Download Emergence of Mirror Neurons in a Model of Gaze Following

Emergence of Mirror Neurons in a Model of Gaze Following
Jochen Triesch , Hector Jasso , and Gedeon O. Deák
Frankfurt Institute for Advanced Studies, Max-von-Laue-Str. 1, D-60438 Frankfurt/Main, Germany
Dept.
of Cognitive Science, 9500 Gilman Drive, La Jolla, CA 92093, USA, triesch,deak @cogsci.ucsd.edu
Dept. of Computer Science and Engineering, 9500 Gilman Drive, La Jolla, CA 92093, USA, [email protected]
Abstract— We present a computational model of the emergence of gaze following, which is the ability to re-direct
one’s gaze to the location that another agent is looking at.
The model acquires gaze following by learning to predict the
locations of interesting sights from the looking behavior of
other agents through reinforcement learning. In doing so, the
model develops pre-motor representations that exhibit many
properties characteristic of mirror neurons. The predicted new
class of mirror neurons is specific to looking behaviors. The
model offers a simple account of how these and other mirror
neurons may acquire their special response properties. In this
account, visual representations of other agent’s actions become
associated with pre-motor neurons that represent the intention
to perform corresponding actions.
Index Terms— gaze following, mirror neuron, reinforcement
learning, temporal difference learning, actor critic architecture,
imitation, response facilitation
I. I NTRODUCTION
Gaze following is the ability to look where somebody
else is looking. This skill is considered to be a foundational
component of humans’ social interaction abilities. Gaze following emerges in a progressive fashion during the first two
years of life [16]. While pre-cursors of gaze following can
be observed in newborns, some gaze following behaviors do
not emerge until 18 month or later. For example, while young
infants will only follow gaze to target objects that are already
inside their field of view, older infants will also follow gaze
to targets behind them [1]. Similarly, while young infants
will be easily “fooled” by additional distractor objects which
are not being looked at, older infants are more accurate in
estimating the correct target of others’ gaze. Finally, there is
also an interesting development in the kinds of visual cues
that infants use for gaze following. While they seem to mostly
follow others’ head movements early on, they will later
become sensitive to the status of the eyes of the other person.
There has been much interest in gaze following in recent
years, because researchers believe that the developing gaze
following capacities in infants may reflect infants’ developing
understanding of others as perceiving intelligent agents that
are “like them.” In fact, many gaze following experiments
have been designed specifically with the goal of elucidating
what the nature of the infant’s understanding of other people
may be.
Over the last years, several groups including our own have
been working on computational models that try to account
for various aspects of the infant’s developing gaze following
abilities and explain this development in neural terms. We
think that it is good modeling practice to keep models as
simple as possible. In doing so, we do not deny that infants
will ultimately develop very sophisticated representations of
themselves and others. Rather, we would like to clarify how
these representations may emerge, how they may be built on
top of earlier and more primitive representations, and what
the underlying developmental driving forces for this process
may be. In order to do so, it is best to start with relatively
simple models and to extend and refine them as needed.
In a companion paper [6], we have proposed a new model
for the emergence of gaze following skills during the first
18 months of life. The model is able to account for a
wealth of experimental findings and is based on neurally
plausible learning mechanisms. An outline of the model
will be presented below. The focus of this paper is the
unexpected finding that the model develops internal premotor representations that share many aspects of so-called
mirror neurons.
A. Mirror Neurons
Mirror neurons are a class of pre-motor neurons originally
found in macaque area F5 [14]. Their defining characteristic
is that these neurons become activated when the animal
performs an action such as reaching for an object and
grasping it or when the animal sees another agent perform the
same action. Because of this property, it has been suggested
that mirror neurons may play a role in the understanding of
other’s actions and recent evidence supports this hypothesis
[5]. Some mirror neurons can be triggered through different
modalities. For example, a mirror neuron may respond to
seeing the action of tearing paper or to hearing the same
action being performed [7]. Interestingly, for some mirror
neurons it is sufficient if the performance of the action can
be inferred, even though it may not be fully visible [22].
Converging evidence points to the existence of a similar
system of mirror neurons in humans. What is currently
unclear, however, is how mirror neurons arrive at their
specific response properties. We find it very unlikely that a
sophisticated mirror system could be innate, in the sense of
a detailed pre-specified connection pattern for every neuron.
Rather, we believe that learning processes must play an
important role in the formation of the mirror system and
below we will demonstrate how such a learning process might
occur.
B. Gaze Following as Imitation
Mirror neurons are thought to play a central role in imitation behaviors and representations of goal-directed actions. In
its most general sense, imitation occurs when an individual
observes another’s behavior and replicates it. In this sense,
gaze following can be viewed as imitation [12], [19]. The
behavior that is being observed is another’s gaze shift to a
particular location in space, and this behavior is replicated1.
Most authors use more strict definitions for “true” imitation,
however, and might prefer to consider acts of gaze following
as a form of response facilitation because the copied behavior
(a gaze shift to a certain location) is not novel but already
part of the agent’s behavioral repertoire (see, e.g., [17]). This
distinction is of little importance for the argument of this
paper, however, and we will not elaborate on this issue. It
is easy to imagine the role that mirror neurons may play in
imitation or response facilitation. If another agent is observed
performing an action, then this leads to the activation of a
population of mirror neurons that code specifically for this
action. Because of the motor properties of mirror neurons,
this representation of the other agent’s action can be used to
trigger execution of the “same” action. As we will see below,
this is exactly how gaze following occurs in the model. The
novelty of this paper is that our model offers an account how
neurons with mirror properties can be learned from scratch
(see also [11] for a proposal of how mirror neurons for objectdirected actions may emerge) and that it predicts a new class
of mirror neurons that have not been observed yet.
II. C OMPUTATIONAL M ODEL OF THE E MERGENCE
G AZE F OLLOWING
OF
The proposed model is a blend of two previous models of
the emergence of gaze following. Like [2], our model is based
on reinforcement learning [18], [20]. In particular, it uses
an actor critic architecture as a biologically plausible model
for reward driven learning. Like [8], our model addresses
spatial aspects of the gaze following problem. In particular,
it allows to model how infants learn to cope with the spatial
1 Since the “behavior” is very simple in this case, it may be more
appropriate to use the term motor act, but the imitative nature of gaze
following is still obvious.
Fig. 1. The model comprises an infant and a caregiver interacting with a
number of salient objects.
ambiguity that results from only being able to observe their
caregiver’s gaze direction but not the precise location of their
focus of attention. Due to space limitations, we can only give
an overview of the model here. A more detailed description
of the model and its behavior are given in a companion paper
[6].
In the model, an infant and its caregiver interact with a
number of salient objects as illustrated in Fig. 1. The infant
receives a reward for looking at salient objects, modeling
the infant’s looking preferences. During learning, the infant
discovers that the caregiver’s direction of gaze is often
predicting the locations of salient objects. The infant learns
to associate a particular gaze direction of the caregiver with
an increased probability of finding interesting visual stimuli
in the locations along the caregiver’s line of sight.
The infant is modeled as a reinforcement learning agent
with an actor critic architecture as shown in Fig. 2. The
infant’s visual system extracts three kinds of feature vectors
from the visual scene. We can think of each of them as
being represented in a layer of model neurons described by
a vector of real numbers. First, the visual system extracts the
locations of salient objects within the infant’s field of view.
For convenience, these are represented in a two-dimensional 2
body-centered representation , where each element of corresponds to one of 64 locations around the infant as
2 The restriction to two dimensions is a matter of convenience and
reflects the fact that most experiments on infant gaze following use a twodimensional layout where infant, adult, and objects are in the same plane, i.e.
at the same height from the floor. We expect our model to easily generalize
to the case of a fully three-dimensional setting.
r
s
w
"V1"
"basal ganglia"
V
delta
h
action selection
m
"STS"
M
e
u
a
"to motor cortex"
"pre−motor cortex"
Fig. 2. The infant model comprises a number of brain areas including different visual cortical areas, basal ganglia, pre-motor cortex, and motor cortex. See
text for details.
indicated in Fig. 2. The components of are given by:
"!$#"%'&()*+
, -*+/.0$'&(+
1
(1)
where is the saliency of object 2 and the sum runs over
all objects present in location # . Location # is considered
visible if it falls within the infant’s current field of view of
345,"6
. Maps of the saliency of different visual stimuli may be
present in primary visual cortex [9] but also in higher visual
areas, particularly in the dorsal pathway. Our assumption of
a body-centered representation (in contrast to a retinotopic
one) is not physiologically accurate but it frees us from
having to model coordinate transformations between different
coordinate systems (although it is an interesting question in
its own right when and how infants learn to compute certain
coordinate transformations).
When the caregiver is inside the infant’s field of view,
the infant will represent the head pose of the caregiver and
the direction of the caregiver’s eyes in vectors 7 and 8
respectively. Each unit in layer 7 (or 8 ) codes for a specific
orientation of the caregiver’s head (eyes). Such representations of head pose and gaze direction may be found in the
superior temporal sulcus (STS) in monkeys [13]. Separate
representations for the caregiver’s head pose and eye direction
allow us to capture the development of the infant’s differential
sensitivity to these cues, although we do not claim that these
representations have to be anatomically separated in the brain.
The three vectors of visual features serve as the input to
the actor and the critic part of the infant. The actor maintains
a representation of competing action plans (in our case,
plans for different gaze shifts) in a pre-motor layer 9 . Each
element in 9 corresponds to a gaze shift to a certain location
in space. These locations are again conveniently represented
in a body centered coordinate system such that there is a oneto-one correspondence between features in the visual saliency
layer and the pre-motor layer 9 . The visual representations
, 7 , 8 activate layer 9 via a matrix of connection weights
:
;
:<;
. Formally, 9 , where is the full vector of features
resulting from concatenating , 7 , and 8 . The actor choses
among the different action plans via a probabilistic soft-max
action selection where the probability of choosing action = ?FEHG
is given by:
>@?
E
,
= BA ?FEHG A
+/CD
A
1
I +JCKD
(2)
where ML is an inverse temperature parameter balancing
exploration and exploitation.
The critic estimates the value of the current situation via a
;
;
linear estimate based on the full feature vector : N MOQP ,
where ORP denotes the transpose of weight vector O . Based
on this estimate it calculates an error signal S :
S MTVU
N
1
(3)
where T is the received reward and N is the estimated value
of the state (see below).
The infant receives two kinds of rewards. First, the infant
receives a positive reward corresponding to the saliency of
the location where the infant is looking. This models infants’
preferences for looking at salient stimuli (moving, high
contrast, etc.). Second, the infant receives a small negative
reward that is proportional to how far the infant is turning
away from the forward direction. This models the discomfort
associated with turning around, e.g., to look at what’s behind
the infant [4].
Learning occurs through adaptation of the weight matrix
:
for the actor and the weight vector O for the critic based
B. Emergence of gaze following
Figure 3 shows a subset of the learned connection weights
to layer 9 after 50000 steps of learning3. Initially, all
weights are set to zero. Soon the connections from layer to layer 9 develop a characteristic one-to-one mapping (not
shown): the infant learns how to make accurate saccades to
salient objects in its field of view. At the same time, the
connections from 7 and 8 to the pre-motor area develop their
specific pattern. The infant learns that specific head poses
and eye directions of the caregiver predict rewarding stimuli
in certain locations which lie along the caregiver’s line of
sight. The model’s behavior nicely reflects the developmental
progression from rudimentary to more sophisticated gaze
following observed in human infants [6]. This development
also results in an interesting transition in the infant’s behavior.
While the initial behavior is purely driven by visual saliency
(bottom-up attention), the later looking behavior becomes
increasingly driven by top-down predictions about the locations of rewards. Since the locations of interesting objects are
more strongly correlated with the caregiver’s eye direction as
compared to the head pose, the weights from 8 get slightly
“sharper” than those from 7 . Behaviorally, this is reflected
in the development of a higher sensitivity to the caregiver’s
eyes as compared to the head.
:
actions
head features
eye features
Fig. 3. Learned connection weights from the head features W and eye
features X to the pre-motor representation Y . Note how the same head pose
of the caregiver has become associated with several locations that lie along
the caregiver’s line of sight.
on the received rewards [3]. The element Z\[^] _ of weight
:
matrix
is updated according to:
?Facb
?Fa
3 A b`de?
>@f
S[J[^] U
;
?ka
AmlnA Seop_
(4)
1 k? a
>@f
;
?ka
Aql is
= gi
where = g is the action taken, is a learning rate,
;
A
the probability of taking action = g in state
, o _ is the r -th
;
component of the state vector , and S [J[ ] is the Kronecker
delta, defined as 1 if = = g , 0 otherwise.
The weight vector O used by the critic to estimate the
Z`[^] _
A
Z`[^]_
d
=hgji
value of a state is updated according to:
?ka
b
O
3 A sO
?ka
btd
A
S
;vu
(5)
III. E XPERIMENTS AND R ESULTS
A. Learning environment
In the following experiments, the infant and the caregiver
interacted with the environment in the following way. The
3,
interaction proceeds in discrete trials lasting
time steps.
There is one salient object positioned in a random location.
The caregiver is looking at this object for the entire duration of the trial. The infant starts the trial looking at the
caregiver. In every time step, first the visual feature vector
;
is computed. Then the activity in the pre-motor layer 9
is calculated. The infant selects an action, which is then
;
executed. This results in a new feature vector , a reward
T , and new activations in 9 and N . Now the weights are
updated according to (4) and (5). This process repeats until
the end of the trial.
C. Formation of mirror neurons in the pre-motor area
At the end of the learning process, the model neurons
in layer 9 share many characteristics with classical mirror
neurons. First, a unit in this layer will usually be active
during the execution of a gaze shift to a certain location
in space. This is because the probability of performing
such a gaze shift is directly related to the activation of
the unit, as described by (2). Second, the unit will also be
active when the model observes another agent performing
the action of looking at this location. This is due to the
learned connection weights from the representation of the
caregiver’s head and eyes in layers 8 and 7 to the pre-motor
units in 9 . The combination of being active during execution
and observation of a motor act is the defining characteristic
of mirror neurons. At the same time, these neurons are not
merely motor neurons. The model will not always perform
a gaze shift when the corresponding pre-motor neuron is
activated. Instead, the pre-motor neurons only represent a
plan or proposal to perform a certain gaze shift from which
the action selection mechanism will select one. This means
that the activation of a pre-motor unit due to a salient stimulus
or the gaze shift of another agent does not automatically lead
to the corresponding gaze shift. Instead, multiple such action
3 A more detailed analysis of the emergence of gaze following in the model
is given in [6].
plans will usually compete for being executed. At the same
time, execution of any action may be inhibited by additional
brain structures which we have G not included in our model.
Clearly, the neurons in layer
have the defining characteristics of mirror neurons. Note that area F5 mirror neurons
selective for grasping typically do not respond to the presence
of a visual stimulus alone, even if that stimulus is of interest
to the animal. In this respect, the mirror neurons in our model
behave differently. A salient visual object to which the model
G
is
not habituated will be sufficient to activate a neuron in layer
. This activation will be stronger, however, if the model also
sees the caregiver looking at this object.
IV. D ISCUSSION
We have presented a computational model of the emergence of gaze following. Despite its simplicity, the model
explains a large number of findings about the emergence
of gaze following in human infants as we have shown in
a companion paper to this article [6]. These include the
progression in expertise when following gaze to targets in
different locations, the improving ability to ignore distractor
objects, and the changing utilization of head pose and eye
cues for gaze following. An earlier model [2], [21], from
which the current one is derived, also explained delays or the
complete absence of gaze following in certain developmental
disorders such as autism or in other species. These models
are based on biologically plausible reinforcement learning
mechanisms. A number of other models of the emergence of
gaze following have been proposed in the past, but, to the
best of our knowledge, none of them accounts for the wide
range of experimental findings that our model can capture.
Our model was designed to offer a simple and parsimonious account of the complicated sequence of behavior patterns observed in the development of gaze following abilities
in human infants. Only after the model was completed, we
realized that the representation in the model’s pre-motor area
shares important properties with the mirror neuron system
in primates. The pre-motor representations in our model are
different from the mirror neurons that have been reported
in monkeys so far in the sense that they are not concerned
with manual or oral motor acts but with gaze shifts. Thus,
the model predicts the existence of a new class of mirror
neurons specific to looking behaviors. If such a class of
mirror neurons could be found, this would lend support
to our model. This raises the important question of where
in the brains of monkeys (or humans) one should look
for such neurons. Electrophysiological and brain imaging
studies suggest some tentative answers. Area F5, where the
first mirror neurons (for grasping) have been reported is
an obvious candidate. More generally, we may expect the
presence of the predicted class of mirror neurons in any area
intermediate between the superior temporal sulcus (STS),
where head and gaze direction sensitive neurons are found,
and eye movement related areas such as the frontal eye fields
(FEF). Some of the predicted mirror neurons may also be
present inside the FEF. The model also predicts that this area
should receive direct or indirect input from a visual saliency
map.
Beyond gaze following per se, our model may have broader
implications for our understanding of the mirror system — in
particular with respect to the question whether mirror neurons
are innate or whether they acquire their properties through a
learning process (e.g., [10]). If the model is in fact an accurate
description of the processes that underly the emergence of
gaze following, and if the predicted class of mirror neurons
does in fact exist, then this raises the possibility that other
classes of mirror neurons acquire their specific properties
in a similar learning process. In the current model, this
process essentially has two (not necessarily successive) steps.
First, the model learns to perform certain motor acts in
the appropriate situations. Concretely, it learns to map the
discovery of visually salient stimuli in certain locations to
gaze shifts to those locations. This corresponds to learning
the appropriate pattern of weights between the representation
of visually salient stimuli in layer to the layer 9 of premotor neurons that encode the intention to make gaze shifts
to specific locations. Second, the model learns to associate
representations of the looking behavior of other agents to
appropriate pre-motor neurons. This corresponds to learning
the appropriate pattern of weights between the representation
of the other agent’s gaze direction in layer 7 and 8 to the
same layer of pre-motor neurons 9 , thereby establishing an
alternative pathway for activating neurons in this layer. This
process is purely driven by the desire to maximize rewards,
which, in this case, are obtained for looking at interesting
visual stimuli. Thus, the gaze following behavior is learned
because the gaze shift of another agent indicates that it is
rewarding to perform the same gaze shift, i.e. to look at the
same location. Is it conceivable that the same mechanism
for learning could also work for other behaviors and other
kinds of mirror neurons? For the “classic” mirror neurons
concerned with the grasping of objects, we find it plausible
that there may be situations where observing an agent grasp
an object (e.g., a food item grasped by the mother in order
to eat it) may be indicative of a reward if the same action
is attempted (grasping a second food item from the same or
another source in order to also consume it). This explanation
of the emergence of mirror neuron properties seems to have
been rejected by some authors. Specifically, Rizzolatti and coworkers write [15]: “In conditions in which mirror neurons
become active, hardly any imitation would be useful.” If this
were generally true, then our proposed learning mechanism
cannot work. For gaze behaviors, we believe that this claim is
certainly not true. With respect to grasping, while there may
in fact be such situations (e.g., when only one food item is
present), we believe that there may also be situations (such
as the one described above) where it is very useful to imitate
a grasping movement and these situations may be sufficient
for the emergence of mirror neurons for grasping. Leaving
aside the specifics of grasping, our reinforcement learning
explanation of the emergence of imitation may be applicable
in many instances where imitation (in its various forms) and
a corresponding set of mirror neurons is observed. To resolve
this issue, it will likely be necessary to study the emergence
of imitation and the mirror system from a developmental
perspective. If the appearance of certain imitative behaviors
(such as gaze following or the imitation grasping movements)
during an individual’s development turns out to coincide with
the appearance of mirror neurons for these behaviors, then
this would be consistent with our hypothesis. More critically,
however, our model predicts that if an animal were raised
without the opportunity to ever observe a specific action
performed by other animals, then no mirror neurons specific
to this action should develop (see also [10] for a different but
related proposal). Furthermore, if an animal were raised in
an environment where behavior A was rewarded whenever
another agent performed an unrelated behavior B, then we
may expect the emergence of “mirror” neurons that respond
to the animal performing A or to the observation of another
animal performing B.
In the context of theories of imitation, our account of the
emergence of gaze following can be considered a simple
associative learning account of response facilitation. It is
worth highlighting that our goal was not a model of imitation,
and our model does not start with any mechanisms for,
say, matching other’s bodies to one’s own. On the contrary,
our model has a generic reinforcement learning architecture.
Nevertheless, it acquires the ability to map other’s motor acts
onto its own behaviors. This finding may be of interest for
the question of the development of higher imitative behaviors.
While it may be the case that specific mappings from other
bodies to one’s own body may be present at birth (e.g., [10]),
we have shown that such mappings can also result from
generic reinforcement learning mechanisms.
ACKNOWLEDGMENT
This work was done as part of the MESA project (Modeling the Emergence of Shared Attention) at the University
of California, San Diego (http://mesa.ucsd.edu). We thank
all members of the MESA team for their continuing collaboration. We also thank Jaime Pineda and Garrison Cottrell
for fruitful discussions. This work was supported by the
National Science Foundation under grant SES-0527756. JT
acknowledges support from the Hertie foundation.
R EFERENCES
[1] G. E. Butterworth and N. Jarrett. What minds have in common in
space: Spatial mechanisms serving joint visual attention in infancy.
British J. of Developmental Psychology, 9:55–72, 1991.
[2] E. Carlson and J. Triesch. A computational model of the emergence
of gaze following. In H. Bowman and C. Labiouse, editors, Connectionist Models of Cognition and Perception II, pages 105–114. World
Scientific, 2004.
[3] P. Dayan and L. F. Abbott. Theoretical Neuroscience. MIT Press,
Cambridge, MA, 2001.
[4] G. O. Deák, R. Flom, and A. D. Pick. Perceptual and motivational
factors affecting joint visual attention in 12- and 18-month-olds.
Developmental Psychology, 36:511–523, 2000.
[5] Pobric. G. and A.F. de C. Hamilton. Action understanding requires
the left inferior frontal cortex. Current Biology, 16:524–529, 2006.
[6] H. Jasso, J. Triesch, C. Teuscher, and G.O. Deák. A reinforcement
learning model explains the development of gaze following. Int. Conf.
on Cognitive Modeling (ICCM), 2006.
[7] Evelyne Kohler, Christian Keysers, M. Alessandra Umiltà, L. Fogassi,
V. Gallese, and G. Rizzolatti. Hearing sounds, understanding actions:
Action representation in mirror neurons. Science, 297:846–848, 2002.
[8] B. Lau and J. Triesch. Learning gaze following in space: a computational model. In Jochen Triesch and Tony Jebara, editors, Proc.
ICDL’04 — Third International Conference on Development and
Learning, San Diego, USA, pages 57–64. The Salk Institute for
Biological Studies, 2004.
[9] Zhaoping Li. A saliency map in primary visual cortex. Trends in
Cognitive Sciences, 6(1):9–16, 2002.
[10] Andrew N. Meltzoff. Imitation and other minds: The “like me”
hypothesis. In S. Hurley and N. Chater, editors, Perspectives on
Imitation: From Neuroscience to Social Science, pages 55–77. MIT
Press, 2005.
[11] G. Metta, G. Sandini, L. Natale, L. Craighero, and L. Fadiga. Understanding mirror neurons: a bio-robotic approach. Interaction Studies,
in press, 2006.
[12] Y. Nagai. Joint attention development in infant-like robot based on
head movement imitation. In Proc. Third Int. Symposium on Imitation
in Animals and Artifacts (AISB’05), pages 87–96, 2005.
[13] D.I. Perrett, P.A.J. Smith, D.D. Potter, A.J. Mistlin, A.S. Head, A.D.
Milner, and M.A. Jeeves. Visual cells in the temporal cortex sensitive
to face view and gaze direction. Proceedings of the Royal Society of
London. Series B, 223:293–317, 1985.
[14] G. Rizzolatti and L. Craighero. The mirror-neuron system. Annu. Rev.
Neurosci., 27:169–192, 2004.
[15] G. Rizzolatti, L. Fogassi, and V. Gallese. Neurophysiological mechanisms underlying the understanding and imitation of action. Nature
Reviews Neuroscience, 2:661–670, 2001.
[16] M. Scaife and J. S. Bruner. The capacity for joint visual attention in
the infant. Nature, 253:265–266, 1975.
[17] S. Schaal. Is imitation learning the route to humanoid robots? Trends
in Cognitive Sciences, 3:233–242, 1999.
[18] W. Schultz, P. Dayan, and P. R. Montague. A neural substrate of
prediction and reward. Science, 275:1593–1599, 1997.
[19] A.P. Shon, D.B. Grimes, C.L. Baker, M.W. Hoffman, S. Zhou, and
R.P.N. Rao. Probabilistic gaze imitation and saliency learning in a
robotic head. In Proc. Int. Conf. on Robotics and Automation (ICRA
05), 2005.
[20] R. S. Sutton and A. G. Barto. Reinforcement Learning: an introduction.
MIT Press, Cambridge, MA, 1998.
[21] J. Triesch, C. Teuscher, G. Deák, and E. Carlson. Gaze following: why
(not) learn it? Developmental Science, 9(2):125–157, 2006.
[22] M.A. Umiltà, E. Kohler, V. Gallese, L. Fogassi, Fadiga L., C. Keysers,
and G. Rizzolatti. “I know what you are doing:” a neurophysiological
study. Neuron, 31:91–101, 2001.