Christopher D. Green & Ellen Munro

York University

©1995 by Chirstopher D. Green & Ellen Munro


Implicit learning for verbal strings generated by a finite state machine (FSM) has been demonstrated repeatedly.  No one, however, has investigated whether such learning can take place when the information to be learned is spatial in nature.  In this study, subjects learned sequences of FSM-generated spatial information displayed on a 3´3 grid. They were able to learn these sequences faster than subjects similarly set to learn random spatial sequences.  As is typical in implicit learning studies, although the subjects in the experimental group were unable to articulate the rules governing the sequences, they were nevertheless able to distinguish new grammatical strings from random ones at a rate far above chance.


Reber (e.g., 1967, 1969, 1976, 1993) pioneered the study of the learning of artificial grammars in the 1960s and has continued to work on it to the present day.  Because he believes his subjects to be learning the structure of such grammar unconsciously -- a very controversial position -- he dubbed the phenomenon "implicit learning." (We use the phrase "implicit learning" in this paper, but remain largely neutral on the question of whether it is unconscious and abstract as Reber claims.)  In the present research we sought to demonstrate the existence of implicit learning in the spatial domain.

Subjects in the typical implicit learning experiment paradigm first learn sets of approximately 20 strings of three to eight written letters. Although these letter strings appear to be random, they have, in fact, been generated by a Finite State Machine (FSM) such as the following:

Figure 1. Finite State Machine used by Reber (1967) and in the present study.  The single letters (T, P, V, X, and S) were used by Reber.  The parenthetical letter-pairs denote locations on the 3´3 spatial grid used in this study (BR=bottom-right, TM=top-middle, TR=top-right, ML=middle-left, and BL=bottom-left).

To produce a string with an FSM one begins at the "start" arrow at the left, and traces around the diagram in the direction of the arrows until one reaches the “end” arrow on the right.  Each transition from one state (circle) to another generates a letter which is added to the end of the string generated thus far.  For instance, some of the letter strings possible with this particular FSM include:

TTS                 TPTS               TTXVS
VVS                VXVS              VVPS

Reber's (1967) main finding was that his subjects could memorize the letter strings generated by the FSMs (i.e., "grammatical" strings) more readily than they could learn truly random letter strings  (see Figure 2). Still, the subjects were typically reported being unaware of any pattern to the letter strings they had learned.  Even after being told explicitly that the strings they had learned were governed by "a complex set of rules" they were unable to give anything but the vaguest characterization of the strings' structure. Although subjects reported being unable to articulate the rules underlying the grammatical strings when asked, when given a forced-choice task with strings they had not previously seen, they were  able to correctly distinguish strings that had been generated by the same FSM from random strings at a rate of nearly 80%.

Figure 2. Implicit learning curves from Reber (1967).  All subjects improved with experience, but the group learning the grammatical strings was faster overall. The interaction was also significant.

Almost immediately the question arose of whether the subjects were learning the "deep" structure of the strings, or just surface features.  To test this Reber (1969) had two groups of subjects learn strings generated by two different FSMs.  He then had half the subjects from each group learn new strings that were generated by the same FSM, but used different symbols  (e.g., replace all the Ts in Figure 1 with Qs, all the Vs with Bs, etc.). The other half of each group learned strings that used the same symbols, but had been generated by an FSM with a different structure.  He found that the subjects who were presented with the strings governed by the same FSM learned the new strings faster, even though they employed new symbols.  The subject learning stings with the old symbols but a new structure, by contrast, were significantly slower.

Another early criticism of Reber's work was that the subjects were learning the structure explicitly, but covertly, and for some reason reluctant to reveal their knowledge to the experimenter (perhaps because it was know to the subject to be imperfect). To test this Reber (1976) told one group of subjects that the strings were governed by a complex set of rules at the outset of the procedure and explicitly instructed them to figure out what rules governed the strings.  A second group underwent the standard procedure.  The performance of the subjects in the explicit condition was worse at both the learning task and the identification of new grammatical strings than that of the subjects in the standard “implicit” condition.

These effects have been replicated and elaborated upon many times in the intervening decades and, although no one seriously doubts the effect, per se, many continue to challenge the idea that the subjects learn the abstract structure (or "grammar") of the strings unconsciously (see, e.g, Brody, 1989; Brooks, 1978; Dulany, Carlson, & Dewey, 1984; Perruchet & Pacteau, 1990; Redington & Chater, 1996; Shanks & St. John, 1993. See also Reber's responses: 1989a, 1989b, 1990, 1992; Reber & Allen, 1978; Reber, Allen, & Regan, 1985; as well as Lewicki & Hill, 1989).  Reber (1993) continues to defend his belief in unconscious abstract learning.

It is not the aim of the present paper to enter into the debate over the correct theoretical interpretation of the phenomenon but rather to extend it to a new domain.  Although implicit learning of verbal material has been demonstrated many times (typically visually, but see Green & Groff, under review, for an extension into the auditory verbal realm), few have ever investigated whether it occurs in modalities other than the verbal. 

One near-exception is the work of Lewicki and his colleagues (Lewicki, Czyzewska, & Hoffman, 1987; Lewicki, Hill, & Bizot, 1988). They had subjects identify the locations of numerals in 2´2 tables.  Unbeknownst to the subjects, the location of the numeral in every seventh trial was primed by its location in some of the previous trials.  Although subjects were apparently unaware of this information -- even sophisticated subjects who suspicious of subliminal manipulation were questioned very specifically about it (Lewicki, et al., 1988) -- their performance improved with experience faster than when the location of the numeral in the seventh trial was not so-primed.  What is more, when the regime of subjects who had been presented with the priming information was changed so as not to prime the location, the subjects’ performance immediately deteriorated to a level worse than that of those who had never received the priming information.

Although Lewicki’s work is interesting and relevant to the present study, it was the primary aim of this research to discover whether, and to what degree, traditional  FSM-governed implicit learning can occur when the material spatial in nature.  To investigate this we used FSMs similar to those used in standard implicit learning experiments, but had them generate sequences of light in different areas of a 3´3 visual display rather than elements of arbitrary letter strings.




The subjects were twenty volunteers from undergraduate psychology classes.  They were paid a small fee to participate.  No course credit was given.


The apparatus consisted of a standard personal computer work station in a well-illuminated room.  On the screen of the computer’s monitor was displayed a 3´3 grid of about 4.5 in.´4.5 in. in size (screen black, lines white). The strings to be learned consisted of sequences of individual squares in the grid lighting up in medium blue for 0.5 seconds each, interspersed with 0.5 second gaps between elements of a given string.  The sequences were six to eight items long.  The grammatical strings were generated by the FSM shown in Figure 1.  In order to achieve maximal superficial similarity between the grammatical and random strings (so that the random ones could not be easily identified by a single uncharacteristic element), the random strings began and ended with the same squares as the grammatical ones, and they contained only those squares that were contained in the grammatical strings (but, of course, in random rather than grammatical order).


The subjects were welcomed to the lab and seated at the computer station normal reading distance (approximately 30 cm) from the monitor.  Instructions for the first phase of the experiment appeared on the screen and were read aloud by the research assistant while the subjects followed visually.  They read:

In the first part of this experiment, you will see a 3x3 grid on the screen.  Six to eight squares in the grid will light up, one after another.  Try to learn this pattern exactly as you see it.  You will be asked to reproduce it on the number pad of the keyboard.

Subjects were then allowed a few practice trials (until they learned one sequence correctly).

In this phase of the procedure (hereafter, the “learning phase”), 18 strings were presented in pairs.  A beep marked the break from one member of the pair to the next.  After both members of the pair had been presented, the subject was required to tap in the correct spatial sequence on the number pad of the keyboard which had been specially marked to resemble the grid on the screen.  The subject was required to learn both elements of each pair before moving on to the next pair.  This continued until all 18 strings had been learned exactly. The 18 strings used in the learning phase were chosen randomly for each subject from among all those strings of 6 to 8 items in length possible for this FSM.

Next, the subject was told that the strings s/he had just learned were not, in fact, random but had been generated by what we called “a complex set of rules.”  The subject was then asked to articulate the rules if s/he could.

To begin the final phase of the procedure (hereafter, the “test phase”), new instructions were displayed on the screen for the subject.  They read:

You will now be shown 32 more patterns.  You do NOT have to learn these.  You only have to guess whether they were organized by the same rules as those you learned before, or by other rules.

If you believe that a particular pattern follows the same rules as those you already learned, press the Y in the lower left of the keyboard.  Press it now.

And then, after correctly pressing the "Y" button:

If you believe that particular pattern does NOT follow the same rules are those you learned, press the N in the lower right of the keyboard.   Press it now.

The subject was then shown 32 more strings on the monitor, one at a time, and asked to identify those that were thought to have been generated by the same set of rules as those that governed the strings seen in the learning phase.  When this was complete the subject was debriefed, thanked, and paid for participating.



Figure 3 plots the mean number trials it took subjects in the two groups (grammatical and random) to learn the 9 pairs of strings in the learning phase.  The random group took, on average, more than 8 repetitions to learn the first pairs of strings whereas the grammatical group took about 7.  Although the performance of both groups improved over the course of the learning phase, the random group’s performance reached asymptote at between 5 and 6 repetitions to learn a pair, whereas the grammatical group’s performance improved to the point that it took only 3 to 4 repetitions to learn a pair of strings.

Figure 3. Implicit learning curves from the experiment. Both groups improved with experience, but the grammatical group learned more quickly than the random group.  There was no significant interaction.

A two-way ANOVA with one repeated measure (pairs) showed that both groups learned the strings significantly faster with more experience (F(8,144)=3.94, p<.0005) but that the grammatical group learned marginally faster overall (F(1,18)=3.96, p=.062).  The interaction was not significant (F(8,144)<1.0, N.S.).

When told that the spatial strings were structured by a “a complex set of rules,” the subjects were unable to advance any serious speculations concerning the nature of that structure.  The best answers identified the squares that had been used (or those that had been not used), but even this would not distinguish between the grammatical and random strings because of the way the random strings had been constructed (see above).  The vast majority of response were far less specific than even this.

For the test phase of the procedure, the number of correct identifications of grammatical strings (Hits) and the number of incorrect identifications of random strings (False Alarms) were computed, The difference was taken between these two numbers (H-FA) for each subject.  The expected value of this number (under the assumption that no learning had taken place) is 0.  The highest possible score is 16 (16 Hits-0 False Alarms). The highest obtained score was 14, from a subject in the grammatical group. The lowest was -8, from a subject in the random group.  The random group's mean H-FA score was  -2.4. This was not significantly different from 0 (t(9)=1.18, N.S.).  The grammatical group’s mean H-FA score was 6.4. This was significantly above 0 (t(9)=3.13, p=.01).  It corresponds to a 70% rate of accuracy, a level similar to that typically found in studies of verbal implicit learning.  A t-test for the difference between the mean H-FA rates of the two groups was, of course, significant as well (t(18)=4.312, p< .0005).  The results of the test phase are plotted in Figure 4.

Figure 4. Results of identification task in the experiment.  The grammatical group correctly identified significantly more new strings (as being grammatical or not) than the random group.



Many past studies have shown implicit learning for visual verbal material.  Lewicki et al. (1987) and Lewicki et al. (1988) were able to show a phenomenon seemingly akin to implicit learning for very simple spatial sequences, but did not employ Reber's traditional FSMs to generate the stimuli.  In this study, we set out to discover whether traditional implicit learning, using FSMs, is possible in the visuo-spatial modality. 

We found that implicit learning for FSM-governed spatial strings seems virtually identical to that found for verbal sequences: (1) subjects learn grammatical spatial strings faster than random ones, (2) they are, for all intents and purposes, completely unable to articulate the rules that govern the strings, and (3) they are nevertheless able to distinguish new grammatical strings from random ones at a rate of a 70%, far above chance and far above that of subjects who learn random strings.

Future research should try to extend the implicit learning phenomenon to new sensory-cognitive modalities (e.g., melodic sequences, color patterns).  It should also test whether subjects are able to transfer knowledge gained in one sensory-cognitive modality to new, highly diverse ones (e.g., can traditional verbal implicit learning be transferred to similarly organized spatial information?).  If so, this would confirm Reber's claim that the information learned by subjects in the implicit learning procedure is relatively abstract in nature.


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Author Note

This research was conducted with the assistance of an Individual Research Grant from the Natural Sciences and Engineering Research Council of Canada.  Correspondence concerning this research, including the computer materials used therein, may be addressed to Christopher D. Green, Department of Psychology, York University, North York, Ontario, M3J 1P3, CANADA; e-mail:; World Wide Web homepage: