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PSYCHE, 2(25), February 1995
http://psyche.cs.monash.edu.au/v2/psyche-2-25-houghton.html

1. Introduction: The Problem of Serial Order

[I]ndications ... that elements of the [sequence] are ... partially activated before the order is imposed upon them in expression suggest that some scanning mechanism must be at play in regulating their temporal sequence. The real problem, however, is the nature of the selective mechanism by which the particular acts are picked out in this scanning process and to this problem I have no answer.

2. Serial Order and Associative Chaining

2.2 To overcome this difficulty, Wickelgren (1969) suggested a form of context-sensitive chaining. Elementary actions were represented by different tokens depending on their immediate context. For example the sequence "E, V, E, R, Y" would be represented as the set of tokens $Ev , eVe, vEr, eRy, rY$, where $ is an end marker, and lower case letters represent local context. Representations based on Wickelgren's idea have proved popular with some neural network modellers (Rumelhart & McClelland, 1986; Seidenberg & McClelland, 1989). Because the approach uses tokens (e.g., standing for particular instances of each "E" in the example) rather than types (standing for the category of actions designated "E"), a chain involving a repeated action can be represented without linking one stimulus to more than one response. In Figure 1b. it is clear that by following the stimulus-response chain from left to right, the target sequence "E, V, E, R, Y" can be generated. However, the token based form of representation is immediately unappealing, because it fails to capture any relationship between different instances of the same item in a sequence. In the above example, the two "E"s are as different from one another as they are from the other letters in the sequence. In fact there is no reason why the action represented $Ev should resemble the action represented by vEr in any way. The scheme thus allows for different orderings of the 'same' actions within the same associative structure, but only by suggesting that the same actions are in fact quite different.

2.3 Context-sensitive coding deals, in a similar fashion, with the problem of the interference between sequences in the same associative structure. In this case, associative chains representing the spoken words cat, tack, and act do not interact. This is because allophonic variants of each speech sound have quite different representations in Wickelgren's scheme. For example, the /a/ in "cat" is represented by a token designated kat, whereas the /a/ in "tack" is represented by completely different token, tak. These units have been termed 'wickelphones' (Rumelhart & McClelland, 1986). The use of different tokens for variants of the same phoneme can be used to provide a weak account of coarticulation simply by assuming that each wickelphone is associated with a different articulatory realization. However, Wickelgren's account fails to provide any explanation for the similarity between the same phoneme occurring in different contexts (e.g., the /a/ sounds in cat and tack from the above example).

2.4 In addition to the unsatisfactory use of a token-based representation, Wickelgren's solution to the problems chaining models face with the representation of repeated items is incomplete. If an action is repeated with identical local context (e.g., in /kankan/), the same wickelphone must be used twice, creating the kind of looping chain shown in Figure 1a. In addition it fails to solve the problem of representing multiple sequences in the same associative structure. For example, all sequences beginning /ka.http://psyche.cs.monash.edu.au/ would begin with the same wickelphone $ka .To generate the sequence "catalyst" it would be necessary to choose between associative chains radiating from the same starting point ( "cat", "camera", "cancel" etc.).

2.5 Some recent neural network models of serial order, in particular Jordan (1986) and related work, overcome some of these problems, while retaining a dynamics dependent on chaining, in that the current output of the network is cued by a learned relationship to some record of its previous responses (or previous internal states, Elman, 1990). These models, made possible by the development of learning algorithms for non-linear mappings, include a static, sequence-specific "plan" input, which helps the networks store different orders of the same items. The use of a history of past outputs, rather than just the last one, as the cue to the next action helps to overcome repetition problems. However, the models require many exposures to sequences to learn them, precluding their use in modeling single trial learning and short-term memory (see below). They also seem to us unlikely to be prone to the kinds of serial order errors discussed below. In addition, the use of chaining still leads to interference between different orders of the same items, constraining learning capacity.

2.6 The attraction of associative chaining lies in its use of well-defined associative learning rules and its avoidance of biologically implausible, computer-based primitives such as "serial buffers" etc. Unfortunately, chaining does not provide a satisfactory basis for the understanding of many aspects of serial learning and recall, whether from long- or short-term memory. There would appear therefore to be room for a theory of serial order which possesses the attractive features of associative chaining (simple learning rules, no intrinsically ordered buffers) while avoiding its limitations.

3. Model 1: Serial Order And Response Competition

"There are indications that, prior to the internal or overt enunciation of the sentence, an aggregate of word units is partially activated or readied" (Lashley, 1951, p. 119).

3.7 In this model, envisaged as a neural network, one layer of nodes (L1) corresponds to Shallice's response schemata. The activation of a response is a continuous variable in some range, represented by the activation value of a given node. Activating inputs (from whatever source) arrive at response nodes in parallel, and more than one node may be simultaneously active. Instead of proposing that conflict resolution must take place at L1, this function is devolved to another layer of units (L2 - the "competitive filter", Houghton, 1990). In the simplest case L1 nodes can activate L2 nodes in a one-to-one fashion. The response activation in L1 is thus copied to L2. It is proposed that the severe lateral inhibitory (competitive) interactions envisaged by Shallice take place at L2, so that the initially most active node suppresses the rest. This scheme means that response selection can take place at L2, without the need to completely suppress the representation of other potentially important responses, which can remain activated at L1. The need to suppress the currently dominant response after completion (to prevent perseveration) suggests the use of some form of inhibitory feedback to L1. In principle this could be quite a complex process, depending on the internal complexity of the response. In the simplest case however, we can imagine that, once selected for output at L2, the activation of the response at L1 is no longer needed. Thus a simple one-to-one inhibitory feedback loop from L2 to L1 will cause the selected response to inhibit itself (Figure 2). Once this is done, the remaining activated responses at L1 can compete to be produced next. It is easy to see that if a set of responses are activated in parallel at L1, but with a "gradient" of activations over them representing response strength, then this mechanism, though entirely parallel in itself, will sequentially select responses in the order dictated by their degree of activation. In other words, serial order can be an emergent property of a parallel mechanism dedicated to resolving response competition.

3.8 If a mechanism with the basic characteristics described above is in place to enable an organism to order its actions in terms of some simple internal measure of response strength, then the organism could produce serially ordered behaviour from memory simply by being able to activate all the responses in some sequence in parallel, but with an activation gradient over the responses, such that the sooner the response is to be produced the more active it is. Specific models with this basic character have been proposed for a number of serially ordered behaviours (Estes, 1972; Grossberg, 1978; MacKay, 1987; Rumelhart & Norman, 1982), though with by far the greatest emphasis on one or another form of linguistic behaviour. A good example is provided by the Rumelhart and Norman (R&N) model of typing. In this model, R&N were particularly interested in the form of typing errors and how they could constrain models. Error data (e.g., MacNeilage, 1964; MacKay, 1970, 1972; Norman, 1981; Reason, 1984) have played an especially important role in the development of the serial order models described below. For instance, many typing errors are transposition errors of the form "trap" ->"tarp". Transposition errors are common in many serial order tasks (e.g., immediate verbal recall tasks) and are highly problematic for most conventional models of serial order. Consider what has to happen to produce the error "trap" ->"tarp". First, at the point at which the "r" should be produced two things occur: the "r" is not produced, but the "a", which should occur later, is produced instead. This provides evidence that upcoming responses are already active before the point at which they are to be produced. Second, at the point at which the "a" should be produced two further things happen: the "a" is not produced in its correct position (i.e., it is not repeated), and the "r" which was omitted at position 2 is now produced. These events provide evidence that the "a" response produced at position 2 has been suppressed, preventing its occurrence at its appropriate position. If this were not so, this would produce an error such as "taap" or "taarp", forms which are rarely, if ever, found. The idea of suppression is further supported by the appearance of the "r" in position 3, indicating that, not having been produced at position 2, it has remained active.

3.9 The Rumelhart & Norman model is outlined in Figure 3. The model is hierarchical, in that specific sequences are represented as "chunks", i.e., sets of individual responses bound together by connections to a higher-level node which spans the chunk. The chunks in the model correspond to words (or parts of words). When a word is to be produced nodes representing the letters in the word are equally activated in parallel by word-to-letter connections. Letter nodes in a chunk have lateral inhibitory connections between them such that each one is inhibited by those nodes representing letters which are to precede it (a scheme suggested by Estes, 1972). The first letter therefore receives no inhibition and later letters receive progressively more. Thus the net excitation (excitation from the word node minus inhibition from letter nodes) received by a letter node decreases the later in the word it is to be produced. This induces an activation gradient over the letter nodes. In combination with a select-and-inhibit mechanism of the type described above (Figure 2), this parallel activation generates serial output.

Figure 3
Schematic diagram of the Rumelhart and Norman (1982) Typing model.

3.10 The R&N model produces errors by the addition of noise to letter node activations. Transposition errors occur when the wrong letter node becomes the most active at the wrong time. Given the activation gradient, this is most likely to be the letter to be produced at the following position - thus most transpositions involve adjacent letters, as is found in the human data. After the wrong response has been produced it is automatically inhibited, preventing it being repeated at its correct position. The omitted response remains active however, allowing it to win the output competition at the next position. The model thus produces these errors quite naturally, in an intuitively satisfying way. R&N also model other a priori puzzling error types, such as "doubling shift" errors of the form "screen" -> "scrren" (discussed in more detail below). In addition, the parallel response activation in the model is independently motivated by its use in modeling co-articulation effects in typing, in which the hand configuration adopted by the typist while making one response is affected by the location (on the keyboard) of upcoming key presses.

3.11 The R&N model illustrates the explanatory value of a serial order model based on the resolution of parallel response competition. What, though, is its status as model of memory for serial order? This question involves the internal representations (connection patterns, in this case) by which it generates the necessary activation gradient over the response set. This has two components. One component, the word-to-letter connections, provides equal excitation to all letters in the word. As this is the only activation letter nodes receive, this input specifies item information, i.e., what letters are in the word. The other component, the lateral inhibitory connections, specifies order information (the activation gradient). This latter component is problematic, for reasons similar to the problems with chaining models discussed above. To be plausible, the model must represent the spelling of all words (or, at least, plausible subword chunks) with the same set of letter nodes. Many words obviously contain the same letters in different orders (e.g., trap, part, rapt). The lateral inhibitory connection pattern needed to specify one of these orders is obviously different from that required for the others. If all the patterns are simultaneously present in memory then they will clearly interfere with each other. Indeed, since the word nodes for the above three words all activate the same letters to the same degree, the lateral inhibitory pattern due to the representation of all three words in memory will lead to exactly the same letter node activation pattern whichever word node is active. Other problems arise for instance in words containing repeats, such as "prop", in which the "p" is first and last, and hence must be simultaneously the least and most inhibited letter. In these cases, R&N have to parse the sequence by making divisions on the occurrence of (non-immediate) repeats. Although such a chunking scheme has some attractions (see Keele & Jennings, 1992, for a similar proposal), it can lead to parsings of words which are not the most intuitively appealing, e.g., trot -> (tro)(t), leaning -> (leani)(ng), disastrous -> (disa)(strou)(s), nonetheless -> (no)(neth)(el)(ess).

3.12 Rosenbaum, in his book on motor control (1991; p. 285), says of the Rumelhart and Norman model that "It represents an important advance in the modeling of human motor control and should serve as a useful starting point for future research". Below we develop models which show similar behavioural characteristics, but which do so on the basis of learned representations of serial order that do not have the problems discussed above.

4. Model 2: Response Competition Under Internal Modulation

4.2 This scheme still faces problems however. One the one hand, the suppression of responses after production makes difficult the storage of a sequence such as prop, as the letter p has to be produced twice. The arrangement shown in Figure 4 would simply produce pro. Conversely, there is also the problem of the undesired reactivation of previously executed responses. Though suppressed, they will continue to receive activation from the word node while it is still on. If suppression decays (as it surely must), then this top-down activation could be sufficient to reactivate items produced early in the sequence (which receive the strongest inputs). This problem would become worse the longer the sequence to be stored.

4.3 Recent CQ models incorporate an important development aimed at solving both of the above problems (Houghton, 1990). The basic idea is to use a dynamical representation of serial position at the level above the items to be sequenced. We may refer to this level in the general case as the "sequence" or "control" level. In the Rumelhart and Norman model, no positional information (i.e., information as to where one is in the sequence) is available from a word node, as this comes on at the beginning of the sequence and then stays on without varying. Sampling of the state of a word node tells one whether the sequence that node stands for is being produced, but not what point in its execution has been reached. Positional information can be incorporated into these models by abandoning the assumption that activation at the sequence ("word") level should be (i) static, and (ii) unidimensional. That is to say, one permits a sequence to be controlled by the activation of a set of "sequence nodes" whose state of activation varies in some regular way during learning and execution of a sequence (Burgess & Hitch, 1992). Formally, the activation of the sequence level, rather than being a scalar constant, becomes a time-varying vector, which we may refer to for convenience as the "control signal". (Figure 5). This vector can be used to implicitly encode positional information. During learning, different states of the signal become associated with different response states, according to simple learning rules (Houghton, 1990). This adds an endogenously dynamic element to these models, so that, in Lashley's words, the input is "never into a quiescent or static system".

Figure 5
Recall in Competitive Queuing (CQ) models employing a time-varying "Control Signal" (CS). The shaded vertical bars in the graphs represent the degree of activation of nodes representing the letters P, R,O during recall of the sequence prop. At each time (t3d1-4), the most active response is selected and subsequently inhibited. the shaded horizontal bar represents the control signal, conceived of as a time-varying vector. The shading of the bar represents the "degree of activation" (magnitude) of components of the control signal vector. Darker shading represents more activation. Different responses are associated with different states of the control signal, and repeated items may be associated with more than one state. This is shown by the arrowed lines from the CS to the letters. The crucial factor in generating the characteristic CQ activation gradient (responses being more active the sooner they are to be produced) is that the state of the control signal changes smoothly and monotonically, being more similar to itself at closer positions in time.

4.4 With this mechanism, a sequence such as PROP can be stored because the two occurrences of the letter P are associated with different states of the control signal. This is illustrated in Figure 5. Here the control signal is represented schematically by the shaded horizontal bar, the degree of shading representing degree of activation, and the change in shading representing changing activation. The arrows from the control signal to the letters represent associations between particular components of the signal and those letters. The P node is activated twice, the first occurrence activated by the "start state" of the signal, and the second by the signal moving towards its end state. The same mechanism solves the problem of the undesired reactivation of responses. If the control signal changes quickly enough, or a response node discriminates sufficiently between successive states of the signal, then a suppressed response will not be reactivated because the evolving state of the control signal will soon cease to be strongly associated with a response once its target "position" has passed. For instance, in Figure 5, the end state of the control signal, which reactivates the P, is not strongly associated with the R, which remains suppressed. If the target word were, say, PROD, then the P would not be associated with the end state and would not be reactivated.

4.5 An important constraint on the form of the control signal is that it should be temporally correlated (more similar to itself at nearer points in time) in order to produce the characteristic CQ activation gradient, whereby responses are more active the sooner they are to be produced. If the CS has this property, then any given state will partially activate responses associated with similar states, and these responses will be ones that occurred at similar times or positions. This is indicated in Figure 5 where the shaded bar changes gradually.

4.6 How complex does the control signal need to be? In the absence of additional specific constraints, it seems desirable to investigate the properties of the simplest that are likely to work. Work by Houghton and colleagues (Houghton, 1990, Houghton et al., 1994) has shown that a control signal generated by two nodes, one starting with high activation and then falling (a "start" node), and the other starting with low activation and then increasing (an "end" node), can encode sequences of lengths up to around seven or eight items, including ones with repeated items. Houghton et al. (1994) use this form of control signal in a model of lexical spelling. The signal is smoothly correlated in time, generating an activation gradient similar to that of the Rumelhart and Norman model, but without the use of sequence specific lateral connections. These models show that it is not necessary to use a "discrete" positional representation, i.e., one in which specific nodes represent specific positions, though such a representation is compatible with the general approach. Burgess and Hitch (1992) use a more powerful "distributed" representation of position (referred to as the context) in which individual nodes represent more than one position, and each position is represented by more than one node. This model is especially effective for single-trial serial order learning, but the complexity of control signal begs the question of its origin.

4.7 The idea that serial behaviour might depend on the existence of such internal dynamics relates to similar ideas in models of time perception, in which the endogenous activation (the internal "clock") is typically generated by oscillators (Church & Broadbent, 1990; Treisman, Cook, Naish, & McCrone, 1994). Similarly, motor sequencing in many species has been found to depend on the generation of repeating patterns of activity by groups of neurons known as "central pattern generators" (Pearson, 1993). The neurons in the pattern generators are distinct from the motoneurons controlling individual responses. Recent work by Burgess, Hitch and colleagues has suggested that the internal signals required for learning and recall in their short-term memory model might be composed of oscillators entrainable to the rhythmic characteristics of the input sequence (Hitch, Burgess, Towse & Culpin, 1995; Hitch, Burgess, Shapiro, Culpin & Malloch, 1995).

4.8 Such mechanisms have been applied in a number of a domains including speech production (Houghton, 1990; Hartley & Houghton, in press), auditory-verbal short-term memory (Burgess & Hitch, 1992; Burgess, 1995; Glasspool, 1995; Hitch, Burgess, Towse & Culpin, 1995; Houghton, Hartley & Glasspool, in press), speech errors in immediate nonword recall (Hartley & Houghton, in press), and serial order errors in spelling (Houghton, Glasspool & Shallice, 1994; Shallice, Glasspool & Houghton, in press). Full review of this work is beyond the scope of the current paper. Instead we will concentrate on two issues covered in this work which provide important sources of constraint on serial order models. The first involves the problem of single-trial serial learning, the second the importance of error data in recall.

Serial Order and Short-Term Memory

Errors in Serial Recall: The Problem of Repetition

5. Serial Order and the Origins of Grammar

"This is the essential problem of serial order: the existence of generalized schemata of action which determine the sequence of specific acts, acts which in themselves or in their associations seem to have no temporal valence" (Lashley, 1951, p. 122).

5.12 In this model, the serial order of phonemes during recall is governed by the cyclical activity of the syllable template. As in the CQ models discussed above, this template is formally a time-varying vector, and acts as a kind of control signal. However, the template does not lead to the activation of specific responses, as in Houghton (1990). Instead, its states are associated with whole classes of responses (phonemes). Which of the set of possible phonemes is to be produced is specified by a separate "content" input. This factoring of serial order information into a separate system means that the endogenous dynamical signals used in such CQ models as Houghton, 1990, Houghton et al., 1994, does not have to be repeatedly represented for every sequence learnt. This represents a considerable simplification, and is only possible in cases where the set of sequences to be learnt conforms to some underlying pattern which can be abstracted; in other words, where there is a grammar.

5.13 Whether such principles can be extended to sequencing outside the linguistic domain depends on whether other forms of action sequencing are susceptible to grammatical analysis, i.e., whether particular sequences can be seen as instantiations of an underlying schema defined, at least in part, in terms of variables. Error data from slips of action in normal subjects (Norman, 1981; Reason, 1984), and acquired disorders of action planning (e.g., Lhermitte, 1983; Luria, 1973; Schwartz, Reed, Montgomery, Palmer, & Mayer, 1991) support the idea that the kinds of sequencing principles we have described can be applied to action sequences generally. For instance, transposition errors in routine actions are commonly found in patients with frontal apraxia. According to Schwartz et al. (1991), such patients are frequently recorded to put on their shoes before their socks, or to put toothpaste onto a tooth brush after having brushed their teeth. Cooper et al. (1994) describe a "hybrid" symbolic-connectionist model of routine action (based on Norman & Shallice, 1986) aimed at understanding such action slips. Routine actions are controlled by schemata activated in parallel, which compete for control of action on the basis of their activation values. Serial behaviour emerges from the model due to schemata being inhibited once their corresponding goals have been achieved. Elements of schemata contain variables which need to be given specific values during execution, for instance "arguments" representing the object on which an action is to be performed. Argument selection is based on activation levels of (representations) of objects, and how well they fit a "feature specification" associated with the schema. This is similar to the mechanism of phoneme selection by the syllable template (or "schema") in the Hartley and Houghton (in press) verbal recall model.

5.14 In addressing the issue of grammar last we do not intend to suggest that schema based sequencing is particularly exceptional or rare, though we do believe that the human capacity for it is greatly developed compared with other animals Indeed, it is nongrammatical sequencing, as found in the single-trial learning of lists of items all belonging to the same class, that may be the comparatively unusual behaviour. The reason these models are addressed last is simply that they are the most complex, and the way in which they explain particular data presupposes that, independently of the operation of the schemata for order, groups of competing responses are being activated in parallel. Why should that be? The explanation we provide is that this parallelism represents one aspect of a more "primitive" form of sequencing. The development of schema based sequencing has not supplanted these basic mechanisms, rather it operates in conjunction with them. This has benefits. First of all, one should be aware that English is a somewhat unusual language in that its word order is highly constrained ("schematised"). Many other languages show much "freer" word order, by which it is meant that constituents in a sentence with a given meaning are not bound to appear in a single particular order (Givon, 1979). Of course, in any actually spoken utterance of such a language, all constituents do appear in some definite order. What determines this order, if it is not completely specified by grammatical schemata, and how does this ordering interact with grammatical ordering? One possibility is that all influences on order, grammatical or otherwise, act on the same competitive queueing output system. The resultant order reflects the relative strengths of these influences, with more strongly activated items appearing earlier (Prentice, 1966; MacWhinney, 1977; Sridhar, 1989). Another benefit of this interactive view of sequencing is that if control by grammatical schemata becomes disorganised or weakened (as may be the case for instance in agrammatism, Saffran, Schwartz, & Marin, 1980; or the frontal apraxia discussed above), the simpler, competition based, mechanisms still ensure that serial behaviour is possible, as long as concrete responses are activated. By contrast, production system models based on symbolic action grammars plus serial recursive processes (e.g. Houghton & Isard, 1987) are completely dependent on the grammar for the specification of the order of actions. If this mechanism breaks down, no behaviour can be produced.

6. Conclusions

"I have devoted so much time to ... the problem of syntax ... because the problems raised by the organization of language seem to me to be characteristic of almost all other cerebral activity...Not only speech, but all skilled acts seem to involve the same problems of serial ordering, even down to the temporal coordination [of] such a movement as reaching and grasping. Analysis of the nervous mechanisms underlying order in the more primitive acts may contribute ultimately to the solution even of the physiology of logic" (Lashley, 1951, p. 122).

Acknowledgements

Notes

References