Exp Brain Res (2007) 181:395–408
DOI 10.1007/s00221-007-0940-1

RESEARCH ARTICLE

Explicit contextual information selectively contributes
to predictive switching of internal models
Hiroshi Imamizu Æ Norikazu Sugimoto Æ Rieko Osu Æ
Kiyoka Tsutsui Æ Kouichi Sugiyama Æ Yasuhiro Wada Æ
Mitsuo Kawato

Received: 8 September 2006 / Accepted: 9 March 2007 / Published online: 12 April 2007
 Springer-Verlag 2007

Abstract Many evidences suggest that the central nervous system (CNS) acquires and switches internal models
for adaptive control in various environments. However,
little is known about the neural mechanisms responsible forthe switching. A recent computational model for simultaneous learning and switching of internal models proposes
two separate switching mechanisms: a predictive mechanism purely based on contextual information and a postdictive mechanism based on the difference between actualand predicted sensorimotor feedbacks. This model canswitch internal models solely based on contextual information in a predictive fashion immediately after alterationof the environment. Here we show that when subjects

Electronic supplementary material The online version of thisarticle (doi:10.1007/s00221-007-0940-1) contains supplementarymaterial, which is available to authorized users.
H. Imamizu (&)  R. Osu  M. Kawato
Department of Cognitive Neuroscience,
ATR Computational Neuroscience Laboratories,
2-2-2, Hikaridai, Keihanna Science City,
Kyoto 6190288, Japane-mail: imamizu@atr.jp
N. Sugimoto
Department of Computational Neurobiology,
ATR Computational Neuroscience Laboratories,
2-2-2, Hikaridai, Keihanna Science City,
Kyoto 6190288, Japan
R. OsuNational Institute of Information and Communication
Technology, 2-2-2, Hikaridai, Keihanna Science City,
Kyoto 6190288, Japan
K. Tsutsui  K. Sugiyama  Y. Wada
Nagaoka University of Technology,1603-1, Kamitomioka, Nagaoka, Niigata 9402188, Japansimultaneously adapted to alternating blocks of opposing
visuomotor rotations, explicit contextual information about
the rotations improved the initial performance at block
alternations and asymptotic levels of performance withineach block but not readaptation speeds. Our simulations
using separate switching mechanisms duplicated these effects of contextual information on subject performance andsuggest that improvement of initial performance wascaused by improved accuracy of the predictive switch
while adaptation speed corresponds to a switch dependent
on sensorimotor feedback. Simulations also suggested thata slow change in output signals from the switchingmechanisms causes contamination of motor commands
from an internal model used in the previous context(anterograde interference) and partial destruction of internal models (retrograde interference). Explicit contextual
information prevents destruction and assists memory
retention by improving the changes in output signals. Thus,
the asymptotic levels of performance improved.
Keywords Sensorimotor learning  Predictive switch 
Sensorimotor feedback  Internal model Computational models

Introduction
Internal models are neural mechanisms that mimic the inputoutput properties of controlled objects (Wolpert et al. 1995;
Brashers-Krug et al. 1996; Kawato 1999; Imamizu et al.
2000). Empirically, two types of information are crucial forthe switching of internal models: contextual informationsuch as color or shape of the objects that can be perceived
before movement execution, and information about thedifference between actual and predicted sensorimotor

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alteration. If contextual information is not given, the estimator solely determines the responsibility signal. In thissituation, switching ability depends on the appropriatenessof the forward internal models gauged by prediction error.
We hypothesize that the appropriateness of the internal
models gradually changes in a similar fashion to performance changes in neural networks (Kawato et al. 1987).
Thus, switching is not immediate or predictive but proceeds gradually in a trial-by-trial fashion. Because thepredictor and estimator are separate architectures, the
MOSAIC model predicts that the existence of contextual
information selectively improves switching by the predictor immediately after the alteration while it does not affect
the gradual switching by the estimator based on sensorimotor feedback.
Previous studies have investigated the effects of contextual information (e.g. color, auditory, or kinestheticcues) on switching or learning in dual tasks, in which
subjects were required to switch between opposing visuomotor rotations or force fields (e.g., Cunningham andWelch 1994; Gandolfo et al. 1996; Wada et al. 2003; Miallet al. 2004; Osu et al. 2004). However, little is separately
known about the effects on the predictive switching
immediately after the alteration and the gradual switchingbased on sensorimotor feedback. In the current study, we
directly manipulated explicit contextual information produced by detailed instruction about the characteristics of
opposing visuomotor rotations and investigated whether
the information gives different effects to the predictive
switch and switching based on sensorimotor feedback. We
conducted a computer simulation of the MOSAIC model inthe current behavioral task and examined whether thesimulation results are consistent with behavioral results.

feedbacks that can be calculated during or after execution. A
computational model for switching of internal models,called MOdular Selection and Identification for Control(MOSAIC), has proposed two separate switching architectures for each type of information (Wolpert and Kawato
1998).
Multiple pairs of forward and inverse internal models
exist in the MOSAIC model. Forward internal models
predict sensory feedback from the efference copy of motor
commands while inverse internal models transform desired
sensory consequences into the motor commands that
achieve them. The MOSAIC model has two architectures
for switching the inverse models: a predictor and an estimator (Fig. 1). The predictor receives contextual information and calculates the degree to which each inverse modelis responsible for the current environment. The estimatoralso calculates the degree based on prediction error, whichis the difference between actual sensory feedback andsensory feedback predicted by a forward model. An inverse
model paired with a forward model that has small prediction error is likely appropriate for the current environment.
In Bayesian statistics, the degree from the predictor corresponds to prior probability regarding the environment
before movement execution while the degree from theestimator corresponds to likelihood based on observed
information. A responsibility signal is a product of priorprobability and likelihood, and determines the final degree
to which each inverse internal model is responsible for thecurrent environment.
If contextual information is given, the predictor cancalculate an appropriate responsibility signal independentof sensorimotor feedback, and the MOSAIC model canconduct an appropriate switch immediately after theSensorimotor
Feedback
3

Contextual
Information

2

θ

Predictor

Estimator

Prior
Probability

Prediction
Error

e1

Likelihood

λ1 Responsibility
SignalInverseinternal θ1
Model

xd
DesiredTrajectory+

Feedforward
Motor u ff
Command1+

x1
Predicted
Sensory
Feedback

ForwardInternal θ1
Model

Sensory
Feedbackx

Object 3
Object 2
Object 1

Efference
Copy

fb

u
Feedback
Controller Feedback+

Motor Commandu
MotorCommandMusculoSkeletal
SystemSensory Feedback

Fig. 1 Architecture of a MOSAIC model during manipulation ofmultiple objects. The model consists of feedback-controller parts(bottom architecture) and feedforward-controller parts (upper architecture). Cyan parts are related to switching mechanisms based on

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contextual information while magenta parts are related to those basedon sensorimotor feedback. Nomenclature for symbols is described in
the simulation parts of the METHODS section and Supplementary
Material

Exp Brain Res (2007) 181:395–408

397

Furthermore, to confirm significance of the separate
architectures for the switching, we also conducted a simulation using a modular network that does not structurally
distinguish the predictor and the estimator, and compared
the results to those of the MOSAIC model.

Methods
Subjects
Ten male subjects (20–35 years of age) participated in thisstudy after giving informed consent. All subjects wereright-handed and naive to the purpose of this institutional
review board-approved study.
Task and apparatus
In each trial, subjects made an out-and-back pointing
movement from the center start zone to one of eight radial
targets (Fig. 2a). The target and a cursor corresponding to thefingertip position were displayed on a computer screen. A

A

CursorScreenTargetScreenyMarkerx

Occluderposition recording system (OPTOTRAK, NorthernDigital,
Canada) was attached to the right index fingertip, and its
position was projected along the coronal plane (x–y plane).
The cursor (a small ‘‘x’’) position on the screen was determined by the projected position. The cursor was visible at all
times, but subjects could not see their arm or hand. The
forearm of the subjects was fixed on a platform, andmovements of the wrist and the metacarpophalangeal joint of
the right index finger were allowed. Surgical tape fixed the
distal and proximal interphalangeal joints of the finger. Armand hand positions were carefully adjusted to remain comfortable to prevent fatigue. Although the pointing movement
may be unstable and inaccurate in comparison to arm
movement using the elbow and shoulder, which is frequently
used in studies on sensorimotor control and learning, we
adopted it considering our future study in the limited space inan fMRI scanner.
The subjects were asked to start movements immediately after the target appears and to move in a fast andsmooth motion without trajectory correction. The eighttargets were located radially in 45 increments (inset in
Fig. 2a). Only one of these targets appeared in each trial.
The distance between the center of the start zone and thetarget was 8.0 cm in hand space. The distance was slightly
magnified on the screen (9.0 cm, a visual angle of 2.29) sothat subjects could easily see the cursor trajectory. The
average interval was 0.52 s (SD 0.13) between the target
onset and the movement onset and 0.56 s (SD 0.28)
between the movement onset and its termination.
ProcedureStart zone
Subject

B

C

Screen
2

3

1
4

2
3

Target

3

2

4

1

T
Trajectory

1
4

E

Hand
y

Start
zone

P

First velocity
peakxFig. 2 a Experimental apparatus (left) and positions of the start zone
and targets on the screen (right inset). b Relationship between
direction of finger movements (black arrows) and cursor movements(white arrows) under 40 CCW and 40 CW rotations. Numbers
indicate correspondence between black and white arrows. C Angularerror (E) in each trial was measured by angular difference between the~ and the vector from
vector from center of start zone to target ðTÞ
center of start zone to the cursor position at the moment of maximal~
outward velocity ðPÞ

Several days before the main experiment, subjects conducted a baseline block consisting of 120 trials without
visuomotor rotations to become habituated to the pointing
task. During the main experiment, the cursor position was
rotated 40 clockwise (CW) or counterclockwise (CCW)
around the center of the screen (Fig. 2b). The ten subjects
were assigned to either an instructed group (n = 5) or a
non-instructed group (n = 5). While Fig. 2b was shown to
the instructed subjects, they were informed of the rotation
as follows. ‘‘The cursor position will be rotated 40
clockwise or counter clockwise around the center of thescreen. Thus, when you move your finger straight right,
the cursor will move in the lower right direction under theclockwise condition but the cursor will move in the upper
right direction under the counter clockwise condition.
Similarly, when you move the finger straight up, the cursor
will move in the upper right direction under the clockwise
condition but the cursor will move in the upper left in the
counter clockwise rotation, etc. To hit the target, you needto rotate the finger trajectory in the opposite direction to theimposed rotation.’’ The non-instructed subjects were not

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informed of the rotations, and their verbal reports indicatedthat none used any conscious or systematic strategy.
The eight targets were presented randomly in each cycleof eight trials. One block consisted of 15 cycles (120 trials)
and lasted 9 min. Each subject underwent ten blocks with a3-min break between the blocks. The rotation type (CW or
CCW) alternately changed at every block, and the order ofrotations was counterbalanced between subjects. The instructed subjects were informed of the rotation type by anexperimenter at the beginning of each block.
Analysis
To gauge performance accuracy, we measured the angularerror between the target direction and the direction of the
cursor movement at the moment of first maximal velocity(Fig. 2c). Outliers within each cycle (eight trials) were
excluded using Grubb’s test (Grubbs 1969). That is, themaximum or minimum
value was expunged
from thedataset if Y  Ymax =SD or Y  Ymin =SD was larger
thanvﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃutð2a=ð2NÞ;N2ÞðN  1Þ u
pﬃﬃﬃﬃ t:N  2 þ tð2a=ð2NÞ;N2Þ
N
Here, N; Y; and SD denote the sample size, mean, andstandard deviation, respectively. t2(a/(2N),N–2) denotes thecritical value of t-distribution with a significance level ofa/(2N). a was set at 0.05. The test was iterated until nooutliers were detected. The maximum number of outliers ineach cycle was two. The errors in the first cycle of eachblock were included in our analyses, whereas they havesometimes been excluded in previous studies (e.g., Krakauer et al. 1999). We confirmed that similar results wereobtained in our study if they were excluded. When we
separately computed the mean error for each subject androtation type (CW or CCW) and performed a t-test, there
was no significant difference between rotation types(t(18) = 1.2). Thus, we omitted the rotation type effects inthe statistical analyses described below.
To examine whether behavioral measures change acrossblocks, we used a nonparametric test for trend (Lehmann1975). A statistical measure D is defined as
D ¼ ðT1  1Þ2 þ ðT2  2Þ2 þ    þ ðTn  nÞ2 :Here, Ti is the rank (from the smallest to the largest) of the
ith value (xi) in a given time series of data (x1, x2, x3, ..., xn).
The Z statistic is calculated as
DE
Z ¼ pﬃﬃﬃﬃ :V

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2

2

ðn1Þ
: Because the distriHere, E ¼ n 6n and V ¼ n ðnþ1Þ
36
bution of Z is approximately a normal distribution, we canreject a null hypothesis that there is not a decreasing trend
if Z is larger than the critical value of a normal distribution
with a significance level of a. This test can also examine anincreasing trend. We computed the mean values of the
behavioral measure for each block and applied the test to
the values.
3

Simulations
We defined a simplified environment of the pointing task
under the visuomotor rotations. When xðtÞ ¼ ½ xðtÞ yðtÞ T
and uðtÞ ¼ ½ ux ðtÞ uy ðtÞ T represent the cursor position
and the motor command at time t respectively, the equationof motion can be described asux ðtÞx€ðtÞ
¼ Rð h Þ;
ð1Þ
uy ðtÞ
y€ðtÞ
where R(h) is the rotation matrix, and the mass of the finger
tip is 1 for simplicity. T represents the transpose of a matrix,
and x€ indicates the second time derivative (acceleration) of
x. Thus, the cursor will be accelerated in the direction
deviating by h [radian] from that of the intended motor
command. Although subjects made an out-and-back pointing movement in the behavioral experiment, we simulated
only the out part of the movement. As mentioned above, theaverage interval was 0.56[s] between the movement onset
and its termination in out-and-back movements. Thus, we
set the interval in the simulation at half of 0.56[s]; that is,
the out movement began at t = 0[s] and terminated at
t = 0.28[s]. The initial position of the cursor was ½ 0 0T at
the beginning of each trial. The path of the desired trajectory ðxd ðtÞ ¼ ½ xd ðtÞ yd ðtÞ T Þ was a line connecting theinitial position with one of the eight targets. The velocityprofile of the desired trajectory was bell-shaped. The timeinterval (Dt) in the simulation was 0.01[s].
The MOSAIC model observes the position (x(t)) andvelocity ð€xðtÞÞ of the cursor at each time point, and calculates a motor command (u(t)). Each forward internal
model in the MOSAIC model estimates the angle of therotation (h). The estimated parameter was represented by ^hi(i = 1, 2, ..., M). Because there were two types of therotations in the current simulation, M was 2 (see Supplementary Material for simulations when M was four). An
initial value of ^hi was set at 5 before learning. The forward€xi Þmodel predicts the acceleration vector of the cursor ð^from the motor command (u) based on the estimated angle:^€xi ðtÞ ¼ Rð^hi ÞuðtÞ:ð2Þ

An inverse model calculates feedforward motor command(uffi ) from the acceleration of the desired trajectory ð€
xd Þ :

Exp Brain Res (2007) 181:395–408

uffi ðtÞ ¼ Rð^hÞ1 €
xd ðtÞ:399

ð3Þ

The total output from the MOSAIC is a summation of
feedback motor command (ufb, see the lower parts ofFig. 1) and the feedforward motor commands weighted by
the responsibility signal.
The simulation was conducted in instructed and noninstructed conditions. The explicit contextual information,i.e. the current angle of visuomotor rotation (h), was fed
into the predictor in the instructed condition and contributed to calculation of the responsibility signal but it was
not fed into the predictor in the non-instructed condition.
Because we investigated the effect of explicit contextual
information produced by detailed instruction about characteristics of visuomotor rotations, we provided the predictor in simulations with the exact current angle ofvisuomotor rotation. Details of simulations are described in
Supplementary Material.
We also conducted a simulation using a modular architecture that has a single switching mechanism (see Fig. S1
in Supplementary Material). This architecture was constructed in a simulation study of object manipulation (Gomiand Kawato 1993) based on a mixture-of-experts model(Jacobs et al. 1991). The mixture-of-experts model involves
expert modules, which are equivalent to internal inverse
models, and a gating module. The gating module is a single
switching mechanism that does not structurally distinguish
contextual information and sensorimotor feedbacks.

Results
Behavioral results
Figure 3 shows angular errors as a function of trial number
from subjects in the instructed and non-instructed groups.
Regarding the baseline block (leftmost gray lines), we
computed the angular error averaged across trials for eachsubject and performed a t-test to check differences inbaseline pointing accuracy between the two groups. Mean
error (±SD) across subjects was 6.89 (±2.06) for the instructed group and 6.73 (±1.83) for the non-instructedgroup. There was no significant difference between groups(t(8) = 0.11). To check the effect of target direction on
angular error in the baseline block, we computed the error
averaged across trials for each subject and target direction
and analyzed the averaged error with a one-way ANOVA.
The directional effect was not significant (F(7,72) = 1.75).
Therefore, we could not identify any difference in pointing
accuracy between the groups or among the target directionsin the natural condition.
Regarding angular errors as a function of trial number inthe main experiment (blue or red lines), the increase oferrors at the beginning of each block replicated performance interference between opposing rotations (Krakauer
et al. 1999; Bock et al. 2001; Tong et al. 2002; Miall et al.
2004). The decrease in the errors within each block has
been characterized as short-term readaptation (Welch et al.
1993). Although trial-by-trial error fluctuates in both the
instructed and non-instructed subjects, the error of instructed subjects sometimes increased more abruptly than
non-instructed subjects. Correspondingly, the number ofdetected outliers (black squares in Fig. 3; see ‘‘Methods’’)
from a total of 1,200 trials was 28.6 (2.38% of the total
trials, SD ±6.69) averaged across the instructed subjects
while it was 8.4 (0.70%, SD ±0.89) averaged across the
non-instructed subjects.
To examine the effects of the explicit contextual information on the short-term readaptation process, we separately calculated mean angular error for the early (trial
numbers 1–40), middle (41–80), and late (81–120) stages
within each block and investigated the instruction effects on
the mean error. The errors were separately averaged acrossblocks for the stages within each subject and analyzed witha two-way (group · stage) ANOVA. Figure 3E shows theerrors averaged across blocks and subjects. The effect ofgroup was significant (F(1,8) = 8.46, P < 0.05), and error
averaged across stages, blocks and subjects in the instructedgroup (mean ± SD 12.12 ± 3.24) was smaller than in the
non-instructed group (22.60 ± 9.51). This indicates a
positive instruction effect on overall performance. Aninteraction effect between the group and the stage wassignificant (F(2, 16) = 7.87, P < 0.01), suggesting a
different instruction effect that depended on the stages.
When we compared error averaged within each stage
between groups, error in the instruction group was mostsignificantly smaller than in the non-instructed group in theearly stage (Tukey’s HSD post hoc test at P < 0.01 level),but there was no significant difference in the late stage. This
result suggests that the effect of the contextual information
was prominent immediately after the alteration of theenvironment.
To examine a long-term change of subject performancesacross blocks, we averaged angular error within each block
across trials and subjects and plotted the averaged error as afunction of block number in the main experiment (Fig. 4a,b). We considered a two-way (instructed/non-instructedgroup · block) ANOVA as a simple analysis, but we also
examined the difference between odd (filled circles) andeven (open circles) blocks because the rotation type wasdifferent between them. Specifically, blocks were divided
into the odd or even groups, and then given an order withineach group, e.g., the first block is the first block in the odd
group, the second block is the first block in the even group,
the third block is the second block in the odd group, thefourth block is the second block in the even group, and so

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Exp Brain Res (2007) 181:395–408

Fig. 3 a–d Angular errors as afunction of trials of four
representative subjects from
instructed and non-instructedgroups. Black squares represent
outliers detected by Grubb’s test(see ‘‘Methods’’). Values larger
than 80 are plotted at 80. e
Angular errors averaged acrosstrials blocks and subjects (±SD)
separately for the early, middle,
and late stages of thereadaptation process. *P < 0.05,**P < 0.01, NS not significant
according to Tukey’ HSD post
hoc test

on. Then, we applied a three-way (instructed/non-instructed group · even/odd block group · block order
within the block group) ANOVA to error averaged withineach block. Error averaged across blocks and subjects in
the instructed group was smaller than in the non-instructedgroup (F(1,8) = 8.49, P < 0.05), indicating a positive
instruction effect on overall performance, as in previous
analysis. The errors in the odd blocks were smaller thanthose in the even blocks (F(1,8) = 7.1, P < 0.05), indicating that the errors remained small for the rotation typepresented in the first block. We identified a significant
effect of block order (F(4,32) = 11.16, P < 0.01), suggesting that error averaged within each block changed
across blocks.

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Time courses along the abscissa in Fig. 4a and b indicates how the error averaged within each block changed
across blocks. Error averaged within the first block was
small in both the instructed and non-instructed groups, andreflects initial performance before subjects experienced the
opposing rotations. We could not identify a significant
difference in the error averaged within the first block
between the instructed and non-instructed groups (Tukey’s
HSD post hoc test at P < 0.05 level). Error averaged withineach block increased in the second and third blocks inwhich subjects experienced opposing rotations and gradually decreased as block number increased. To examine if along-term change of performance across blocks occurredunder interference between opposing rotations, weExp Brain Res (2007) 181:395–408

401

Fig. 4 a, b Angular error averaged within each block as a function ofblock number. Error within each block is averaged across trials andsubjects (±SD). Filled and open circles correspond to odd and evenblocks, respectively. Broken curves indicate exponential functions
fitted to the averaged errors in even blocks. Solid curves indicate

functions to the averaged errors in odd blocks (from the third to theninth blocks) + P < 0.10 (marginally significant), *P < 0.05,**P < 0.01, NS not significant. Arrows indicate results of tests fortrends. Dashed line across panels indicate results of Tukey’ HSD post
hoc test

separately applied a test for trend (see ‘‘Methods’’) to theerror averaged within each block for the odd and evenblocks. We did not include the error averaged within thefirst block in the test because performance in the first blockis free from interference. A decreasing trend was significant for even blocks in both the instructed (P < 0.05) andnon-instructed groups (P < 0.01), and marginally significant for odd blocks in both groups (P < 0.10). These results suggest a positive long-term change of performance,
especially in the even blocks. However, we could not
determine whether the decrease in error was caused by the
improvement of performance immediately after block
alterations, the speed of short-term readaptation, theasymptotic performance after readaptation within eachblock, or combinations of these components because error
averaged within each block can be affected by all of thesecomponents.
To separately investigate the effect of explicit contextual information for these components, we fitted the following curve to a time course of trial-by-trial error in eachblock, as shown by the green curves in Fig. 5a and b:tion was identified in asymptotic level (a) (F(1,8) = 9.00,
P < 0.017) and initial increase of error (b) (F(1,8) = 24.9,
P < 0.0011). Specifically, the parameter values of a and b
in the instructed group were smaller than the values in the
non-instructed group. The small value of b in the instructedgroup corresponds to the small angular error in the earlystages within each block in comparison to the error in the
non-instructed group (Fig. 3e). However, we could not
identify a significant effect on adaptation speed (c)(F(1,8) = 0.01).
The middle and right panels in Fig. 5c, d and e shows
the parameters averaged across subjects as a function ofblock number. We investigated long-term changes ofparameter values across blocks (from the second to thetenth blocks) in the same fashion as Fig. 4. Regarding
parameter a, time courses of parameter value were similar to those in Fig. 4. We could not identify a significant
decreasing trend of the value across the even blocks inthe non-instructed group (dashed curve in middle panelof Fig. 5c), but the value markedly decreased from thesecond to the remaining even blocks. Error averaged
within each block also markedly decreased in the evenblocks in the non-instructed group (dashed curve in
Fig. 4a). A marginally significant decreasing trend(P < 0.10) was found for the odd blocks in the noninstructed group (solid curve in middle panel of Fig. 5c).
The same trend was also found for error averaged withineach block in the odd blocks in the non-instructed group(solid curve in Fig. 4a). A decreasing trend of a-value
was marginally significant (P < 0.10) in the even blocks
in the instructed group (dashed curve in right panel ofFig. 5c), and the trend of error averaged within eachblock in the even blocks in the instructed group was
significant (P < 0.05, dashed curve in Fig. 4b). Althougha decreasing trend was marginally significant in error

y ¼ a þ b expðc  xÞ:
Here, x and y represent trial number and error, respectively.
As illustrated in the inset of Fig. 5b, parameter a corresponds to the asymptotic level within each block whenshort-term adaptation is completed. Parameter b corresponds to the initial increase of the error at block alterations from the asymptotic level. Parameter c reflects
adaptation speed within in each block. Each estimatedparameter was separately analyzed with a two-way (instructed/non-instructed group · block) ANOVA. The left
panels in Fig. 5c, d and e shows the parameters averaged
across blocks and subjects. A significant effect of instruc-

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Baseline

A

1

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5

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9

10 block

80
60
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B

1200

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c

80

b
a

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1

120 1

200

400

Asymptotic level (a)

C

600

800

1000

1200

Trial number

Non-instructed group
P < 0.017

Estimated a

Fig. 5 a, b Examples of
exponential curves (green) fitted
to error time courses of two
representative subjects(different from subjects in
Fig. 3a–d). Inset illustrates how
an exponential curve (y = a +b exp (–cx)) changes dependingon each parameter. Conventions
follow Fig. 3. c–e Left panels
estimated parameters averaged
across blocks and subjects(±SD). P-values indicate theresults of a two-way (group andblock) ANOVA. Middle andright panels parameters
averaged across subjects andplotted as a function blocknumber (±SD). The right axis ofe indicates a time constantcorresponding to a time when
fitted exponential curve decays
to 37% of total decay.
Downward or upward arrows
indicate a decreasing or
increasing trend, respectively,
based on a test for trend (see‘‘Methods’’). Other conventions
follow Fig. 4

Exp Brain Res (2007) 181:395–408

N.S.

+
+

N.S.

N.S.

1

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1

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Initial increase of error at block alterations (b)

D

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Estimated b

P < 0.0011
50

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4

Adaptation speed (c)0.15(arbitrary units)

0.15

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N.S.
0.10

0.10

0.10

10

N.S.

*
0.05

0.05

0.00

0.00

Non-instructed Instructedcondition condition

averaged within each block in the odd blocks in the
instructed condition (solid curve in Fig. 4b), a significant
trend could not be identified in the odd blocks in the
instructed condition (solid curve in right panel ofFig. 5c). Although statistical significances weakened inFig. 5c, we found similar patterns of time courses in
Figs. 4 and 5c, suggesting a similarity to a certain degree
between error averaged within each block and asymptotic
level.

20
30
40
50

0.05

*
1

2

3

4

N.S.

5

6

7

8

Block number

9 10

N.S.

0.00

1

2

3

4

5

6

7

8

Time constant(trials)E
Estimated c

*

30

N.S.

1

123

50

N.S.

9 10

Block number

Regarding the initial increase of error at block alterations (Fig. 5d), the b-value in the non-instructed group did
not decrease across blocks and remained around 40 forboth the odd and even blocks (middle panel). We identified
a significant decreasing trend (P < 0.05) in the instructedgroup in the even blocks but not in the odd blocks (rightpanel). The b-value in the odd blocks was small acrossblocks in the instructed group. Regarding adaptation speed(Fig. 5e), c-values significantly increased (P < 0.05) in theExp Brain Res (2007) 181:395–408

403

non-instructed group both in the odd and even blocks(middle panel). However, we could not identify a significant trend in the instructed group (right panel).
To examine the validity of exponential fitting, we
computed the sum of squares due to error (SSE) associatedwith the exponential model (y = a + b exp (–cx)):SSEðExponential ModelÞ ¼nX

ðyi  y^i Þ;

i¼1

where n, yi and y^i denote the number of trials in the main
experiment for each subject, observed angular errors andvalues predicted by the model, respectively. The outliers
above mentioned were not included in this analysis. As areduced model for comparison, we fitted a linear model(y = a + b x) to the angular errors, computed SSE
associated with the linear model, and calculated the ratio
F¼½SSEðLinearModelÞSSEðExponential ModelÞ=ðpkÞ:SSEðExponential ModelÞ=ðnpÞ

Here, p and k denote, the numbers of parameters in the
exponential model (i.e., 3) and in the linear model (i.e., 2),
respectively. The ratio has F distribution with (p – k) and(n – p) degrees of freedom, and the large ratio indicates thatthe exponential model is more effective than the reduced
linear model (Chatterjee and Price 1991). We conducted thisanalysis for each subject and identified the significant
effectiveness of exponential fitting in all subjects. That is,even the smallest ratio among subjects (F(1, 1188) = 4.64 in
subject MS) was larger than the F value at the P < 0.05
level. This result suggests the significance of parameter c.
Simulation results
Figure 6 shows results of the simulation using the MOSAIC model. Figure 6a and c indicates time courses of the
responsibility signals for the CW and the CCW internal
models. A significant difference between the instructed andthe non-instructed conditions was observed immediately
after alteration of the environment. The responsibility
signal rapidly changed in the instructed condition (cyancurves) while the signal changed slowly in the noninstructed condition (magenta curves).
Figure 6b and d indicates the angle of the visuomotor
rotation estimated by each internal model (^hi see ‘‘Methods’’ section). These parameters are closely related to thedegree of learning acquisition of internal models. Theirvalues were initially set at 5 and approached 40 as
learning proceeds. The gray regions correspond to blocks
in which the other internal model was appropriate for theenvironment. Time courses of the parameter values slightly

dropped in the gray regions. The drop of the time course in
the instructed condition was smaller than in the non-instructed condition. Consequently, time courses in the instructed condition were superior to those in the noninstructed condition.
The increase in angular error immediately after thealteration was small in the instructed condition (Fig. 6e)corresponding to rapid change in the responsibility signals.
In contrast, the error greatly increased after the alteration in
the non-instructed condition (Fig. 6f). Gray bars in Fig. 6e
and f indicate error averaged within each block acrosstrials. As the block number increased, the averaged error in
the instructed condition decreased more rapidly than in the
non-instructed condition, suggesting a positive instruction
effect on performance. We fitted exponential curves to thetime courses of trial-by-trial error in each block in simulations (green curves) and compared the parameters averaged across blocks (from the second to the tenth blocks) in
the instructed condition to those in the non-instructedcondition, as shown in Fig. 6g. A significant difference was
identified in both parameters a (t(16) = 2.39, P < 0.030)
and b (t(16) = 5.81, P < 0.000026), but not in parameter c(t(16) = 0.28), which is consistent with the behavioral
results (left panels in Fig. 5c–e).
Figure 7 shows results of the simulation using themodular architecture based on a single switching mechanism (i.e., the mixture-of-expert model). Figure 7a and cindicates time courses of the responsibility signals. The
amplitude of the correct responsibility signal tends to belarger in the instructed condition (cyan curves) than that in
the non-instructed condition (magenta curves). However,there was not much difference in the values of the responsibility signals for the two conditions immediately after thealteration of the environment. Figure 7b and d indicates theangle of the visuomotor rotation estimated by each internal
model ð^hi Þ: We could not find any significant effect of the
instruction on the time courses of the learning. Figure 7e
indicates angular error as a function of trial numbers. There
was little difference in error immediately after the alteration
between the instructed and the non-instructed conditions inparallel with the time courses of the responsibility signals.
The learning in the modular architecture was very slow
(Fig. 7b, d, e: note that horizontal axes are partially magnified). We tried a large parameter value for the learning
rate (gexpert, see Supplementary Material), but the switchingoccurred much too frequently within each block and theperformance became unstable.
Discussion
We confirmed performance interference (Krakauer et al.
1999; Bock et al. 2001; Tong et al. 2002; Miall et al. 2004)

123

404
Fig. 6 Results of simulation
using MOSAIC. Change in
responsibility signals (a, c) andlearning acquisition of internal
models (b, d) and angular errors(e, f) when the MOSAIC learns
the CW task in the first block.
Green curves indicate the fitted
exponential curves. g Estimatedparameters for exponential
curves averaged across blocks

Exp Brain Res (2007) 181:395–408
Instructed condition
Non-instructed condition
2nd
3rd
4th
Block 1st
Task CW CCW CW CCW

A Responsibility
Signal for
CW Internal
Model

B Learning
Acquisition of
CW Internal

10th
CCW

1.0
0.5
0.0
40
20
0
0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

0

200

400

600

800

1000

C Responsibility 1.0
Signal for
CCW Internal
Model

D Learning
Acquisition of
CCW Internal

0.5
0.0
40
20
0

E

60
40

Instructedcondition

20
0

F

60
40

Non-instructed20
condition0

Initial increase of error
at block alterations (b)6030

Estimated b

Estimated a

10

0

40
30
20
10
0

Non-instructed Instructedcondition conditionand short-term readaptation (Welch et al. 1993) whensubjects simultaneously adapted to alternating blocks of
opposing rotations (Fig. 3a–d). Regarding short-term readaptation, the effect of explicit contextual information
was prominent immediately after alteration of the environment (Fig. 3e). To examine the long-term change ofsubject performance under interference, we investigated
how angular error averaged within each block changed
across blocks (from the second to the last blocks). Especially in the even blocks, error averaged within each block
decreased both in the instructed and non-instructed groups
as block number increased (Fig. 4), suggesting a positive
long-term performance change under interference.
Based on the results of exponential fitting, both theasymptotic level after short-term readaptation (a) and the

123

0.15

50

P<0.030
20

Adaptation speed (c)P<0.000026

Non-instructed Instructedcondition condition(arbitrary units)

Asymptotic level (a)Estimated c

G

1200

trials

0.10

N.S.
0.05

0.00

-0.05

Non-instructed Instructedcondition condition

initial increase of error at block alterations (b) became
small if explicit contextual information existed (left panels
in Fig. 5c, d). We investigated long-term changes of theseparameters from the second to the last blocks. Regarding
the even blocks in the instructed group, a significant
decreasing trend was identified in both the a and b-values(dashed curves in right panels of Fig. 5c and d), although it
was only marginally significant in the a-value. This suggests that both the asymptotic level and the initial performances at block alterations improved as block number
increased. We could not identify a significant decreasing
trend in the odd blocks in either the a- or b-values (solidlines in right panels of Fig. 5c and d). This is probably
because the values were small already in the early blocks,e.g., the third block, and difficult to decrease further in theExp Brain Res (2007) 181:395–408
Fig. 7 Results of simulation
using a modular architecture
based on the mixture of experts
model. Change in responsibility
signals (a, c), learning
acquisition of internal models(b, d) and angular errors (e)when the architecture learns the
CW task in the first block. Notethat the horizontal axes in b, d,and, e are partially magnified

405
Instructed condition
Block 1st
Task CW

A

B

Responsibility
Signal for
CW Internal
Model (experts)
Learning
Acquisition of
CW Internal

Non-instructed condition

2nd

3rd

4th

10th

CCW

CW

CCW

CCW

1.0
0.5
0.0
15
10
5
0

200

400

600

800

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1200

trialsResponsibility
Signal for

C CCW Internal

Model (experts)

D

Learning
Acquisition of
CCW Internal

1.0
0.5
0.0
15
10
5
0

200

400

600

800

1000

1200

0

200

400

600

800

1000

1200

40

E

30
20

late blocks (‘‘floor effect’’). These results indicate that asignificant long-term decrease of error averaged withineach block in the even blocks of the instructed group(Fig. 4b) was caused by improvement of both the asymptotic level and the initial performance at block alterations.
Regarding the non-instructed group, we could not
identify a significant decreasing trend of the a-value in theeven blocks (dashed curve in middle panel of Fig. 5c) but
the value markedly decreased from the second to theremaining even blocks. The a-value in the odd blocks(solid line) decreased as block number increased, although
the trend was marginally significant. The b-values did notchange from around 40 in either the even or odd blocks(middle panel of Fig. 5d). The c-value, which corresponds
to adaptation speed, gradually and significantly increased
across blocks in both the odd and even blocks in the noninstructed group (middle panel of Fig. 5e). Therefore, along-term decrease of error averaged within each block in
the non-instructed group (Fig. 4a) was caused by
improvement of both the asymptotic level and short-term
adaptation speed.
In the simulation results using the MOSAIC model, we
found a difference in the changes of responsibility signals(Fig. 6a, c), the learning acquisition of internal models(Fig. 6b, d), and the error time courses (Fig. 6e–g) between
the instructed and non-instructed conditions. However, in
our simulation using modular architecture based on a single
switching mechanism (mixture-of-expert model), we could
not find a difference in the change of responsibility signals
at block alterations (Fig. 7a, c), the learning acquisition ofinternal models (Fig. 7b, d), or the error time courses(Fig. 7e) between the two conditions. These results suggestthat the MOSAIC model can better explain differences inthe behavioral results between the instructed and non-instructed groups than modular architecture based on a single
switching mechanism.
In the MOSAIC model, the changes of responsibility
signals affect the short-term changes of errors and the longterm acquisition of internal models as follows. Below,(CW, CCW) denotes a pair of responsibility signal values
for the CW and CCW internal models. In the instructedcondition (cyan curves in Fig. 6a, c), the predictor can set
the values at (0.75, 0.25) with a priority on the CW rotation
based on instructions at the beginning of the first block. In
the non-instructed condition (magenta curves), however,the predictor cannot contribute to the calculation of thevalues, and thus the values are (0.5, 0.5). At the beginningof the second block in the instructed condition, the predictor contributes to the calculation and the responsibilitysignal values rapidly shift to nearly (0, 1). However, thechange in the responsibility signal is slow in the non-instructed condition. The intermediate values of the responsibility signals, e.g., (0.7, 0.3), during the transition evokes
two types of negative effects on switching and learning: (1)output signals from the CW internal model consist of 70%of the motor command, despite the fact that the subject
should perform the CCW task in the second block. Thus
error increases more than when a subject performs the
CCW task in the first block (Fig. 6f). (2) Memory in the
CW internal models is disrupted (the downward black

123

406

arrows) in proportion to the responsibility signal values.
The degrees of the negative effects in the non-instructedcondition are larger than those in the instructed condition
because of the slow change in the responsibility signals.
In the above framework, the initial increase of error atblock alterations (b) is caused by contamination of motor
commands from an internal model used in the previous
block (first type of negative effect). If explicit contextual
information is given, the predictor can calculate appropriate responsibility signals immediately after block alteration. Thus, the initial increase of error at block alterations
is small. Therefore, the b-value reflects the accuracy of thepredictive switch based on explicit contextual information.
Asymptotic level (a) within each block corresponds to theerror when responsibility signals completely change toappropriate values for the current context and switching iscompleted. Therefore, the a-value reflects the performanceof an internal model for each rotation. Adaptation speed (c)corresponds to the speed of the gradual change of
responsibility signals based on sensorimotor feedback.
As mentioned in the introduction, the MOSAIC model
predicts that the existence of explicit contextual information selectively improves the predictive switch immediately after alteration without affecting the gradual switch
based on sensorimotor feedback. This prediction is consistent with our behavioral results indicating that the initial
increase of error at block alterations (b) became small if
explicit contextual information existed, but that adaptation
speed (c) did not change (left panels of Fig. 5c–e).
In MOSAIC simulations, the time courses of the learning acquisition of internal models in the instructed condition (cyan curves in Fig. 6b–d) were always superior to the
non-instructed condition (magenta curves), suggesting
better performance of internal models in the instructed thanin non-instructed conditions. This is consistent with our
behavioral results indicating that asymptotic level (a)averaged across blocks was smaller in the instructed groupthan in the non-instructed group (right panel of Fig. 5c).
Regarding long-term performance changes, MOSAIC
simulations indicated that performance of the internal
models gradually improved across blocks, especially in the
instructed condition (cyan curves in Fig. 6b and d), andthat initial error at block alterations decreased acrossblocks in the instructed condition (Fig. 6e). Our behavioral
data indicated decreases of both the asymptotic level andthe initial increase of error at block alterations in the evenblocks of the instructed group (dashed curves in rightpanels of Fig. 5c and d). These results suggest that
long-term improvements of the internal models and thepredictive switch occur if explicit contextual information is
given. In simulations, performance of internal models also
gradually improved in the non-instructed condition acrossblocks (magenta curves in Fig. 6b and d), but error at block123

Exp Brain Res (2007) 181:395–408

alterations did not decrease (Fig. 6f). These results correspond to behavioral results indicating that asymptotic level
decreased to some degree (middle panel of Fig. 5c), butthat initial increase of error at block alteration did notchange from around 40 (middle panel of Fig. 5d).
Anterograde and retrograde interferences have beensuggested in adaptation to opposing kinematics and/or
dynamics. Anterograde interference is the negative influence of the preceding task on the subsequent task while
retrograde interference is a consequence of the subsequenttask disrupting memory in the preceding task (Robertson
et al. 2004). We found similar interferences in the
MOSAIC simulations. That is, the contamination of motor
commands from the internal model used in the previous
context (rightward arrows in Fig. 6) corresponds toanterograde interference. The partial destruction of internal
models (degradation of ^h) when they become modifiablestates in inappropriate contexts (downward arrows) corresponds to retrograde interference. These interferences
occur when the responsibility signal does not rapidlychange in response to context changes.
Our simulation using the MOSAIC model could not
duplicate the following behavioral results. First, the increase of errors at the beginning of each block in the instructed condition was small in the simulation (Fig. 6e) incomparison to the behavioral result (e.g., Fig. 5a). Thissuggests that the predictor in the simulation is more complete than that in the behavioral data, and the responsibility
signal rapidly changed. Second, errors averaged withineach block tended to be larger in the even blocks than in
the odd blocks (Fig. 6e, f). However, the difference wasvery small in comparison to the behavioral data (Fig. 4a,b), and the simulation could not duplicate the difference inslopes of error reduction between the conditions (curves inFig. 4a, b).
On questioning after the experiment, most of the noninstructed subjects did not realize the rotations, andattributed reasons of the error increase after the alterations
to loss of skill or knack during the rest periods (seeSupplementary Material). According to a previous study(Vetter and Wolpert 2000), when a virtual reality systemshifted a perceived finger position gradually and alternately upward or downward from the actual position,subjects could adaptively track a moving target withoutawareness of the shift. These suggest that switchinginternal models in the non-instructed condition is based on
sensorimotor feedback that can be processed at the subconscious level.
Although a systematic questioning was not done for the
instructed subjects, some subjects reported that they tried touse the cognitive strategy to counteract the imposed rotation (see ‘‘Methods’’ section) but that the strategy often
failed because they were required to start movements

Exp Brain Res (2007) 181:395–408

immediately after a target appears. Consistently with thisreport, the trial-by-trial error of the instructed subjects
sometimes abruptly increased and became noisy, and thenumber of detected outliers in the instructed group waslarger than in the non-instructed group (e.g., Fig. 3a, b).
We calculated correlation coefficients between the measured error in each trial and the error predicted by the
exponential model in 100 cases (10 sessions · 10 subjects) and compared the coefficients between the instructed
and non-instructed groups. The coefficients in the instructed group were significantly smaller than those in the
non-instructed group (t(98) = 6.97, P < 0.0001), suggesting that the model for trial-by-trial readaptation based on
sensorimotor feedback fits the error time courses of the
instructed subjects less than those of the non-instructedsubjects. The failure of the cognitive strategy and noisy
performance in the instructed group is consistent with astudy suggesting a conflict between the cognitive strategy
and implicit learning (Mazzoni and Krakauer 2006).
The reduction of the error during the early stage of eachblock in the instructed condition was unlikely caused byintentional cancellation of the rotation for the following
reasons. First, we could not find significant difference inparameter b of the second block between the instructed
and the non-instructed groups (Tukey’s HSD post hoc test
at P < 0.05 level). If the subject could reduce the initialerror by using conscious cancellation, it would also be
possible in the second block but this was not possible,
suggesting that the interference could not be reduced
solely by such a strategy. Second, Osu et al. (2004) also
instructed subjects how to cancel the force fields bypresenting figures illustrating effects of the fields. However, significant interference could be identified between
adaptations to the opposing force field, suggesting theinterference could not be reduced by only the conscious
compensation. They also could not identify a significant
progress of the conscious compensation. Thus, the main
reason for the reduction in the error is probably the rapidchange of the responsibility signal as our simulation with
the MOSAIC model suggests.
Previous functional imaging studies (Imamizu et al.
2003, 2004) also supported the MOSAIC model andsuggested that a prefrontal region (Brodmann area 46)
contributes to the predictor while loops between theparietal regions (Pisella et al. 2000) and the cerebellum
contribute to the estimator. The current behavioral study
in the context of previous computational (Wolpert et al.
1995; Wolpert and Kawato 1998; Kawato 1999) andimaging studies (Imamizu et al. 2004) suggests that, toachieve adaptation to multiple environments, a predictive
mechanism, possibly located in the frontal cortex, needs
to switch multiple internal models residing in the cerebellum.

407

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