideational structure of broad scope, conceived by t h e h uman imagination, that encompasses a family of empirical (experiential) laws regarding regularities existing in objects and events, both observed and posited. A scienti c theory is a structure suggested by these laws and is devised to explain them in a scienti cally rational manner. Theories must explicitly and accurately describe the phenomena under consideration, but descriptive adequacy is, of course, not su cient: Theories are expected to explain things. The notion of \explanation," however, is not an easy term to de ne, and it is unclear what exactly scientists and philosophers mean by terms such a s \explain" or \understand." Intuitively, what counts as an appropriate explanation depends on a collection of criteria. To explain is \to make plain." In general, the process of explanation can be viewed as presenting some phenomenon that we d o not understand in terms of other concepts that we believe w e understand, or which are deemed to be simpler, or maybe which are generally accepted.
Some examples may help clarify what constitutes an appropriate scienti c explanation. Newton's law o f u n i v ersal attraction is a prototypical instance of a useful theory in physics. It is (at least at a macroscopic level) descriptively correct, its formulation is extremely synthetic, and it is universal since it applies to an in nite number of situations. The law of universal attraction provides an explanation for a number of phenomena. Note, however, that Newton's laws are not the nal word: As such, they do not o er any explanation of why bodies are attracted at a distance. In other words, we do not yet fully understand the causal mechanism that determines the attraction between bodies.
Another example from a eld of psychology with which w e are familiar, concerns the nature of the determinants of reading ability. Current theories of reading acquisition state that there is a causal relation between children's ability to understand spoken words as a sequence of phonemic segments and their later success in reading. This claim is supported by s e v eral empirical observations that have been replicated often by di erent research groups in various languages (see, e.g., Morais, Alegria & Content, 1987Rohl & Pratt, 1995Wagner & Torgesen, 1987 for reviews). We d o not know, at this time, how c hildren come to understand speech as a discrete string of segments, nor why s o m e c hildren fail to develop such segmental representations. Yet, the notion of a causal relation between phonological awareness and reading acquisition has important implications, most notably in the domain of reading instruction as well as for the prevention of learning di culties and the correction of reading disabilities.
Some authors apparently believe that the di erence between descriptive a n d explanatory adequacy is in terms of predictive p o wer: A good theory should not only describe accurately what is already known, but should also be able to predict new phenomena. Pylyshyn (1984), for instance, argues that cognitive explanations must be stated in terms of cognitive v ocabulary because this is the level at which useful generalizations and predictions can be made. Other researchers point o u t that predictive p o wer in itself is not a su cient criterion and argue that explanatory adequacy depends on conformity to universal, independently motivated principles or constraints (e.g., Chomsky, 1965Johnson-Laird, 1983Seidenberg, 1993.
Both of the above examples, di erent as they may be, constitute statements of reliable and established regularities that may be empirically observed and veri ed. Any phenomenon that appears as a logical consequence of such regularities would naturally be considered explained by them, although the regularities themselves are only descriptive. Ideally then, a complete theory should reduce phenomena to a limited set of general or even universal principles. However, the available explanations are often more limited in scope and, apparently, the \grand uni ed theory" of psychology is nowhere close to emerging. Whether such a theory is at all possible in psychology is even debatable. Thus, what seems crucial in accepting an explanation for some phenomena is that the phenomena appear as logical consequences of independently motivated explanatory statements. We cannot a ord to ignore this type of partial knowledge, which happens to be the rule rather than the exception in psychology. So the critical question regards how to pursue simultaneously the quest for the most general principles and the discovery of such local generalizations and explanations.

Models
What is the di erence between a theory and a model? According to Merriam-Webster Collegiate Dictionary, a model can be a miniature representation of something : : : an example for imitation or emulation : : : a description or analogy used to help visualize something (as an atom) that cannot be directly observed : : : a system of postulates, data, and inferences presented as a mathematical description of an entity or state of a airs. These various de nitions all capture some of the uses of the notion of model in scienti c circles. Our own idea is that a model is a particular type of theoretical elaboration, which is most often expressed as a metaphorical device: Proposing a model of a system amounts to devising another system in such a w ay that its behavior will mimic relevant aspects of the target system behavior of the target system. This will allow to explain these properties of the target system by referring them to the relevant c haracteristics of the model.
Of course, models can be formulated in di erent guises, and need not be made of real stu , and one can think of various types of models: concrete ones (such as plastic models of complex molecules), symbolic or iconic ones (such as, within cognitive psychology, those expressed in the box-and-arrow-diagram-ow t ype of symbolism), mathematical models, or computer models. One could even extend the notion to verbal models, which w ould then be descriptions of imaginary devices (such as Morton's, 1969, notion of logogens).
We suggest that the essential di erence between theories and models is in terms of the conceptual media employed to express the ideas, but that this di erence in media also entails di erences in scope. Theories are generally expressed in the form of abstract principles of general applicability. When facing complex phenomena, in which m ultiple factors interact in intricate ways and vary dynamically over time, it may be di cult or even impossible to specify or imagine the behavior of the system from the general principles alone. Models serve the function of making the interplay of the general abstract principles more concrete and more accessible to our understanding, within a delimited domain. Thus, most psychologists would use the term \theory" to refer to the notion of spreading activation and would refer to Quillian's \model" of semantic memory. The notion of spreading activation refers to a general principle of how information ows, whereas Quillian's model applies that principle in one more circumscribed domain. Similarly, one can read about information \theory," and of its application to human attention in Broadbent's lter \model." In other domains, likewise, one can distinguish between general laws and their applications. Meteorology, for instance, illustrates the gap between general physical laws and physical processes (such as heat radiation, convection or conduction) and their intervention in models of global climatic change, local weather, hurricane dynamics or the greenhouse e ect. In the latter example, despite the universal acceptance of the general laws, it appears that most phenomena have not received a detailed and satisfactory model yet.
In sum, models can be seen as simpli ed representations of some parcel of reality. They are instantiations of general theoretical hypotheses, in a form that lends itself to more detailed investigation. By virtue of their analogical structure, they provide intuitive understanding of their object. Indeed, several psychologists studying human reasoning and inference have argued that much of our understanding in everyday life settings is based on the elaboration of mental models of the situation or problem domain. To quote Johnson-Laird (1983, p. 2): the psychological core of understanding consists in your having a \working model" of the phenomenon in your mind. If you understand ination, a mathematical proof, the way a computer works, DNA or a divorce, then you have a mental representation that serves as a model of an entity i n m uch the same way as, say, a c l o c k functions as a model of the earth's rotation. How do theories and models come into play i n p s y c hological research? One basic tenet of modern cognitive psychology is the belief that interesting explanations are to be found in the understanding of the mechanisms at work. Palmer and Kinchi (1986) have tried to identify the fundamental assumptions of the information processing framework from a psychological viewpoint. They consider ve assumptions, of which t wo seem more directly relevant in the present c o n text. These are the assumptions they call informational description, a n d recursive decomposition. T h e principle of informational description states that mental phenomena can be described as informational events, consisting of three parts: the input information, the operation performed on the input, and the output information. The principle of recursive decomposition states that any complex (i.e., nonprimitive) informational event at one level of description can be speci ed more fully at a lower level by decomposing it into (1) several components, each of which is itself an informational event, and (2) the temporal ordering relations among them that specify how the information \ ows" through the system of components (p.39). Flow diagrams have been used abundantly in the form of box and arrow representations. they provide a compact description and a clear decomposition of a process into a sequence of stages. This strategy of process decomposition has received much attention in some domains (especially when strong interactions with neuropsychology were possible). In fact, in some areas, the strategy of process decomposition has been so in uent that the issue of componential architecture became for some time a major focus of the research e ort, culminating in the modularity h ypothesis.
The endeavor is nicely illustrated by the following quotation from the physicist Lord Kelvin (cited by Johnson-Laird, 1993): I n e v er satisfy myself until I can make a m e c hanical model of a thing. If I can make a mechanical model I can understand it. As long as I cannot make a m e c hanical model all the way through I cannot understand : : : Lord Kelvin's saying could be taken as a motto for cognitive psychology. I ndeed, one underlying driving force to current research m ust be the belief that we will reach some understanding of mental life and behavior by analyzing perception, recall, language and reasoning as information-processing mechanistic systems. For instance, MacKay (1988 1993) contrasts two research strategies in psychology, which he labels the empirical and the theoretical epistemology respectively. T h e mission assigned to science by an empirical epistemology is to gather a body of reliable facts and regularities, whereas for a theoretical epistemology it is to develop theories that explain available facts. MacKay attributes the unsatisfactory state of advancement of knowledge in psychological research t o o ver-reliance on the empirical, result-centered strategy. H e t h us appeals to a more theoretically oriented research strategy in psychological science, and claims (1993, p. 237) that the sine qua non of theories within the theoretical epistemology is mechanistic explanation: Theories are not just descriptive, but explain phenomena in terms of underlying mechanisms. Therefore, it comes as no surprise that most current theorizing is about models. In a sense, the program of modern cognitive psychology could be seen, or even de ned, as the project of modeling mental activity. So, why not use the best tools available?
3. Verbal models and data One widely accepted strategy in science is empirical falsi cation. Thus, in principle, one should start with a theoretical hypothesis (induced from preliminary observations or inferred from established results), and generate an empirical prediction, as a relation between one or several dependent v ariables and one or several independent variables. Then, one would design an experiment manipulating the independent variables and monitoring the e ect on dependent v ariables. According to the falsication principle, the interesting case is when the data do not t with the theory, since this should trigger its revision or its rejection. In short, science would make progress through negative feedback.
Within cognitive psychology, m a n y authors have pointed out the limitations of the falsi cation strategy (MacKay, 1993Newell, 1990. Moreover, attempts to conform to the falsi cation precepts have generally resulted in disappointment a n d disillusion. This state of a airs may be attributed to three di erent factors: the complexity of the phenomena under scrutiny, the lack of speci cation of verbal models, and the general issue of model identi ability.

Complexity of phenomena
The e ects upon modeling of the complexity faced in characterizing language processing can be illustrated by examining the history of models of spoken word recognition. The original cohort model (Marslen-Wilson & Welsh, 1978) represents the rst attempt to provide a systematic description of spoken word recognition. The model assumes two successive stages of processing. During the rst, all words that exactly match the onset (i.e., the initial one or two segments) of the target word are activated, thus creating a set of competitors which constitute the initial cohort of the target. This initial activation phase is followed by a stage of deactivation during which the cohort members that do not match later sensory input are eliminated from the cohort. The number of cohort members decreases as more stimulus information becomes available. This model makes precise predictions about the moment a t w h i c h a n y w ord can be recognized in a given lexicon from an analysis of its cohort members. The recognition point is assumed to correspond to the word's uniqueness point, or the moment that the word becomes unique with respect to all other words in the lexicon. A given target word spoken in isolation is assumed to be recognized when it is the only word remaining in the cohort. For example, a word like \elephant" heard in isolation is predicted to be identi ed at the sound /f/, since there are no other words in the lexicon sharing the initial sequence /elef/.
By its clarity and simplicity, cohort I generates precise predictions about the time-course of recognition: Recognition should be a linear function of the position of the uniqueness point. The fact that these predictions can be tested and falsi ed makes the model attractive. However, some critics were quick to point o u t v arious ways in which this simple description fails to account for the robustness of human language perception (e.g., Norris, 1990).
To incorporate some psychologically more realistic assumptions, Marslen-Wilson (1987) proposed a new version of his model, cohort II. This model appeals to the notion of level of activation to express the varying degree of match possible between the input and di erent lexical competitors. Cohort members vary in activation as a function of their t with the input but also as a function of their frequency. While the status of words in the original model is binary (either in or out of the cohort), in the new formulation of the model cohort membership is a matter of degree. Still, the model does not specify how the frequency of words and their degree of match with the input determine activation.These factors and their relative c o n tribution to lexical activation cannot be quanti ed in a verbal model, so no precise de nition of the competitor set is yet available in cohort II. The preceding discussion of the two v ersions of the cohort model illustrates a general dilemma confronting e orts to model lexical processing. cohort I m a k es clear and testable predictions, but at the price of several simplifying assumptions.
In contrast, cohort II is a more complex verbal model and presumably ts better with what we k n o w about lexical processing. However, it does not provide direct answers to the questions concerning the competitor set and therefore cannot predict the time-course of word recognition.
We take the lesson to be the following. Simple, verbal models are helpful in shaping and formalizing questions and issues: As far as they capture the major dimensions of the problem, they provide a good account of it. However, psychological phenomena are generally a ected by a large number of variables, and language performance is no exception. Some factors that must be dealt with in word recognition research include the form properties of words (quality of sensory input, length, phonological structure, etc.), the grammatical and abstract properties of words (syntactic form class, semantic category, w ord frequency and morphological structure) and the properties of the lexicon (number of competitors, form properties of competitors, grammatical and abstract properties of competitors). Most of these factors cannot be adequately taken into account using dichotomous categories, and psycholinguistics is often faced with intricate interactions and covariations of multiple factors.
Because verbal models are intrinsically limited in their ability to describe the in uence of multiple factors and their interactions, they lead to inappropriate simpli cation for the sake of prediction. Simpli cation takes two forms: limiting the number of factors taken into account, and treating the factors as dichotomous rather than multi-valued.
One important consequence of these characteristics is the introduction of a bias toward an analytical methodology. T ypical experimental designs manipulate only a small number of independent v ariables (often de ned in a binary fashion) and attempt to control or neutralize other potential factors. While this analytical approach m a y be appropriate at a rst stage in experimental research, it clearly fails to deal with the full complexity of cognitive phenomena. As we will argue below, the addition of computer simulation helps overcome this hurdle.
Another unfortunate consequence of the approach is that it leads to local theorizing, and (in MacKay's, 1993, terms) empirical theorization which i s d a t a d r i v en, and domain speci c. There are several risks to local theorizing. One is the lack o f integration of the research. This is abundantly illustrated in the often blamed paradigm driven research strategy. A s p o i n ted out by MacKay and others, miniature models designed to account for a small number of results have proliferated rather than merged into a single general theory (MacKay, 1988Newell, 1973Norman, 1980. Moreover, because local theorizing proceeds in isolation, a further danger is that it rarely refers to general principles and thus remains inherently descriptive o r at best, weakly explanatory. Accounts of phenomena such as lexical decision performance provide a good example of this. Lexical decision has mainly been studied as a speci c language task, rather than as an example of a binary decision task applied to the domain of language, and thus without consideration of what is known about the mechanisms of binary decision tasks in general.

Underspeci cation
A related di culty is that verbal models and information ow diagrams most often leave many details unspeci ed. The focus on the global architecture induced by t h e functional decomposition strategy has generally resulted in insu cient explicitness in the description of both the nature of representations at each stage, and the processing mechanisms operating from one stage to the next. Many models of visual word recognition proposed in the last twenty y ears could be taken as illustrations of that limitation: Word recognition is decomposed in a sequence of transcoding operations, which are only speci ed in terms of their input-output relations. Little is known about the transcoding processes themselves. This feature is epitomized in Neisser's (1976) caricature of an information processing model of perception, in which the three successive b o xes are labeled \processing," \more processing," and \still more processing," respectively. E v en when the nature of the representations or the transcoding operations are more clearly speci ed, one important dimension that is not explicitly handled is the dynamic characterization of the processing| particularly for chronometric data (see Parisi & Burani, 1988, for further discussion). For instance, despite the large impact of the dual route model of visual word recognition, the nature and the time course of grapheme-phoneme conversion have never been explicitly included in the formulation of the verbal models, and this has prevented attempts to disentangle the dual-route model from competing lexical analogy accounts. Thus, the lack o f a t t e n tion to the detailed picture often makes it hard to generate predictions that can be put to empirical test. 3.2.1. System Identi ability Even if fully speci ed verbal models were available, however, they would not be immune to a third problem, that of model or system identi ability. The notion of system identi ability is discussed in some detail by Massaro and Cowan (1993). It was introduced by Moore (1956) in the context of formal automata theory, a n d refers to the problem of describing the inner workings of a machine when only its input and outputs are available. Moore demonstrated that any input-output mapping can be reproduced by m a n y di erent automata, so that it would in general be impossible to uniquely identify the processing mechanism underlying some set of input-output pairs. Applied to psychological research, this claim seems to strongly undermine the information processing enterprise. However, as Massaro and Cowan aptly point out, there is only a partial similarity b e t ween the problems addressed by psychological inquiry and formal automata theory. One di erence is that psychological investigation does not need to restrict its observations to the inputs and outputs of a processing component. It can extend the database by considering other measures of performance, such a s c hronometric data, neuropsychological or developmental observations. Furthermore, one can add other constraints on the space of potential models by taking into account formal conditions such as simplicity and parsimony (see Jacobs & Grainger, 1994 for an extended discussion), external sources of evidence, such as neural limitations or neuroanatomical characteristics, or general principles of processing. Whether such external constraints will ever be su cient t o s o l v e t h e issue of model identi ability is perhaps a matter of faith. However, one important consequence to which w e will return later is that external constraints are crucially needed to restrict the set of admissible models. 4. The computational approach 4.1. A de nition Appealing again to the Encyclop dia Britannica, a computer simulation refers to the use of a computer to represent the dynamic responses of one system by the behavior of another system modeled after it. A simulation uses a mathematical description, or model, of a real system in the form of a computer program. This model is composed of equations that duplicate the functional relationships within the real system. When the program is run, the resulting mathematical dynamics form an analog of the behavior of the real system, with the results presented as data. We will restrict ourselves to a general discussion of the advantages, potential drawbacks and limitations of the modeling approach. We will not elaborate on the issue of model evaluation, which has been discussed recently by others in psycholinguistic research (see, e.g., Dijkstra & de Smedt, 1996Jacobs & Grainger, 1994). Nor will we e n ter here into the debate about which particular modeling framework (e.g., symbolic, connectionist, distributed) is preferable or optimal.
Computational modeling refers to the use of computer programs to simulate some set of phenomena. Two bene ts to the use of computer modeling in psychology are often mentioned. One is the requirement of full speci cation of the process under consideration, and the other is the model's ability to deal with empirical complexity. In view of the limitations of verbal accounts that we h a ve described in the previous section, these advantages are important, and deserve further discussion.
These bene ts are particularly relevant within a perspective on model construction in which the designer starts with a verbal model and aims at implementing it as a computer program. However, we think that there is more to the modeling enterprise and that this restrictive vision of modeling-as-theory-implementation severely limits the bene ts we can expect from the modeling endeavor. Borrowing partly from an analogy previously proposed by McCloskey (1991), Jacobs and Grainger (1994) describe two strategies for model construction that appeal to two di erent professions: the architect and the gardener. The architect starts from an explicit (verbal) theory of the target function, and implements it in a computational system. The gardener's strategy consists of growing a model or network that mimics in some respect a human cognitive function, without necessarily having an explicit theory of that function (p. 1327). In recent y ears, the gardener's strategy has become more feasible and promising, thanks to the availability o f p o werful automated learning algorithms in various elds of computer science, such as arti cial neural networks, symbolic manipulation systems (see, e.g., Ling & Marinov, 1993), or probabilistic systems such as hidden Markov models.
Yet, it would probably be misleading to associate the gardener's approach t o o closely with the use of arti cial neural networks, or even with the deployment o f automatic adaptive procedures. The architect and the gardener are two extremes on a continuum ranging from a strict implementation strategy to a mere data tting strategy. It seems likely that every architect is endowed with a bit of the gardener's art, and that every gardener secretly entertains a sketch of its accomplishment. In other words, interesting modeling work involves elements from an intentional and theoretically-based design, but also unexpected features that emerge from the interplay o f t h e a s s e m bled mechanisms. There are many examples in the history of Arti cial Intelligence illustrating how unforeseen consequences arise from computational implementations.
In the remaining part of this section, we rst discuss the three issues identi ed earlier from the architect's perspective, namely, detail speci cation, complexity, a n d system identi ability, and then continue by developing the speci c issues that may arise from adopting the gardener's point of view.

Detail speci cation
Designing a running model of a given set of phenomena obviously forces the modeler to ll the details missing in the verbal theory, and this immediately pays o by permitting detailed, quantitative tests of predictions derived from the model's actual behavior. However, xing the details to transform an abstract scheme into a working system is not easy. A s a n y architect would know, the nal appearance of the work may depend on the wallpaper choice as much as on the initial blueprints. Similarly, in creating a computer model, designers will encounter many unsettled issues and their decisions|even totally arbitrary ones|may h a ve a crucial in uence on the performance of the system.
In this regard, it is instructive to examine the evolution from the verbal formulations of cohort I to a related computational realization, the trace model. There is a direct liation between these two models, as the following quotation testi es: Although the cohort] m o d e l i s v ague and fails to address many important issues, it is attractive enough so that we h a ve used it as the basis for our initial attempt to build an interactive model of speech perception. (Elman & McClelland, 1984, p. 349). It is thus interesting to examine how the models diverge from each other, and to establish what the constraints are that play a role in the implementation process.
trace is an interactive activation model made up of distinctive features, phonemes, and word units that represent h ypotheses about the sensory input. These three types of units are organized hierarchically (see Figure 1). There are bottom-up and top-down facilitatory connections between units on adjacent l e v els (featurephoneme, phoneme-word, and word-phoneme) and inhibitory connections between units within levels (feature-feature, phoneme-phoneme, and word-word). Incoming sensory input provides bottom-up excitation of distinctive feature units which in turn excite phoneme units. Phoneme units are activated as a function of their match with the activated distinctive features so that several alternative phonemic units are activated for a given input. As the phonemes become excited, they increase the level of activation of words that contain them. As words receive some activation, they begin to inhibit each other. In addition, as words become activated, they also excite the phonemes that they contain in a top-down fashion.
trace diverges from the cohort model in its assumptions concerning information or activation ow. These assumptions are derived from the principles of interactive activation models. Unlike cohort, trace includes both lateral inhibition between word units and top-down activation from the word to the phoneme level. By the lateral inhibition mechanism, the target word inhibits its competitors, but is also inhibited by them. The degree to which o n e w ord inhibits another depends on the former's activation level: The more activated a word is, the more it can inhibit its competitors. The dynamics of interactive activation and, in particular, this lateral inhibition of competitors allows trace to keep the actual activated competitor set small and to converge on a single lexical entry despite the mass of lexical candidates that contend for recognition. According to the top-down activation mechanism, activated words provide top-down excitatory feedback t o t h e phoneme units they contain by increasing the latter's level of activation. These phoneme units can in turn excite the connected word units.
The sequential and continuous properties of speech create a major challenge for computational models like trace. Indeed, since words can, in principle, begin at any point in the signal, trace must be able to represent e v ery lexical candidate for each incoming input segment and to assign these candidates a position in the signal. trace proposes that time is represented spatially. F or each time-slice, it constructs a complete network in which all the units at every level are represented. Thus, to recognize an input made up of four phonemes, trace constructs at least four (in fact, 4 6 since each phoneme extends over 6 time-slices) complete lexical networks and retains the time cycle at which e a c h lexical unit begins. This solution of spatial reduplication is neither psychologically realistic nor e cient, as was pointed out by Norris (1990) who suggested that an alternative solution to the problem of representing time is provided by recurrent n e t works (see also Content & Sternon, 1994).
We can thus distinguish three essential sources in the elaboration of the trace model: the pre-existing cohort model, the general assumptions derived from the interactive activation framework (graded activation, cascade processing, lateral inhibition, top-down excitation), and implementation constraints (i.e., the particular way the whole network is reduplicated to account for the time dimension).

Some implementation decisions on which trace is based have directly in uenced
the course of empirical research and have c o n tributed to launch new issues or to reshape existing ones (see Frauenfelder, 1996 for a discussion). For instance, the role of lateral inhibition has led researchers to explore the nature and in uence of lexical neighbors on auditory word recognition. Similarly, the reduplication of the network in time makes it possible to investigate the processing of continuous sequences of words, and has attracted attention to the issue of lexical segmentation and to the processing of words embedded in longer words (see Frauenfelder & Peeters, 1990).

Other examples abound. There is a similar liation between the interactive activation model of visual word perception (McClelland & Rumelhart, 1981) and
Morton's logogen model (1969): Our model also draws on earlier work in the area of word perception. There is, of course, a strong similarity b e t ween this model and the logogen model of Morton (1969). What we h a ve implemented might b e called a hierarchical, nonlinear, logogen model with feedback b e t ween levels and inhibitory interactions among logogens at the same level. We have also added dynamic assumptions that are lacking from the logogen model (McClelland and Rumelhart, 1981, p. 388).
Yet, the two models have largely diverged in their in uence on subsequent research. The logogen model has essentially inspired discussions in the neuropsychological literature about the componential architecture of the lexical function, leading to a multiplication of speci c subsystems (Ellis & Young, 1988Morton, 1980. The interactive activation model, besides its adoption in various areas of language and cognitive processing, has promoted renewed interest on more microscopic issues about lexical processing, such as the in uence of lexical neighbors in the recognition process. Design decisions can be motivated by di erent concerns ranging from general theoretical postulates, empirical ndings, epistemological considerations (such as Occam's razor principle), to pragmatic constraints such as expediency and e ciency. As we h a ve argued previously, i t i s a l w ays the case that neither the preexisting verbal theory nor the empirical database fully determines the model. This poses a problem in that pragmatic constraints may lead to decisions that are theoretically unmotivated, arbitrary, or ad hoc. One common problem involves representational choices in connectionist modeling. As noted by Dijkstra and de Smedt (1996), present empirical techniques provide scanty information regarding the format of mental representations. Thus, model designers are forced to refer to other constraints. For instance, the use of \wickelgraph" and \wickelfeature" representations in Seidenberg and McClelland's (1989) distributed model of visual word recognition and Rumelhart and McClelland's (1986) model of past-tense acquisition was partly guided by design considerations. In both cases, the authors acknowledged that their choices were meant to facilitate generalization, given other known characteristics of the connectionist framework adopted.
Critics and skeptics have been quick to question the role of such implementation choices in shaping the models' behavior. If, as some asserted (Bever, 1992Lachter & Bever, 1988, these trics (\The Representations It Crucially Supposes") are primarily responsible for the models' successes, the interest of the demonstration is strongly undermined. More recent s i m ulation work by Plaut, McClelland, Seidenberg and Patterson (1996) indeed suggests that the nature of the orthographic and phonological representations has a direct in uence on the model's ability t o generalize.
Two potential strategies may help clarify the extent t o w h i c h the behavior of models depends on theoretically irrelevant implementation details. One is to test the robustness of the behavior across variations of implementation details. An example of this approach i s p r o vided by Plaut and Shallice's (1993) simulations of deep dyslexia, in which the authors carefully showed that the main behavioral characteristics resisted variations in network topology, sites of lesion, and training algorithms. A complementary approach is to abstract away the general design principles that are operating and which account for the functional characteristics of the realized model (Stone & Van Orden, 1994Van Orden & Goldinger, 1994Van Orden, Pennington & Stone, 1990.
One question that may arise from the previous discussion is whether the modeling endeavor is worthwhile, given the apparent insu ciencies of the empirical database. Should we not wait until we k n o w enough? Our answer is to turn the claim the other way around: We believe that the modeling enterprise provides an important s i d e bene t, besides the immediate outcome of having a running computer model. By facing the constraints of implementation directly, modelers are forced to identify theoretical issues that might otherwise be overlooked. If we do not face these implementation constraints, we m a y remain ignorant o f o u r o wn ignorance.

Complexity
Human behavior unfolds in time and is subtly sensitive t o a h uge number of factors. It thus seems natural to resort to dynamic systems to describe, formalize and simulate the complex interactions that determine the observed phenomena. Indeed, other sciences which share some of the same characteristics, such as economics or meteorology, gradually moved to computer modeling when hardware and software of su cient p o wer became available.
Within psychology, a similar move is occurring and modeling techniques appear more and more as the appropriate interface between theoretical formulations and empirical observations. For instance, in a recent i n troductory paper on mathematical models in psychology, Estes (1993) notes: \Models are essential to set the stage for tests of hypotheses about theoretical concepts." Furthermore, he adds (p. 9{10), We are dealing with complex systems in which processes or mechanisms do not exist alone. ...] Models are also essential to the analysis of complex situations. In psychological research, we are always dealing with complex systems in which a n y observed behavior can be the resultant o f many di erent, and often interacting, causal factors. Thus the outcomes of experiments can only be interpreted by comparing what is observed with what was expected from some simpli ed view of the situation, that is, a model. What appears as one major achievement of computer models is (or should be) the generation of precise and detailed predictions encompassing rich ensembles of factors from a simple and limited set of assumptions. Besides the obvious precision gain (which m a y not be in itself the most interesting feature, given the limitations of empirical techniques), we s e e t wo more important improvements that depend upon the availability of more realistic simulation models. In short, we argue that simulation models may p r o vide a partial solution to the limiting in uence of the analytical bias in empirical research and to the ubiquitous problem of observational fragility.

Avoiding analytic bias
The power of current computing technology makes it possible to develop models which apply to relatively large bodies of stimulations. In recent y ears, many published simulation studies have incorporated realistic stimulus sets.When models compare adequately in scale, one immediate consequence is the possibility o f comparing simulation and empirical results at the most detailed, ne-grained level.
The availability of real scale models makes it possible to obtain estimates of simulated performance for large sets of words, and thus to transcend some limitations associated with the standard factorial design in experimental research. Indeed, in the recent y ears, an increasing number of research t e a m s h a ve begun to augment t h e standard experimental methodologies with studies using much larger stimulus samples and multivariate statistical analysis techniques (Seidenberg, Plaut, Petersen, McClelland & Patterson, 1994Treiman, Mullennix, Bijeljac-Babic & Richmond-Welty, 1995. These methods nicely complement the more traditional approach. First, they provide a welcome relief to those enduring the torturing task of searching for appropriate language stimuli varying along many selected dimensions and controlled for even more other dimensions (Cutler, 1980). Second, they go beyond factorial manipulations in handling the combination and interaction of factors that are characteristic of the real world. Moreover, when combined with appropriate simulations, they provide extremely powerful tools to assess the ne-grained adequacy of the model. 4.3.2. Observational fragility Broadbent (1987) argued that small-scale computational models may o er a response to what he calls \the problem of observational fragility," that is, the fact that a minimal variation in task demands or experimental conditions can drastically modify the outcome of the experiment, leading researchers to question the generality of their accounts. Broadbent further suggested that this state of a airs is primarily due to the use of theoretical terms that are too imprecise and that do not capture the details of the experimental conditions or do not allow direct and explicit comparisons between predictions and observations. He illustrated the point by showing how a simple random walk model could account for the four typical result patterns observed in visual and memory search experiments, through limited variations of the model's parameters. McClelland (1988) reported another illustrative example showing how the recourse to simulation with the interactive activation model helped reconcile ndings that previously appeared contradictory.
Interestingly, observational fragility o r v ariability m a y be a problem for computer systems as much as it is a problem for experimentation. We r e c e n tly experienced such di culties in simulating the experimental results of a set of studies devoted to examining how the presence of an initial minimalmismatch in an auditory word (i.e., \shigarette," \focabulary") a ected recognition. Our ndings (Frauenfelder, Content & S c holten, 1995) suggested that such a minimal deviation did not prevent t h e activation of the target word. We then set up simulations to assess whether trace could account for the observations. Unfortunately, the implementation c haracteristics of the model (only a subset of the phoneme inventory of English is available) prevented us from using exactly the same stimuli as in the experiment. However, it was possible to run a \simulation experiment" that was close to the human situation. One intriguing result of the simulation was that the ability of the model to recover the intended word despite a minimal deviation was far from clear and varied to a large extent as a function of several factors.
With the original lexicon (which contained only about 200 words) and the parameter set provided by the authors, simulations con rmed that trace could recognize a fair proportion (75%) of stimuli with one feature onset mismatch. However, this nding was not replicated for a larger lexicon (approximately 1000 words) for which recognition performance on minimal onset deviations plummeted to below 25%. This result is quite unexpected since part of the original justi cation for the model (McClelland & Elman, 1986) was its supposed ability to activate words despite minor initial mismatches (as in the \shigarette" example). In addition, when the parameter controlling the top-down feedback from word to phoneme was turned o , the recognition rate for the original but especially for the mismatch stimuli improved considerably with the larger lexicon. Nonetheless, the words were still recognized relatively poorly with mismatching inputs (about 50% for minimal mismatches). The results suggest that, contrary to what is generally believed, trace does not reliably recognize words with minimal mismatches. Limited recognition of such stimuli can only be achieved at the expense of the key mechanism of top-down feedback required to account for lexical e ects at the phoneme level.
This example drawn from our current research illustrates several issues. One is the problem of scaling. Because the behavior of the system depends in complex ways on its database, there is little guarantee that properties observed with a limited lexicon will generalize to a larger, more realistic one. Note however that the only way to assess the in uence of corpus size is to explore it directly through simulations, and this, obviously, is only possible when a computer model is made available.
Second, it is extremely interesting that trace displays variability in its ability to recover from minimal mismatches. One could, of course, wonder whether this pattern corresponds to variability observed in human subjects. One way to answer that question would be to directly compare the performance of the computer system with the human data across stimuli, and to examine the t on a point-to-point basis.
Unfortunately this cannot be done with the current v ersion of trace. Another approach is to consider the computer system as an object of study in itself, and to use experimental and statistical techniques to identify the factors that explain the observed variability in its behavior. Frauenfelder and Peeters (1990) appealed to quantitative lexical analyses to understand the behavior of trace. Their objective w as to nd the members of the activated lexical competitor set and their in uence on the time-course of word recognition in trace. They tried to determine how the simulated recognition durations for a set of words could be predicted by di erent de nitions of the competitors of these words (for example, candidates matching the input exactly or those with a small mismatch in their onset like those in the experiments just described). The results show that competitors that match and are aligned with the target input, the cohort competitors, play the dominant role in determining the time-course of word recognition. Words with mismatching onsets did not a ect the recognition time-course. This approach of relating the simulation results to quantitative analyses of the properties of the lexicon gives the researcher some leverage to pry open the blackbox and to understand the model's behavior. Indeed, although trace can generate activation curves and word recognition latencies for each w ord in its lexicon, it is still di cult to understand how it produces these results and to predict the outcome for a new input. As we h a ve seen, the model often shows unexpected patterns of behavior. Part of the di culty lies in understanding the complex interaction between the processing mechanisms (bottom-up activation, lateral inhibition and top-down activation)postulated by i n teractive activation theory. In this context, simulation models lead us well beyond the exercise of formalizing and implementing a v erbal theory. Computer models are also of great heuristic value. As proposed by McCloskey (1991), they give us the equivalent of concrete animal models which allow further exploration, permit identi cation of neglected factors, lead to new research questions which deepen our understanding of the target cognitive system. 4.3.3. Locus of complexity Loftus (1993) expressed the concern that the availability of extremely powerful automatic computation resources would deter researchers from the quest for general and simple principles. There is unanimous agreement that theories must be simple and general. However, the notion of simplicity is itself far from transparent, and there is no accepted scale to evaluate the simplicity of a theory or a model (but see Jacobs and Grainger, 1994, for some suggestions). Furthermore, simplicity, a s a feature of the description of the system (human or arti cial) should not be confused with simplicity a s a c haracteristic of the system's behavior. Anybody who has ever approached dynamic system theories, chaos or fractals is aware of the paradoxical complexity associated with extremely simple mathematical functions.
The complexity of the phenomena that we are studying is a feature that we c a n enjoy or deplore, but we can do nothing to change it. As noted by S e i d e n berg (1993), the issue is far from new in psychology. T o quote from a classical source (Miller, Galanter & Pribram, 1960): \No benign and parsimonious deity has issued us an insurance policy against complexity" (p.182). By contrast, the use of simulation tools that embody simple mechanisms while producing complex behavior, the familiarity with their functioning and the analytic understanding of their properties is most likely to generate insights leading to simpli ed accounts.

System Identi ability
We h a ve m e n tioned previously the general problem of system identi ability: Any input-output mapping is compatible with an in nite equivalence class of algorithms. This raises the possibility that the whole enterprise of developing process models (be they verbal or computational) of cognitive abilities is futile and doomed to undecidability, unless cognitive science can provide further constraints that reduce search space. How d o w e c hoose between models that appear equivalent a s t o descriptive adequacy?
A partial response is that theoretical models should be preferred not only based on their descriptive adequacy, but also in view of other characteristics, such as their simplicity, scope, generality, heuristic value, and conformity to general principles.
Another element of response to this di culty i s t h e o b s e r v ation that theories may be confronted with a rich empirical database, including other measures than inputoutput pairings. In most research areas in cognitive psychology, c hronometric data are available, and could be used to assess the validity of theoretical models. As many authors have noted, most verbal models cannot predict latency patterns directly. Parisi and Burani (1988) argue that most verbal models are static, because they rarely specify the ne-grained operations of the hypothesized components. At t h e very best, they make predictions on nominal (the regularity e ect in visual word naming) or ordinal scales (the frequency e ect, see Jacobs and Grainger, 1994), although the dependent v ariable used is based on a ratio scale. In contrast, certain computational models 1 can predict mean latencies at the level of an interval or ratio scale and, if they involve some stochastic component, they might e v en be used to account for variations in distributions (see Grainger & Jacobs, in press).
Models of a wider generality are now appearing, that handle not only the nal state of a particular cognitive ability but also its development, its inter-individual uctuations, and its pathological deterioration. As discussed above, thanks to their speci cation of implementational details, process models can be confronted with a much richer set of observations and be submitted to more stringent empirical tests.
Finally, one additional source of constraints that may help limit the search s p a c e is the appeal to a limited set of computational principles that de ne a metatheoretical framework (or a scienti c paradigm) for information processing theories. An example of such a set of general principles is delineated by McClelland (1993 see also Plaut et al., 1996) under the acronym of \grain" (Graded Random Adaptive I n teractive Nonlinear) networks. Other principles central to this approach involve the notions of distributed representations and distributed knowledge. Obviously, neither this particular set of statements nor any other is currently universally adopted or even accepted by the scienti c community. Shouldn't we then rst focus on the abstract general principles, such as the componential structure of the system, the characteristics of information ow, or the nature of computational primitives and representations rather than building detailed models and thereby incurring the risk of getting lost in a forest of implementation details?
The trouble is that it may w ell be impossible to evaluate the validity of principles in isolation. In discussing the psychological motivations of each principle, McClelland (1993) insists on their interdependence, and a similar argument w as made by Newell (1973), in his twenty-question paper. Besides, such general abstract computational principles cannot be subjected to the empirical test of the falsi cation strategy. Rather, as argued by MacKay (1993), among others, the fundamental assumptions that de ne a theoretical framework emerge gradually and gather support through their repeated successes in generating simple, elegant and appropriate accounts of speci c cognitive and linguistic processes they are eliminated only when an alternative set of principles becomes available.
A useful illustration of this process comes from the debate between supporters of the connectionist framework and partisans of the symbolic approach concerning the acquisition of morphology. Critics of the initial simulation study have pushed the conclusion that the connectionist approach w as in principle unable to account f o r the facts of language acquisition. Yet further research (MacWhinney & Leinbach, 1991Plunkett & Marchman, 1989Plunkett & Marchman, 1990 has shown that none of the criticisms was beyond the reach of connectionist techniques. Although it is still unclear which of the current approaches has the best chances of providing the most accurate and parsimonious account of morphological acquisition, rejecting the whole frameworkbecause of the inadequacy of a particular instantiation is logically unsound. Another example can be found in an ongoing controversy about the e ect of word context upon phoneme processing. Massaro (1988Massaro ( , 1989b observed that the interactive activation model incorrectly predicted an interaction between phoneme and context information, because of the feedback connections from word to phoneme units. He thus concluded that the interactivity assumption was inappropriate. Yet, McClelland (1991) later showed that the inclusion of a stochastic component i n the network changed the system's behavior, in a way t h a t w as more compatible with empirical observations. Thus here also, two assumptions (stochasticity a n d interactivity) may h a ve i n terdependent consequences.
In sum, given the interdependency of various assumptions, modeling projects provide the most appropriate testing ground for the general principles that they instantiate. Yet designers should pay a t t e n tion not only to the descriptive adequacy of their models but also to the relation between their models and general principles. 4.5. The gardener's problem: from simulation to theory One conceptual di culty that sometimes a icts discussions of the role of modeling techniques is the con ation between the computer program and the theory. Some authors have gone as far as claiming that \Theories can be stated as computer programs" (Simon, 1992, p 152). In contrast, we consider that it is crucial to insist on the distinction and complementarity b e t ween the simulation system and the accompanying theoretical gloss. Computer simulations complement rather than replace verbal descriptions. A clear statement of this complementarity appeared in Palmer & Kimchi (1986), who argue against the notion that the computer program as such constitutes a psychological theory, and insist on the importance of the accompanying description: a running simulation is only an IP information processing] theory by virtue of the fact that it too can be described by a o w diagram plus mini-mapping theories of its components (p. 57). Their major argument is that a computer program can be described at various levels of speci cation, and that it may be di cult, without a verbal account, to decide which levels of description are psychologically relevant. This is the problem of mapping hypothetical constructs in the model onto their psychological counterparts. There is also, however, a related but distinct di culty, which w e call the redescription problem. Modelers must specify the properties and characteristics underlying the model's functioning at a level of abstractness that permits useful and appropriate generalizations. 4.5.1. The mapping problem The rst point m a y seem obvious. A model is a metaphor, and a metaphor is illuminating only as far as one clari es the relevant features that the metaphorical object shares with the target system, or better, the relevant l e v el(s) of analysis at which a correspondence may be established between the two systems. Yet, in practice, expliciting and understanding the relationship between a simulation model and the corresponding human process is far from trivial. A major cause of this di culty i s that both human cognitive processes and computer programs are complex objects that allow f o r a m ultiplicity o f l e v els of description.
One well-known reference on the issue of description levels is a well-known proposal by D a vid Marr (1982) that identi es three levels of analysis of information processing tasks. The three levels correspond to the computational description of the system (the input-output mapping that the system realizes), its algorithmic description (the algorithm used to perform the mapping) and its hardware implementation. Marr's discussion makes it clear that all three levels may contribute to the understanding of the observed phenomena: some being explicable through hardware properties (afterimages), others (the Necker cube) requiring consideration of both hardware properties and algorithmic description. Furthermore, the notion of algorithmic description masks the fact (known to everyone who has engaged in any sort of computer programming project) that an algorithm can be described with various grains, independently of the hardware speci cations (cf. Palmer and Kinchi's notion of recursive decomposition).
Given the multiplicity o fp o t e n tial algorithmic descriptions, a simulation model at the algorithmic level could in principle be constructed to match the real function at many di erent l e v els, from the most abstract level of the input-output mapping (as happens, for instance, if a regression technique was used to derive a mathematical function), to the nest-grained level of elementary processes, with all intermediate possibilities (such as, for instance, in Massaro's, 1989a, Fuzzy Logical Model of Perception, which assumes three stages of perceptual processing|evaluation of perceptual features, integration and decision|but restrict the simulation to an abstract mathematical description of the integration and decision operations). Concerning evaluation, it seems obvious that a (hypothetical) simulation model in which t h e c o rrespondence goes down to the most elementary level is better, in scope and power, than a model restricted to the most abstract level of mapping. Nevertheless, this does not mean that starting at the most detailed level is the best research strategy. As Marr suggested, it may be easier to start from a broad abstract characterization of the function, and gradually focus the microscope.
These issues pertain not only to symbolic approaches to modeling, but also to the arti cial neural networks framework. Willshaw (1995) describes a formal technique through which sets of symbolic and subsymbolic algorithms may be organized hierarchically in terms of their level of abstraction and implementation, and concludes that \symbolic and subsymbolic algorithms are not neatly divided into two distinct classes, with the one being at a 'higher' level than the other" (p. 16). 4.5.2. The description problem The problem of redescription|extracting an appropriate description of the model functioning from simulation results and knowledge of its design to allow useful generalizations|may appear more acute if one adopts the gardener's approach, though in no way w ould we argue that it is speci c to that strategy. A s w e h a ve repeatedly stated, any reasonably complex model may at some point produce unexpected behavior. Indeed, our recent results with trace illustrate one case in which the behavior of the system did not correspond to the description given by its designers. It is the job of the designers (or, for that matter, of any serious user of the model) to explore the details of the system performance, the way i t c hanges with variations of the stimulus set, or parameter values, and to provide principled and accurate accounts of how and why the system behaves the way i t d o e s .
The gardener's approach m a y, with much know-how and perhaps a bit of luck, lead to an outcome that matches the empirical observations. Still, that is only the beginning of the hard work. Simulations are not explanations. If we d o n o t understand the simulation process any more than we understand the real one, having a running simulation of a given function is of little help. To borrow from a judicious analogy introduced by F orster (1994), this would be no more helpful than having a next-door neighbor capable of predicting, without explaining how, the outcome of any experiment that we m i g h t design and run. To some extent, the problem is similar to the use of statistical data-tting techniques: A mathematical equation may provide a descriptively and predictively adequate account of some regularity, but not an explicit description of the process that produces the regularity itself, and this strongly restricts possible generalizations.
This issue has arisen in recent y ears in the context of the assessment of the distributed arti cial neural networks framework, and the discusion has centered on Seidenberg and McClelland's (1989) model of visual word recognition and naming, and its more recent derivatives (Plaut & McClelland, 1993Plaut et al., 1996. Note that the issue is not whether any of these models is empirically adequate, but rather whether they provide or even lead to adequate theories of cognitive functions. McCloskey (1991) argued that the theoretical claims formulated by Seidenberg and McClelland are vague and too general, and that the theoretical elaboration fails to describe how the network accomplishes its task, because of our limited understanding of complex connectionist networks. Yet, such a description of processing is certainly no less appropriate or informative than any other type of model currently available. As noted by S e i d e n berg (1993), \there is a rich theory here: it has only to be acknowledged" (p.233). Granted, the description leaves many details unspeci ed, it may be incomplete, the mechanics of the model is based on new and unfamiliar notions, it is implausible in some respects, and many aspects of its performance could be further explored. However, similar remarks could be made about any other modeling e ort. McCloskey (1991) concluded by arguing that the design (or, for that matter, the growing of) connectionist networks should be viewed more as analogous to the use of animal models than as simulations of theories of human cognitive functions. He further stated that, just like animal models, connectionist systems are objects of study in themselves, which m a y aid in developing theories of cognitive systems thanks to their similarity to the human system. We w ould simply add that one di erence between animal models and computer models is that the availability o f the former is limited and constrained by natural selection, whereas the latter are a orded through design principles and constrained by preexisting theoretical hypotheses. From that perspective, the study of arti cial simulation systems may b e the only way to examine the implications of a set of computational principles and assess their validity in accounting for human information processing.

Conclusions
We started our discussion by asking some simple questions: why use computer modeling in cognitive psychology? In what ways does the exercise of computer modeling techniques modify the nature of psychological research?
We consider that a de ning characteristic of cognitive psychology is the search for a particular kind of scienti c explanations that consist in accounting for the behavioral characteristics of human performance in terms of the organization and mechanisms of mental functions. Thus, empirical regularities observed in performance are used to draw a n umber of conclusions regarding a hypothetical mental function, the architecture and components it requires and its probable mode of operation, so that the empirical observations can be reduced to logical and necessary consequences of the characteristics of that mental machinery.
In this framework, it seems to us that a useful heuristic|perhaps even the only heuristic|is to create models, that is, to produce theoretical elaborations that describe the relevant c haracteristics of the function, and to explore how w ell they account for the empirical observations. The use of computer modeling is a natural and obvious extension of this endeavor. Rather than limiting themselves to a verbal description of an imaginary mechanism, designers of computer models attempt to concretize the mechanism as a computer program.
Is this modeling enterprise worth the e ort? We h a ve analyzed several types of di culties encountered in current empirical research, and have argued that computer modeling provides appropriate tools to confront these problems.
One basic problem stems from the great complexity of our object of study, that is, the graded and multidimensional nature of mental functions. Computer modeling provides a good way of dealing with this intrinsic complexity and with the dynamic nature of information processing systems. In contrast, verbal models can make only simple processing predictions and our capacity to grasp these predictions is even more limited. Very limited, indeed: those readers who have tried to present in any detail the subtleties of the dual-route model of visual word recognition to their students may know h o w limited our capacity to compute mentally the logical consequences of a (very) simple architecture may b e . F ew of us can imagine without external help the combined evolution of more than two elementary di erential equations over time.
We h a ve also argued that modeling forces researchers to elaborate more detailed and fully speci ed accounts. Although any implemented model involves many arbitrary decisions, the \full speci cation constraint" is positive pressure that may d r i v e scienti c progress. In fact, any arbitrary implementation c hoice hides a potential empirical issue: it su ces that another designer suggest a di erent solution, and that the resulting models perform di erently or lead to distinct predictions.
We h a ve also suggested that the use of modeling techniques helps delimit the space of potential explanations by enlarging the scope of theoretical accounts and also by referring to general principles of processing. By exploring the intrinsic characteristics of the model, psychologists may be led toward accounts that are more strongly motivated theoretically. Models are also concrete objects, which lend themselves to further study. Access to computational models gives psychologists collections of hypothetical devices that may be constructed, deconstructed, and manipulated at will. We h a ve illustrated how the elaboration of computer models leads to the identi cation of new research issues, and how the exploration and the systematic study of their performance may be helpful to understand the behavioral characteristics of hypothetical processing systems.
Finally, w e h a ve claimed that to be useful from a psychological viewpoint, computer programs should be accompanied by an appropriate description. Jointly these make it possible to establish how the elements of the designed system map onto the real function, and how the behavioral characteristics of the system emerge from its design features. In our view, the major change that computer models introduce into psychological research is that they allow a d y adic confrontation between empirical observations and verbal models to be transformed into a triadic and interactive confrontation between data, theories and implemented simulation systems.