Predictive Learning of Sensorimotor Information as a Key for Cognitive Development, Yukie Nagai

Cognitive
Neuroscience
Robotics
Predictive Learning of
Sensorimotor Information as a
Key for Cognitive Development
Yukie Nagai
Graduate School of Engineering, Osaka University
Open Lecture on Cognitive Interaction Design
Kyoto Institute of Technology, July 12, 2015

Development of joint attention
[Nagai et al., 2003; 2006; Nagai, 2005]
Imitation based on mirror neuron system
[Nagai et al., 2011; Kawai et al., 2012]
Infant-directed action
[Nagai & Rohlfing, 2009]
Gaze-head coordination in social interaction
[Schillingmann et al., 2015]

Cognitive Developmental Robotics
[Asada et al., 2001; 2009; Lungarella et al., 2003]
•  Aim at understanding the principle of human cognitive
development by means of constructive approach
–  Bridge the gap between neuroscience (micro level), and
psychology and cognitive science (macro level)
–  Build human-like intelligent robots

Various Cognitive Abilities in Infants

Development as a Continuous ProcessCognitivedevelopment
Theory of
mind
Imitation
Self-other
cognition
Cooperation
Joint
attention
Goal-directed
action
Language
use
Understanding
intention

CognitivedevelopmentDevelopment as a Continuous Process
Theory of
mind
Imitation
Self-other
cognition
Cooperation
Joint
attention
Goal-directed
action
Language
use
Understanding
intention
What is the underlying mechanism
for cognitive development
(i.e., the root of the tree)?

Our Hypothesis [Nagai, in press]
Predictive learning of sensorimotor information (i.e.,
minimizing prediction error ei(t+1)) leads to cognitive development.
Prediction error
ei(t+1) = si(t+1) − ŝi(t+1)
Sensory state
si(t)
Motor command
aj(t)
Sensory feedback
si(t+1)
Sensorimotor
system
Predicted sensory feedback
ŝi(t+1)
Predicted motor command
âj(t+1)Efference copy
Predictor

Our Hypothesis [Nagai, in press]
Predictive learning of sensorimotor information (i.e.,
minimizing prediction error ei(t+1)) leads to cognitive development.
(1) Learn the predictor through
sensorimotor experiences
! Self-other cognition
! Goal-directed action, etc.
(2) Produce an action in
response to other’s action
! Imitation
! Altruistic behavior, etc.
ei(t+1)
si(t)
aj(t)
si(t+1)Sensorimotor
system
ŝi(t+1)
âj(t+1)
Predictor
ei(t+1)
si(t)
aj(t)
si(t+1)Sensorimotor
system
ŝi(t+1)
âj(t+1)
Predictor

Outline
1.  Cognitive development in robots based on predictive
learning
–  Self-other cognition [Nagai, Kawai, & Asada, ICDL-EpiRob 2011]
–  Goal-directed action [Park, Kim, & Nagai, SAB 2014]
–  Altruistic behavior [Baraglia, Nagai, & Asada, ICDL-EpiRob 2014]
2.  Autism spectrum disorder (ASD) caused by atypical
tolerance for prediction error
–  Theory of underlying mechanism of ASD [Nagai, in press]
–  Simulator of atypical perception in ASD [Qin, Nagai, Kumagaya,
Ayaya, & Asada, ICDL-EpiRob 2014]

Infants Start Discriminating
Self from Others in FirstYear of Life
[Rochat & Morgan, 1995]
[Bahrick & Watson, 1985]
[Rochat & Striano, 2002]

Our Hypothesis about Self-Other Cognition
•  Spatiotemporal predictability in sensorimotor
information discriminates the self from others.
–  Self = perfect predictability, others = lower predictability
–  Perceptual development leads to the emergence of
Mirror Neuron Systems (MNS).
(1) Immature perception
! self-other assimilation
(3) Matured perception
! self-other correspondence
(2)
Self
Others
Temporal
predictabilitySpatial
predictability
Frequency
[Nagai et al., ICDL-EpiRob2011; Kawai et al., IROS2012]

Computational Model for Emergence of MNS

Early Stage of Development

No differentiation
between Self and Others
Motor output
Visual input
[Nagai et al., ICDL-EpiRob 2011]

Computational Model for Emergence of MNS

Later Stage of Development

MNS =
Self’s
motion
Others’
motion
Motor output
Visual input

Result 1: Self-Other Discrimination through
Visual Development
No differentiation Self’s motion Others’ motion
Visual development
Self
Others

Result 2: MNS Acquired in
Sensorimotor Mapping
Self’smotionOthers’motion
Motor
command
(a) w/ visual development
high
lowMNS
(b) w/o visual development

Result 3: Imitation Using Acquired MNS
ei(t+1)
si(t)
aj(t)
si(t+1)Sensorimotor
system
ŝi(t+1)
âj(t+1)
Predictor

Infant Action is Goal-Directed – Why?
[Carpenter et al., 2005]
[Bekkering et al., 2000]
DownloadedBy:[UniversityofBielefeld]At:15:4428July2008
156 BEKKERING, WOHLSCHLAÈ GER, GATTIS
paused for a few seconds before initiating the next trial. Both model and participant returned hands
to standard position between items. Each response was followed by encouragement. A video camera
placed behind the experimenter, focused on the upper body parts of both the child and the experi-
menter, recorded the movements for each action. The ®nal hand position was then analysed from the
video recording. Although latency data were also collected, they yielded results that mimic those
obtained with errors and will therefore not be reported.
FIG. 1. An illustration of the six hand movements used as target actions in Experiment 1.
paused for a few seconds before initiating the next trial. Both model and participant returned hands
to standard position between items. Each response was followed by encouragement. A video camera
placed behind the experimenter, focused on the upper body parts of both the child and the experi-
menter, recorded the movements for each action. The ®nal hand position was then analysed from the
video recording. Although latency data were also collected, they yielded results that mimic those
obtained with errors and will therefore not be reported.
Results and Discussion
Children always produced one of the six possible movements, but not always the match-
ing movement. Overall, participants produced errors in 24.5% of the trials, most of which
occurred in response to contralateral modelled movements. In 40.0% of the contralateral
trials, children produced ipsilateral movements instead–a so-called contra-ipsi error (CI-
error). In contrast, ipsilateral movements were usually imitated correctly: children made a
FIG. 1. An illustration of the six hand movements used as target actions in Experiment 1.
F16 Malinda Carpenter et al.
related if the hopping or sliding action was accompanied
by a task-related sound, or if the infant looked at the
action or at E while performing it. Infants also had to
hold the mouse by its body (not tail or hair) for hop-
ping, and put pressure on the mouse while sliding. For
each trial, infants’ behavior was coded as making the
mouse hop or slide (i.e. matching or mismatching E’s
demonstration), moving the mouse directly to the loca-
tion (i.e. picking it up and putting it there without
touching the mat in-between), some other action style
(e.g. throwing the mouse to the location), or no relevant
response (e.g. throwing the mouse off the table).
We also coded whether infants copied E’s sound
effects. Here, a match with the adult sound effect was
scored when infants made any repeated syllables (e.g.
‘dedede’) in the hopping condition or any long, single
syllable (e.g. ‘teeee’) in the sliding condition. Finally, we
coded whether infants went to the same location (left or
right) as E did. A match was scored in the House con-
dition if infants put the mouse in, on top of, or directly
in front of the same house as E, and in the No House
condition if infants put the mouse in the same left or
right area of the middle of the mat as E.
Because infants did not always respond on every trial,
we analyzed the percentage of matches (the number of
trials in which infants matched divided by the total
number of trials in which they produced a task-related
response) for each of the measures. To determine
whether infants were more likely to produce a match
than a mismatch, we also analyzed the percentage of
matches after subtracting the percentage of mismatches
(e.g. the hopping style or sound effect in the sliding con-
dition, or the left location when E went to the right one).
This corrected score produced the same overall results as
the percentage of matches. Only infants’ first responses
Matching action style
Figure 2 presents the overall percentage of trials in
which infants matched the adult’s action style in the
two experimental conditions. Infants matched E’s action
style significantly more often in the No House than in
the House condition, F(1, 98) = 117.32, p < .001, and older
infants produced significantly more matches than
younger infants, F(1, 98) = 20.07, p < .001. There was
also an interaction between age and condition, F(1, 98)
= 20.19, p < .001: although the effect of condition was
significant for both ages, the magnitude of the effect was
larger in 18-month-olds, t(65) = 13.2, p < .001, than in
12-month-olds, t(33) = 3.85, p < .001. The analyses of
the corrected percentage of matches mirrored these
results and also showed that both 12-month-olds (t(34)
= 1.82, p < .05) and 18-month-olds (t(68) = 7.59, p <
.001) produced more matches than mismatches.
The same pattern of results held for each action style
Figure 2 The overall percentage of matches in action style
across conditions as a function of age.
Infants copy goals F15
© Blackwell Publishing Ltd. 2005
Materials
A stuffed toy mouse and two identical black 51.5 cm ×
64.5 cm mats were used. Attached to the top of one of
the mats were two houses made of a rectangular 6 cm ×
6 cm × 12 cm tube and a cardboard roof (see Figure 1).
The houses were 18 cm apart from each other and cen-
tered on the mat. The other mat was plain, with nothing
attached.
Procedure
Infants sat on their parents’ laps across the table from a
female experimenter (E). First, E gave the mouse to
infants briefly so they could become familiar with it. E
then placed the assigned mat (see below) on the table, let
infants explore it briefly, and then began the tests.
There were eight trials, four in each of two conditions:
House and No House, corresponding to the two mats.
The four trials of each condition were blocked and the
order of the blocks was counterbalanced. In both condi-
tions, E performed exactly the same actions, to the same
location on the mat; the only difference between condi-
tions was whether there was a house on the mat in the
final location. For each trial, E obtained the infant’s
attention and then moved the mouse to the final location
using one of two action styles: hopping or sliding. For
the hopping action style, E made the mouse jump in a
straight line to the location, breaking contact with the mat
approximately eight times. Each hop was accompanied
by a [bi] sound (so infants heard ‘beebeebeebee . . .’).
For the sliding action style, E moved the mouse in a
straight line to the location, never breaking contact with
the mat. This action was accompanied by one long
‘beeeeeeeee’ sound.
Half the trials in each condition were to the left loca-
tion and half were to the right. In half of each of these
trials, E made the mouse hop and in half she made it
slide. For each infant, the order of left/right and hop/
slide trials was the same for each of the two conditions’
blocks. E held the mouse in her right hand for actions to
her right side and in her left hand for actions to her left
side. She started the action from the middle of her side
of the mat.
In each of the eight trials, after a single demonstration
of E moving the mouse to one of the locations and leav-
ing it there for a few seconds, E picked up the mouse
and placed it in front of infants in the middle of their
side of the mat. E told infants, ‘Now you.’ E waited until
infants made a relevant response or else made it clear
that they did not wish to respond (e.g. by throwing the
mouse or giving it back to E), and then E took the
mouse and went on to the next demonstration.
Coding
It was not possible to code infants’ responses blind to
experimental condition (House/No House) because houses
were present or not throughout the response period.
However, coders did not watch demonstrations and so
were blind to the action style and sound effects E used,
and the left/right location in which she put the mouse.
The main measure of interest was whether infants
copied E’s action style differently in the House versus
No House conditions. All hopping and sliding move-
ments were coded, even those not directed at the correct
locations. Hopping was coded if infants made the mouse
break contact with the mat more than once and sliding
was coded if infants pushed the mouse on the mat with-
out breaking contact. However, because coders noted
that infants sometimes banged or slid the mouse around
randomly, we added the additional criterion that the
hopping or sliding needed to be task-related, but the
pattern of results was the same at the overall level when
all responses were included. Actions were coded as task-
Figure 1 (a) The mouse at the start location in the House
condition. (b) The mouse at the end location in the No House
condition.
g Ltd. 2005
s the overall percentage of trials in
tched the adult’s sound effect in the
conditions. Infants matched E’s sound
more often in the No House than in
on, F(1, 98) = 6.82, p < .01. This was the
ng sound separately as well, F(1, 80) =
matches than mismatches (18-month-olds: t(68) = 2.32,
p < .02; 12-month-olds: t(34) = 4.52, p < .001).
Combinations of responses
Because we were also interested in infants’ social learn-
ing skills above and beyond their understanding of the
llpercentageofmatchesofthedemonstrated
conditions as a function of age.
Figure 5 The overall percentage of matches of location across
conditions as a function of age.
Goal-match Means-match
adedBy:[UniversityofBielefeld]At:15:4428July2008
FIG. 2. Percentage of errors for the different conditions in Experiments 1±3. The blank bar represents errors
Contralateral
Ipsilateral
[Gleissner et al.,
2000]

•  Difference in prediction error produces hierarchical
development of actions.
–  Goal: large dynamics ! larger error ! learned first
–  Means: small dynamics ! smaller error ! learned later
Our Hypothesis about
Hierarchical Representation of Action
Means
Goal
Init
[Park, Kim, & Nagai, SAB 2014]

Learning Goal-Directed Actions Using
RNNPB
•  Recurrent Neural Network with Parametric Bias (RNNPB)
[Tani & Ito, 2003]
–  Represent multiple time-series of data using PBs
–  Learn with back-propagation through time
PB1
PB2
Before learning
PB1
PB2
After learning
(t) C(t)
C(t+1)
PB
(t+1)

Result 1: Developmental Change in PBs &
Generated Actions (t = 0)
A, B: Goal
0, 1, 2: Means
: Desired trajectory
:Acquired trajectory

Generated Actions (t = 1,000)
A, B: Goal
0, 1, 2: Means

A, B: Goal
0, 1, 2: Means

Result 2:Action Generation by Robot
A1 B1
A1 B1
Middle stage of learning:
! Goal only
Later stage of learning:
! Goal + means
(t = 3,500)
(t = 200,000)

Infants Help Others Even Without Reward
– Why?
[Warneken & Tomasello, 2006]

TwoTheories for Altruistic Behaviors
[Paulus, 2014]
•  Emotion-sharing theory
–  Understand other person as an
intentional agent [Batson, 1991]
–  Be motivated to help other based on
empathic concern for other’s needs
[Davidov et al., 2013]
–  Self-other differentiation
•  Goal-alignment theory
–  Understand other’s goal, but not his/
her intention [Barresi & Moore, 1996]
–  Take over other’s goal as if it were
infant’s own
–  No self-other discrimination[Warneken & Tomasello, 2006]

Emergence of Altruistic Behavior
1.  Learn the predictor by
minimizing the prediction
error ei(t+1) through the
robot’s own experiences
Cover
Push
[Baraglia, Nagai, & Asada, ICDL-EpiRob 2014]
ei(t+1)
si(t)
aj(t)
si(t+1)Sensorimotor
system
ŝi(t+1)
âj(t+1)
Predictor

1.  Learn the predictor to
minimize the prediction
2.  Estimate ei(t+1) while
observing other’s action
si(t+1)
Predict
(Other person)
ei(t+1) "
si(t)
aj(t)
si(t+1)Sensorimotor
system
ŝi(t+1)
âj(t+1)
Predictor

Push
1.  Learn the predictor to
minimize the prediction
2.  Estimate ei(t+1) while
observing other’s action
si(t+1)
3.  Execute the action âj(t+1)
to minimize ei(t+1) if
ei(t+1) > threshold
! Altruistic behavior
ei(t+1) #
si(t)
aj(t)
si(t+1)Sensorimotor
system
ŝi(t+1)
âj(t+1)
Predictor

Result: Emergence of Altruistic Behavior

Autism Spectrum Disorder (ASD)
•  Difficulties in communicating
with other people [Baron-Cohen, 1995;
Charman et al., 1997; Mundy et al., 1986]
–  Lack of theory of mind
–  Less eye contact
–  Difficulty in joint attention, etc.
•  Atypical perception & weak
central coherence [O’Neill & Jones,1997;
Happé & Frith, 2006;Ayaya & Kumagaya, 2008]
–  Hyperesthesia/hypoesthesia
–  Weak ability to integrate
information, etc.
Perception
Social

Atypical Perception in ASD
[Behrmann et al., 2006]
116
[Ayaya & Kumagaya, 2008]
Original
ASD

Our Hypothesis about Mechanism of ASD
•  ASD might be caused by an atypical tolerance for
prediction error in predictive learning.
[Ayaya & Kumagaya, 2008; Nagai, in press]
Sensorimotor information
Typically developing people
Proper tolerance for
prediction error
People with ASD
Atypical tolerance for
prediction error
(smaller tolerance ! hyperesthesia)
(larger tolerance ! hypoesthesia)

[Qin et al., ICDL-EpiRob 2014; Nagai et al., Japanese CogSci 2015]
Simulator of Atypical Perception in ASD

Cognitive
Neuroscience
Robotics
Conclusion

Our Hypothesis about Mechanism of ASD
•  ASD might be caused by an atypical tolerance for the
prediction error in predictive learning.
[Ayaya & Kumagaya, 2008; Nagai, in press]
Sensorimotor information
Typically developing people
Proper tolerance for
prediction error
People with ASD
Atypical tolerance for
prediction error
(small tolerance ! hyperesthesia)
(large tolerance ! hypoesthesia)

Increasing Interest in Predictive Learning
Predictive coding under the free-energy principle
Karl Friston* and Stefan Kiebel
The Wellcome Trust Centre of Neuroimaging, Institute of Neurology, University College London,
Queen Square, London WC1N 3BG, UK
This paper considers prediction and perceptual categorization as an inference problem that is solved
by the brain. We assume that the brain models the world as a hierarchy or cascade of dynamical
systems that encode causal structure in the sensorium. Perception is equated with the optimization or
inversion of these internal models, to explain sensory data. Given a model of how sensory data are
generated, we can invoke a generic approach to model inversion, based on a free energy bound on the
model’s evidence. The ensuing free-energy formulation furnishes equations that prescribe the
process of recognition, i.e. the dynamics of neuronal activity that represent the causes of sensory
input. Here, we focus on a very general model, whose hierarchical and dynamical structure enables
simulated brains to recognize and predict trajectories or sequences of sensory states. We first review
hierarchical dynamical models and their inversion. We then show that the brain has the necessary
infrastructure to implement this inversion and illustrate this point using synthetic birds that can
recognize and categorize birdsongs.
Keywords: generative models; predictive coding; hierarchical; birdsong
1. INTRODUCTION
This paper reviews generic models of our sensorium
and a Bayesian scheme for their inversion. We then
show that the brain has the necessary anatomical and
physiological equipment to invert these models, given
sensory data. Critically, the scheme lends itself to a
relatively simple neural network implementation that
shares many features with real cortical hierarchies in
the brain. The basic idea that the brain tries to infer the
causes of sensations dates back to Helmholtz (e.g.
Helmholtz 1860/1962; Barlow 1961; Neisser 1967;
Ballard et al. 1983; Mumford 1992; Kawato et al. 1993;
Dayan et al. 1995; Rao & Ballard 1998), with a recent
emphasis on hierarchical inference and empirical Bayes
(Friston 2003, 2005; Friston et al. 2006). Here, we
generalize this idea to cover dynamics in the world and
consider how neural networks could be configured to
invert hierarchical dynamical models and deconvolve
sensory causes from sensory input.
This paper comprises four sections. In §1, we
introduce hierarchical dynamical models and their
inversion. These models cover most of the models
encountered in the statistical literature. An important
aspect of these models is their formulation in generalized
coordinates of motion, which lends them a hierarchal
form in both structure and dynamics. These hierarchies
2. HIERARCHICAL DYNAMICAL MODELS
In this section, we look at dynamical generative models
pð y; wÞZpð y j wÞpðwÞ that entail a likelihood, p(yjw), of
getting some data, y, given some causes, wZ{x, v, q},
and priors on those causes, p(w). The sorts of models
we consider have the following form:
y Z gðx; v; qÞ Cz;
_x Z f ðx; v; qÞ Cw;
ð2:1Þ
where the nonlinear functions f and g of the states are
parametrized by q. The states v(t) can be deterministic,
stochastic or both, and are variously referred to as
inputs, sources or causes. The states x(t) meditate the
influence of the input on the output and endow the
system with memory. They are often referred to as
hidden states because they are seldom observed
directly. We assume that the stochastic innovations
(i.e. observation noise) z(t) are analytic, such that the
covariance of ~zZ½z; z0
; z00
; .ŠT
is well defined; simi-
larly, for w(t), which represents random fluctuations on
the motion of hidden states. Under local linearity
assumptions, the generalized motion of the output or
response ~yZ½ y; y0
; y00
; .ŠT
is given by
y Z gðx; vÞ Cz x0
Z f ðx; vÞ Cw
Phil. Trans. R. Soc. B (2009) 364, 1211–1221
doi:10.1098/rstb.2008.0300
on 30 March 2009rstb.royalsocietypublishing.orgDownloaded from
REVIEW
Predictive coding: an account of the mirror neuron system
James M. Kilner Æ Karl J. Friston Æ Chris D. Frith
Received: 21 February 2007 / Revised: 19 March 2007 / Accepted: 21 March 2007 / Published online: 12 April 2007
Ó Marta Olivetti Belardinelli and Springer-Verlag 2007
Abstract Is it possible to understand the intentions of
other people by simply observing their actions? Many be-
lieve that this ability is made possible by the brain’s mirror
neuron system through its direct link between action and
observation. However, precisely how intentions can be
inferred through action observation has provoked much
debate. Here we suggest that the function of the mirror
system can be understood within a predictive coding
framework that appeals to the statistical approach known as
empirical Bayes. Within this scheme the most likely cause
of an observed action can be inferred by minimizing the
prediction error at all levels of the cortical hierarchy that
are engaged during action observation. This account
identifies a precise role for the mirror system in our ability
used to execute that same action (Jeannerod 1994; Prinz
1997). Interest in this idea has grown recently, in part due
to the neurophysiological discovery of ‘‘mirror’’ neurons.
Mirror neurons discharge not only during action execution
but also during action observation, which has led many to
suggest that these neurons are the substrate for action
understanding.
Mirror-neurons were first discovered in the premotor
area, F5, of the macaque monkey (Di Pellegrino et al.
1992; Gallese et al. 1996; Rizzolatti et al. 2001; Umilta
et al. 2001) and have been identified subsequently in an
area of inferior parietal lobule, area PF (Gallese et al. 2002;
Fogassi et al. 2005). Neurons in the superior temporal
sulcus (STS), also respond selectively to biological
Cogn Process (2007) 8:159–166
DOI 10.1007/s10339-007-0170-2
only underlies motor but cognitive and social skills as well”. Interest-
ingly, they note consolidation of memory traces after the initial acqui-
sition can “result in increased resistance to interference or even
improvement in performance following an offline period”. This is a
fascinating observation that suggests optimisation of the brain's gen-
erative model does not necessarily need online sensory data. Indeed,
there are current theories about the role of sleep in optimising the
brain's generative model, not in terms of its ability to accurately pre-
dict data, but in terms of minimising complexity. Mathematically, this
is interesting because surprise or model evidence can be decomposed
into accuracy and complexity terms; suggesting that model evidence
can be increased by removing redundant model components or pa-
rameters (Friston, 2010). This provides a nice Bayesian perspective
on synaptic pruning and the issues considered by Németh and
Janacsek (2012-this issue).
4. Active inference
As noted above, a simple extension to predictive coding is to con-
sider their suppression by the motor system. In this extension, predic-
tion errors are not just suppressed by optimising top-down or
descending predictions but can also be reduced by changing sensory
input. This does not necessarily mean visual or auditory input but
the proprioceptive input responding to bodily movements. As noted
above, the suppression of proprioceptive prediction errors is, of
error related negativity reviewed by Hoffmann and Falk
(2012-this issue); who consider the “monitoring of one’s o
tions” and its role in adjusting behaviour. Again, the focus is
suggesting that even within single trial recordings, the neuro
logical correlates of behaviour-dependent prediction errors
observed empirically. In their words: “The initiated response
pared with the desired response and a difference; i.e., misma
tween both representations induces the error negativity”. Thi
the proprioceptive prediction error that drives reflex arcs but
level perceptual (or indeed conceptual) prediction error; sug
that the long-term hierarchical predictions of unfolding senso
kinematic changes have been violated. In other words, the
nomena speak again to separation of temporal scales and hier
in providing multimodal predictions to the peripheral senso
motor systems.
Active inference means that movements are caused by top
predictions, which means that the brain must have a model o
caused these movements. This begs the interesting questio
whether there is any sense of agency associated with represen
In other words, if I expect to move my fingers and classical m
flexes cause them to move, do I need to know that it was me w
tiated the movement? Furthermore, can I disambiguate betw
as the agent or another. These are deep questions and mov
to issues of self modelling and action observation:
Fig. 1. This figure illustrates the neuronal architectures that might implement predictive coding and active inference. The left panel shows a schematic of predictive coding sc
which Bayesian filtering is implemented by neuronal message passing between superficial (red) and deep (black) pyramidal cells encoding prediction errors and conditi
dictions or estimates respectively (Mumford 1992). In these predictive coding schemes, top-down predictions conveyed by backward connections are compared with co
expectations at the lower level to form a prediction error. This prediction error is then passed forward to update the expectations in a Bayes-optimal fashion. In active i
this scheme is extended to include classical reflex arcs, where proprioceptive prediction errors drive action — a (alpha motor neurons in the ventral horn of the spinal-cord
extrafusal muscle contractions and changes in primary sensory afferents from muscle spindles. These suppress prediction errors encoded by Renshaw cells. The right panel p
schematic of units encoding conditional expectations and prediction errors at some arbitrary level in a cortical hierarchy. In this example, there is a distinction between hidd
xx that model dynamics and hidden causes xv that mediate the influence of one level on the level below. The equations correspond to a generalized Bayesian filtering or p
coding in generalized coordinates of motion as described in (Friston, 2010). In this hierarchical form f(i)
:=f(xx
(i)
,xv
(i)
) corresponds to the equations of motion at the i-th le
g(i)
:=g(xx
(i)
,xv
(i)
) link levels. These equations constitute the agent's prior beliefs. D is a derivative operator and Π(i)
represents precision or inverse variance. These equati
used in the simulations presented in the next figure.
250 K. Friston / International Journal of Psychophysiology 83 (2012) 248–252

ThankYou!
Osaka University
•  Minoru Asada
•  Jimmy Baraglia
•  Yuji Kawai
•  Shibo Qin
•  Many students
University ofTokyo
•  Shinichiro Kumagaya
•  Satsuki Ayaya
KAIST
•  Jun-Cheol Park
yukie@ams.eng.osaka-u.ac.jp
http://cnr.ams.eng.osaka-u.a.jp/~yukie/

Predictive Learning of Sensorimotor Information as a Key for Cognitive Development, Yukie Nagai

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