Implicit Transfer of Reversed Temporal Structure in Visuomotor Sequence Learning


  • Kanji Tanaka,

    Corresponding author
    1. Research Center for Advanced Science and Technology, The University of Tokyo
    2. Japan Society for the Promotion of Science
    • Correspondence should be sent to Kanji Tanaka, Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8904, Japan. E-mail:

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  • Katsumi Watanabe

    1. Research Center for Advanced Science and Technology, The University of Tokyo
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Some spatio-temporal structures are easier to transfer implicitly in sequential learning. In this study, we investigated whether the consistent reversal of triads of learned components would support the implicit transfer of their temporal structure in visuomotor sequence learning. A triad comprised three sequential button presses ([1][2][3]) and seven consecutive triads comprised a sequence. Participants learned sequences by trial and error, until they could complete it 20 times without error. Then, they learned another sequence, in which each triad was reversed ([3][2][1]), partially reversed ([2][1][3]), or switched so as not to overlap with the other conditions ([2][3][1] or [3][1][2]). Even when the participants did not notice the alternation rule, the consistent reversal of the temporal structure of each triad led to better implicit transfer; this was confirmed in a subsequent experiment. These results suggest that the implicit transfer of the temporal structure of a learned sequence can be influenced by both the structure and consistency of the change.

1. Introduction

Implicit learning of behavioral sequences is common in our daily life. Implicitly acquiring skills improves our cognitive abilities (e.g., language usage, playing the piano, typing on a keyboard, and driving a car), and how people implicitly learn behavioral sequences has been a key question of interest in cognitive science (Abrahamse, Jiménez, Verwey, & Clegg, 2010; Perruchet & Pacton, 2006). Several implicit learning paradigms have been studied (e.g., Serial Reaction Time [SRT] task, Nissen & Bullemer, 1987; visuomotor button press task, Sakai, Kitaguchi, & Hikosaka, 2003; artificial grammar learning [AGL], Reber, 1967; Pothos, 2007). Most studies have claimed that people learn not only the elements of a sequence but also a higher-order structure of that sequence. For example, Stadler and Neely (1997) showed that the structure of a sequence had a larger impact than the length of that sequence on learning in the SRT task. Thus, they suggested that some structures in response sequences are easier to learn than others (see also Cohen, Ivry, & Keele, 1990). In the visuomotor button press task, Sakai et al. (2003) observed that when an order of element sequences was shuffled whereas individual elements remained identical, performance became slow and inaccurate. These results suggested that a higher-order sequence (i.e., a sequence of element sequences) was learned. In the AGL task, people might implicitly learn fragments or chunks of two, three, or four letters (e.g., Perruchet & Pacteau, 1990; Servan-Schreiber & Anderson, 1990).

Previous studies have reported that people discriminate reversed or mirrored temporal structures of musical melodies, even when unaware of the structure (e.g., Dienes, Kuhn, Guo, & Jones, 2012). For example, Dienes and Longuet-Higgins (2004) used sequences of 12 tones, where the first six tones were randomly generated and the second six tones were altered from the first tones with some specific rules. Participants were told that the melody they heard during the learning phase obeyed some specific rules, and in the test phase, participants were asked to classify whether the musical melody they heard obeyed the rules. The results showed that people who had background experience with atonal music could implicitly detect transformed melodies (e.g., reversals). Similarly, Kuhn and Dienes (2005) observed that trained participants preferred mirrored melodic structures to non-mirrored structures; this was referred to as a structural mere exposure effect (see also Jiang et al., 2012). Taken together, these results indicate that people can implicitly learn abstract rules of melodies.

In this study, we were interested in whether the type and consistency of an alternation rule would influence the implicit transfer of visuomotor sequential learning. Much of procedural and sequential learning in daily life includes two stages of processing: the controlled exploration of patterns and the process of automatization after a pattern has been discovered (Anderson, 1982). To investigate the effects of the alternation rule on implicit transfer in sequential learning (in a condition similar to everyday situations), we employed a sequential button press task (e.g., Hikosaka, Nakamura, Sakai, & Nakahara, 2002; Hikosaka, Rand, Miyachi, & Miyashita, 1995; Hikosaka et al., 1996). Hikosaka et al. (1999) reviewed the characteristics of this type of visuomotor sequence learning task and summarized that the early trial-and-error stage was controlled and explicit processes and those in the late learning stage were automatic and implicit. In this study, a fixed visuomotor sequence of seven triads of button presses was generated for each participant. After participants learned the sequence by trial-and-error, they were required to perform another sequence, in which all the triads were generated by a specific alternation rule. We prepared three alternation rules, where an order of the triad was reversed (hereafter called “reversal rule”), partially reversed (hereafter called “partial reversal rule”), or switched without overlap (hereafter called “no-overlap rule”). In 'Experiment 1', our interest was whether the implicit transfer of a learned sequence would depend on the type of change in the components of that sequence.

2. Experiment 1

In Experiment 1, we investigated the effects of the type of alternation rule on the response order within each triad of implicit transfer. In the first block, participants were required to complete visuomotor sequence learning without any instruction. In the subsequent block, all response orders of the triads within the sequence were consistently reversed, partially reversed, or non-overlapped.

2.1. Method

Sixty-six right-handed participants (35 males, 31 females; Mage = 21.3 years, SD = 2.62) participated in the experiment. All participants had normal or corrected-to-normal visual acuity, normal motor functions, and were naïve to the purpose of this study.

We adopted a basic experimental paradigm used in previous studies (e.g., Watanabe, Ikeda, & Miyao, 2010). The experimental device consisted of 16 LED buttons mounted in a 4 × 4 matrix and another LED button (called the “home key”) at the bottom (Fig. 1A). Participants used their right index fingers to press the buttons. When participants pressed the home key for 500 ms (Fig. 1B), three buttons turned on simultaneously (Fig. 1C). Participants were required to press the illuminated buttons in the correct order, which they uncovered through trial-and-error. If the button presses were successful, the LEDs turned off, one by one, and a different triad was illuminated, for which the participants were again required to discover the correct order. When participants pressed the wrong button, all LEDs were briefly illuminated, and then had to restart from the home key. Seven triads were presented in a fixed order to comprise a sequence. A trial was considered successful when participants completed the sequence. The same sequence was repeated until participants completed it successfully for 20 times (called a “block”; see Fig. 1D). Participants were required to perform the task as quickly and accurately as possible.

Figure 1.

Experimental device and schematic flow of this study. Participants were instructed to learn the correct order by trial-and-error. The LED buttons were square in shape (10 × 10 mm) and 8 mm apart. (A) The experimental device used in this study. (B) The status that the home key was turned on. (C) An example of a triad, with three of 16 LED buttons turned on simultaneously. (D) Flow diagram of the present experiment. Left flow shows a main flow and right flow shows the flow of the sequence function. A rounded rectangular corner indicates the terminal (i.e., start and end). A normal rectangle shows the process and a rhombus shows judgment of the operation. The next operation follows an arrowed process (i.e., “yes” or “no”). The “sequence” in the rectangle with two lines (on the left side) refers to the defined function (the sequence function on the right). Participants were required to discover a correct order by trial-and-error. A trial was considered successful when participants completed a sequence, and a trial was considered an error when participants pressed the wrong button in all the triads. For example, if participants press the wrong button in Triad 5, they would need to start over from the home key. A block is finished when participants successfully completed a sequence 20 times. (E) The order of the button press in each sequence. The Original sequence was randomly generated for each participant. For each triad, the three buttons were defined in ascending order of [1][2][3]. In other sequences, the spatial configurations of the triads were the same, but the sequence of the correct order of button presses was changed. The participants needed to press the buttons in an order of [3][2][1] with the reversed, [2][1][3] with the partially reversed, and either [2][3][1] or [3][1][2] with the no-overlap sequences. Note that the number shown on the LED button was not displayed during operation.

We prepared four types of sequences: “Original,” “reversed,” “partially reversed,” and “no-overlap” (see detail, Fig. 1E). All participants first performed a block with the Original sequence and then a block with the reversed, partially reversed, or no-overlap sequences, which were randomly assigned. The two blocks were separated by a 5-min break. No information was given regarding the alternation rule. To specifically examine the implicit form of transfer, participants were interviewed after the experiment; they were asked how they performed and whether they found anything in the second block. If participants spontaneously reported (i.e., verbalized) the alternation rule, they were excluded from our analyses. Next, the experimenter explained the alternation rule to the participants. If the participants recognized the alternation rule, these participants were also excluded from our main data analyses.1 However, in later analyses, we used excluded data to investigate effects of rule awareness.

As a measure of accuracy, we counted the number of error trials before completing one trial. To evaluate speed, we measured the time that had elapsed from the moment the home key was pressed to the moment the third button of the final (7th) triad was pressed for each successful trial. Similar parameters have been employed in previous studies (e.g., Watanabe, Ikeda, & Hikosaka, 2006; Watanabe et al., 2010). We divided the 20 successful trials into five trial sections and calculated mean performance times within each trial section. To compare the magnitude of transfer among participants who differed on initial performance, we defined mean performance times during the final section (i.e., 17–20th trials) of the first block as a baseline for each individual participant. We then calculated adjusted performance by subtracting the baseline from performance times during the second block (the reversed, partially reversed, or no-overlap sequences) and divided by the baseline. This adjusted performance time [(Psecond block−Pbaseline)/Pbaseline] represents the transfer magnitude of participants' performance times. A value smaller than zero indicates that the performance time in the second block is faster than the baseline in the first block. Any difference in adjusted performance times indicates a difference in magnitude of transfer among different sequences in the second block.

2.2. Results and discussion

We excluded six participants who were unable to complete the task.2 Twenty participants remained for each of the reversed, partially reversed, and no-overlap sequences. Ten participants could verbalize the reversal rule in the reversed sequence, and two verbalized the partial reversal rule in the partially reversed sequences. We additionally excluded one participant in the partially reversed and another in the no-overlap sequences because their performances in the second block were slower than 2 SDs from each group's average. The selection procedure resulted in 10, 17, and 19 unaware participants with acceptable performance, for the reversed, partially reversed, and no-overlap groups, respectively.3

Through this study, we mainly conducted two-way mixed anovas with the five trial sections as a within-subjects factor and the three sequences as a between-subjects factor, which was called simply “anova” hereafter, and post hoc tests with the Shaffer's method when performed (called “post hoc test”). For all sequence groups, a significant decrease was found in both accuracy and speed measures in the first block, indicating that non-specific learning had occurred (Fig. 2A and B; anova; F(4, 172) > 69.7, p < .0001; for both measures); there were no differences among the sequence groups (anova; F(2, 43) < 0.61, p > .54; for both measures). The accuracy measure decreased rapidly in the first few completed trials, whereas the speed measure decreased more gradually (e.g., Sakai et al., 1998, 2003).

Figure 2.

Performance in 'Experiment 1'. Error bars show the standard errors of the mean. All participants performed the Original sequence in the first block. The adjusted performance in the second block was computed as follows: [(Psecond block − Pbaseline)/Pbaseline]. (A) Average performance time for successful trials in the first block. (B) Average number of errors before the successful completion of each trial in the first block. (C) Average adjusted performance times in the second block. (D) Average number of errors before the successful completion of each trial in the second block.

In the second block, the mean adjusted performance times were generally faster (i.e., more transfer was found) in the reversed group compared with the partially reversed and no-overlap groups (Fig. 2C). The anova revealed significant main effects of sequence (F(2, 43) = 4.26, p < .05; post hoc test, reversed < partially reversed = no-overlap, p < .05) and trial section (F(4, 172) = 72.76, p < .001; 1st > 2nd > 3rd > 4th = 5th section, p < .05). The interaction was not significant (F(8, 172) = 0.09, p = .99). Regarding the number of errors (Fig. 2D), the anova revealed significant main effects of sequence (F(2, 43) = 3.41, p < .05; post hoc test, reversed < no-overlap, p < .05, reversed = partially reversed, p = .073) and trial section (F(4, 172) = 146.6, p < .0001; 1st > the other sections). The interaction was also significant (F(8, 172) = 2.95, p < .01).

The results of the interaction showed that the magnitude of transfer in both speed and accuracy were better with the reversed sequence than with the partially reversed and no-overlap sequences, even when the participants were not able to verbalize the alternation rule. Therefore, it seemed that the participants were somehow able to retain the learned order of each triad from the first block and implicitly apply it to the reversed structure of the second block. It should be noted that the number of component changes in the reversed sequence was the same as in the partially reversed sequence (i.e., two buttons were switched); hence, the differential magnitudes of transfer were not due to the amount of conflict between component changes in learned and to-be-learned triads.

A Pearson's chi-squared test revealed a significant difference in the proportion of participants who noticed the alternation rule between the reversed and partially reversed groups (χ2 = 6.26, p < .05), and this indicated that the reversal rule might be easier to notice than the partial reversal rule. Although we focused on implicit transfer, and the effect of rule awareness was not the main focus of this study, this might partially explain why accuracy within the reversed sequence was higher than the no-overlap sequence. This is because subthreshold awareness of the reversed order might prime performance within the subsequently reversed triads. In addition, we examined whether the performances of those groups (Aware vs. Unaware) in the reversed sequence were different. In the first block, we confirmed that performance did not differ between the groups (Fig. 3A and B; F(1, 18) < 2.13, p > .13; for speed and accuracy measures). In the second block, we found that the adjusted performance time was faster and accuracy was lower when participants were unaware of the reversal rule. For performance time (Fig. 3C), a two-way mixed anova revealed significant main effects of awareness (F(1, 18) = 10.19, p < .01; Unaware < Aware) and trial section (F(4, 72) = 110.72, p < .0001), as well as a significant interaction (F(4, 72) = 4.02, p < .01). For accuracy (Fig. 3D), a two-way mixed anova revealed significant main effects of awareness (F(1, 18) = 41.17, p < .0001; Unaware > Aware) and trial section (F(4, 72) = 73.81, p < .0001), as well as a significant interaction (F(4, 72) = 53.40, p < .0001). These results confirmed that once participants obtained the reversal rule (i.e., explicit knowledge), they could clearly perform the sequence with fewer errors (e.g., Watanabe et al., 2006). Interestingly, we observed faster performance among participants who did not notice the rule. This might indicate that explicit knowledge interferes with speed improvement. However, as the main focus of this study was implicit transfer, we leave this question for future research with a more balanced sample.

Figure 3.

Performance of participants who noticed the reversal rule (“Aware”) and who did not (“Unaware”) in 'Experiment 1'. Error bars indicate standard errors of the mean. The adjusted performance in the second block was computed as follows: [(Psecond block − Pbaseline)/Pbaseline]. (A) Average performance time for successful trials in the first block. (B) Average number of errors before the successful completion of each trial in the first block. (C) Average adjusted performance times in the second block. (D) Average number of errors before the successful completion of each trial in the second block.

3. Experiment 2

The increased transfer of speed with the reversal rule than with the partial reversal rule might have two possible explanations. For one, the reversed triads might be easier to transfer; that is, each triad independently contributed to transfer learning. Alternatively, the consistent application of the reversal rule might facilitate transfer; thus, participants were applying the abstract rule to implicit learning transfer. To investigate the effect of consistency in the alternation rule, we mixed reversed and partially reversed triads within a sequence for 'Experiment 2'.

3.1. Method

Twenty-two right-handed participants took part (11 females; Mage = 21.1 years, SD = 1.45). The procedure was the same as 'Experiment 1' except for the following. In the second block, the participants were randomly assigned to one of the following sequences that comprised a mixed sequence of reversed (R) and partially reversed (PR) triads: R-PR-R-PR-R-PR-R; PR-R-PR-R-PR-R-PR; R-R-PR-PR-R-R-PR; PR-PR-R-R-PR-PR-R (mixed sequences).

First, performances of the mixed ('Experiment 2'), reversed, and partially reversed sequences ('Experiment 1') were simply compared. Then, data from individual reversed (or partially reversed) triads of the mixed sequences were compared with those of the reversed (or partially reversed) sequences in 'Experiment 1' (Fig. 4). For this comparison, in the mixed sequences, response times from the presentation of each individual triad to the third button press were calculated. The response times were summed separately for reversed and partially reversed triads, divided by the number of triads (i.e., 3 or 4) within each sequence and then multiplied by 7 (i.e., total number of triads in the sequence). Then, the baseline (the mean performance time in the final trial section of the first block) was subtracted from those values and then divided by the baseline [(7 × (summed response time/numbers of triads) − Pbaseline)/Pbaseline]. Values computed from this formula should be comparable to those from 'Experiment 1'. For performance accuracy, the number of errors was summed separately for reversed and partially reversed triads, which were divided by the number of triads within each sequence and multiplied by seven (adjusted number of errors).

Figure 4.

Performance with reversed or partially reversed triads in 'Experiment 1' (consistent change) and those in 'Experiment 2' (mixed). Error bars indicate standard errors of the mean. The adjusted performance was computed as follows: [(7 × (Summed response time/Numbers of triads) − Pbaseline)/Pbaseline]. (A) Average adjusted performance times (speed transfer index) for successful trials with reversed triads. (B) Average adjusted number of errors (accuracy transfer index) before the successful completion of each trial with reversed triads. (C) Average adjusted performance for successful trials with partially reversed triads. (D) Average adjusted number of errors (accuracy transfer index) before the successful completion of each trial with partially reversed triads.

3.2. Results and discussion

Two of twenty-two participants were excluded due to incompletion of the task. No participants noticed the alternation rules (and believed that the temporal sequence of button presses was altered randomly). We further excluded two participants by using the same criteria regarding speed as 'Experiment 1', thereby resulting in 18 participants.

Again, a significant decrease was found in both the performance times and the accuracy measure in the first block (F(4, 168) > 63.77, p < .0001; for both measures), and there were no differences observed between the three groups with the different sequences (i.e., mixed, reversed, and partially reversed) (F(2, 84) < 3.24, p > .05; for both measures).

First, the mixed sequences did not produce faster speeds than the partially reversed sequences from 'Experiment 1'. A significant main effect of sequence (F(2, 42) = 8.87, p < .001) was observed, which was due to a significant difference between the reversed sequence from 'Experiment 1' and both the partially reversed sequence from 'Experiment 1' and the mixed sequences (post hoc test, p < .05). The main effect of trial section was significant (F(4, 168) = 81.79, p < .001), but the interaction was not significant (F(8, 168) = 1.6, p = .12). For accuracy, the mixed sequences did not lead to fewer errors than the partially reversed sequences. The main effect of trial section was significant (F(4, 168) = 165.0, p < .0001; post hoc test, 1st > the other sections), but the main effect of sequence was not (F(2, 42) = 2.77, p = .07). The interaction was significant (F(8, 168) = 2.68, p < .01), but we did not find any significant main effect of sequence in each trial section (post hoc test, p > .05).

Fig. 4 displays performance with reversed or partially reversed triads in 'Experiment 1' (consistent change) and those in 'Experiment 2' (mixed). The adjusted performance times with the reversed triads in the mixed sequences were significantly longer than in the reversed sequences (F(1, 26) = 13.28, p < .01). The main effect of trial section was significant (F(4, 104) = 47.11, p < .0001), but the interaction was not (F(4, 104) = 0.99, p = .41). This result indicated that it was the consistent reversal of all triads that led to overall better transfer in 'Experiment 1'. On the other hand, for the comparison between the partially reversed triads in the mixed sequences and the partially reversed sequences from 'Experiment 1', the main effect of sequence failed to reach significance (F(1, 33) = 1.87, p = .18). The main effect of trial section was significant (F(4, 132) = 53.35, p < .0001), as was the interaction (F(4, 132) = 2.63, p < .05). Post hoc tests indicated that this interaction was due to the adjusted performance times with partially reversed triads in the mixed sequences being longer than the consistently partially reversed triads from 'Experiment 1' (only in the first trial section; p < .05). These results indicated that the repetition of the same type of change (i.e., higher consistency of the alternation rule) contributed to better transfer, even when the participants were unaware of the alternation rules. In addition, the pattern of contribution might depend on the alternation rule; consistency of reversal triads had more general effects on implicit transfer than partial reversal triads.

The adjusted number of errors with the mixed sequences in 'Experiment 2' were not different from the number of errors in 'Experiment 1' for both the reversed triads (F(1, 26) = 0.63, p = .43) and the partially reversed triads (F(1, 33) = 0.10, p = .74). The main effects of trial section were significant (reversed: F(4, 104) = 81.61, p < .0001; partially reversed, F(4, 132) = 143.69, p < .0001) with no significant interaction (reversed: F(4, 104) = 0.78, p = .53; partially reversed: F(4, 132) = 0.22, p = .92).

4. General discussion

We examined the effects of type and consistency of alternation in response order on implicit transfer of visuomotor sequential learning. We found that (a) consistent reversal of the response order of sequence elements led to generally better transfer of learning even when the participants did not notice the reversal rule; (b) the effects of individual reversed triad did not fully explain this enhanced transfer; and (c) the partially reversed order of sequence elements did not seem to enhance transfer.4

The reversed sequence produced the better transfer than the partially reversed sequence in 'Experiment 1'. Previous studies reported that people implicitly discriminated reversed or mirrored structures of musical melodies (e.g., Dienes & Longuet-Higgins, 2004; Dienes et al., 2012), indicating that people can implicitly understand relationships between original and reversed sequences of tones. The present results suggest that the participants implicitly used the rule or structure with reversed sequences but not to the same extent with partially reversed sequences. Therefore, the present results support those of previous studies and suggest that not all rules contribute equally to transfer.

There might be at least four possibilities for enhanced transfer with the reversal rule. The participants might not be able to (implicitly) represent the relationship between the Original and partially reversed sequences. It could also be that the relationship is represented but not used to transfer implicit knowledge to the operation. This might be because the partial reversal rule is more difficult than the reversal rule in terms of learning of switching stimulus-response compatibility (Morin & Grant, 1955). Alternatively, mirror symmetries (in our experiments, the reversal rule) were easier to be learned than others because the implicit learning system was biased toward certain structures (i.e., those with a prior probability of being useful; e.g., symmetries appear in language constructions, music, cultural artifacts, or nature) (e.g., Chen et al., 2011; Jiang et al., 2012; Ziori & Dienes, 2008). Another possibility might be that participants learned movement lines in the first block and could implicitly reverse the directions in the second block, whereas participants in the partially reversed sequence could not do so because the movement lines of the partially reversed triads were different from those of the original triads (cf., Richard, Clegg, & Seger, 2009). These possibilities are open to further investigation.

In addition to the type of alternation rule, consistency in the alternation rule also contributed to the magnitude of transfer. This indicated that consistency of the alternation rule was used to learn the altered sequence without participants noticing the alternation rule or consistency. Our detailed analysis indicated that there might be an initial enhancement of transfer even within the (consistent) partially reversed triads as compared with the partially reversed triads in the mixed sequences. Thus, the effects of the type and consistency of the alternation rule interact to produce better implicit transfer.

The implicit use of consistency of the alternation rule might share similar processes for learning AGL sequences. Implicit transfer has been reported in the transfer between AGL tasks (e.g., Beesley, Wills, & Le Pelley, 2010; Brooks & Vokey, 1991; Gomez, Gerken, & Schvaneveldt, 2000; Lotz & Kinder, 2006; Vokey & Brooks, 1992). Although several studies suggest that rules with a randomly changing mapping could be used for transfer (Manza & Reber, 1997; Vokey & Higham, 2005; Whittlesea & Dorken, 1993), the magnitude of AGL transfer is typically better when a one-to-one (i.e., consistent) mapping between training and test vocabularies is adopted (e.g., Vokey & Higham, 2005). Similarly, the single mapping (i.e., higher consistency) of the sequences used in 'Experiment 1' might lead to better transfer than those of 'Experiment 2', where two mappings coexisted.

In the SRT task, participants pressed one of several spatially corresponding keys (e.g., DeCoster & O'Mally, 2011), and the order was directly mapped onto a spatial configuration. On the other hand, here, triads were randomly configured but remained the same for all altered sequences. Therefore, the reversal was in terms of the learned order of response elements (triads) rather than a predetermined association between spatial configuration and participants' responses. Thus, it is worth mentioning that this study is the first to confirm implicit transfer of learned sequences that are dissociated from spatial configurations.

Historically, the idea that an abstract rule could aid the transfer of learning has been important within perceptual learning studies (e.g., Gibson, 1969; Gibson & Gibson, 1955). In addition, limitations in statistical learning (e.g., Saffran, Aslin, & Newport, 1996) without abstract rule representations have been reported (Seidenberg, MacDonald, & Saffran, 2002). The present results may have broader implications as to how abstract rules are learned and used implicitly. We observed transfer of learning with the reversal rule only when the rule was applied consistently. This indicates that participants generalized the rule of reversal and implicitly applied it to the subsequent triads. Although in this study, we cannot determine whether rule-based and statistical learning processes would interact with each other (Peña, Bonatti, Nespor, & Mehler, 2002), the present results suggest that an abstract rule could be learned and transferred implicitly, which favors the notion of rule learning (e.g., Marcus, Vijayan, Rao, & Vishton, 1999; Saffran, Pollak, Seibel, & Shkolnik, 2007).


This work was supported by Grant-in-Aid for JSPS Fellows and Japan Science and Technology Agency (CREST).


  1. 1

    Methods for distinguishing explicit and implicit knowledge are still under debate. Some studies have used subjective measures based on confidence ratings (e.g., Ziori & Dienes, 2006, 2008). In contrast, some studies defined implicit learning as participants being unable to verbalize what they learned (e.g., Ashby, Alfonso-Reese, Turken, & Waldron, 1998). In this study, as we only focused on whether participants noticed the alternation rule, we defined explicit knowledge as participants being able to recognize the alternation rule.

  2. 2

    For participants who could not accomplish first successful trial within 15 min in the learning block, we stopped them to perform. As all the remained participants in this study accomplish the learning block (i.e., 20 successful trials) within 15 min, we thought that the time limit was moderate.

  3. 3

    Sample sizes were quite unequal between groups, which might be a caveat for the comparison across groups and an inherent limitation of this study.

  4. 4

    We highly appreciate an anonymous reviewer's inquiry that the present results might be due to the slower baseline in the Reversed sequence. Although the inequality of participants among conditions is an inherent caveat (and one of the main result) of the present paradigm, to examine this possibility, we newly recruited 20 participants and added them to the Reversed sequence group (Aware, 11 participants; Unaware, 9 participants), which resulted in 21 participants in the Aware group and 19 participants in the Unaware group. With this addition of participants, we did not find any tendency of the significant difference of the baseline both in Experiments 1 and 2. And we still observed the same results as in the main manuscript. Therefore, we concluded that the slower baseline in the Reversed sequence was not the direct cause of the present result, but the type and consistency of alternation rule pertained to implicit transfer.