dynamic field theory part 4: the memory trace and preshape · formation as the simplest form of...
TRANSCRIPT
Summary/recall
action, perception, and embodied cognition takes place in continuous spaces. peaks = units of representation are attractors of the neural dynamics
neural fields link neural representations to these continua
stable activation peaks are the units of neural representation
peaks arise and disappear through instabilities through which elementary cognitive functions (e.g. detection, selection, memory) emerge
Summary/recall
inhomogeneities in the field may be amplified into peaks through the (boost-driven) detection instability
boost-induced detection instability
dimensionactivation
preshape
dimensionactivation
dimensionactivation
self-excited activation peak
boost
boost
preshape
preshape
… emergence of categories?
if we understand, how such inhomogeneities come about, we understand the emergence of categories…
inhomogeneities from simplest from the memory trace
~ habit formation (?) William James: habit formation as the simplest form of learning
habituation: the memory trace for inhibition..
the memory trace
mathematics of the memory trace
⇥mem u̇mem(x, t) = �umem(x, t) +
�dx� wmem(x � x�)�(u(x�, t))
⇥ u̇(x, t) = �u(x, t) + h + S(x, t) + umem(x, t)
+
�dx� w(x � x�) �(u(x�))
1
⇥mem u̇mem(x, t) = �umem(x, t)
+
�dx� wmem(x � x�)�(u(x�, t))
⇥ u̇(x, t) = �u(x, t) + h + S(x, t) + umem(x, t)
+
�dx� w(x � x�) �(u(x�))
1
memory trace only evolves while activation is excited
potentially different growth and decay rates
Wilimzig, Schöner 2006
slow
fast
memory trace reflects history of decisions formation
020
4060
805
1015
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20
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00.20.4
memorytrace
dimension
activation
time
dimension
time
categories may emerge ...
Wilimzig, Schöner 2006
preshape
is a decisive concept, it turns out, in how selection decisions are studied in the laboratory
reaction time (RT) paradigm
time
imperative signal=go signal
response
RT
task set
the task set
is the critical factor in such studies of selection: which perceptual/action alternative/choices are available…
e.g., how many choices
e.g., how likely is each choice
e.g., how “easy” are the choices to recognize/perform
because the task set is known to the participant prior to the presentation of the imperative signal, one may think of the task set as a “preshaping” of the underlying representation (pre=before the decision)
DFT: preshape
movemen
t
param
eter
time
activation
1.0
taskinput
movement parameter
0.0preshapedfield
-0.4 0.0
preshapedfield
specific inputarrives
specific input
weak preshape in selection
specific (imperative) input dominates and drives detection instability
[Wilimzig, Schöner, 2006]
0
500
1000
1500
0
parameter, x
time,
t
activ
atio
n u(
x)
specific input + boostin different conditions
preshape
0
2
4
parameter, x
S(x)
-20
-10
0
10
u(x)
parameter, x
boost
using preshape to account for classical RT data
Hick’s law: RT increases with the number of choices
-4
-3
-4
-3
-4
-3
-4
-3
200 300 400 500 600
05
10
parameter, x
time, t
pres
hape
d u(
x)u m
ax(t)
1 2 4 8
[Erlhagen, Schöner, Psych Rev 2002]
metric effect
predict faster response times for metrically close than for metrically far choices
0 45 90 135 180
150 200 250 300 350 400 450-4
-2
0
2
4
time
pres
hape
d ne
ural
fiel
d
movement direction
peak
leve
l of a
ctiv
atio
n
wide
narrow
[from Schöner, Kopecz, Erlhagen, 1997]
faster
slower
experiment: metric effect
[McDowell, Jeka, Schöner ]
-4
-3
-2
0
2
4
-4
-3
250 350 450 550-2
0
2
4
time
-4
-3
0
2
4
250 350 450 550time
250 350 450 550time
pres
hape
d ac
tivat
ion
field
mai
xmal
act
ivat
ion
movement parameter
same metrics, different probability different metrics, same probability
highprobability
highprobability
highprobability
lowprobabilitylow
probability
lowprobability
movement parameter movement parameter
[from Erlhagen, Schöner: Psych. Rev. 2002]
WideFrequent
WideRare
NarrowFrequent
NarrowRare
320
300
280
260
240
220
200
Target
7
6
5
4
3
2
1
0Wide
FrequentWideRare
NarrowFrequent
NarrowRare
Target
[from McDowell, Jeka, Schöner, Hatfield, 2002]
wide narrow
Reaction Time P300 Amplitude Fz
Tim
e (
ms)
Am
plitu
de (
mic
roV
)
rarerare
frequent
frequent
this was: weak preshape relative to the imperative stimulus
specific (imperative) input dominates and drives detection instability
[Wilimzig, Schöner, 2006]
0
500
1000
1500
0
parameter, x
time,
t
activ
atio
n u(
x)
specific input + boostin different conditions
preshape
0
2
4
parameter, x
S(x)
-20
-10
0
10
u(x)
parameter, x
boost
strong preshape relative to the imperative stimulus
[Wilimzig, Schöner, 2006]
=> field responds categorically
[Wilimzig, Schöner, 2006]
categorical responding
based on categorical memory trace and boost-driven detection instability
distance effect
common in categorical tasks… e.g., decide which of two sticks is longer => RT is larger when sticks are more similar in length (1930s’)
interaction metrics-probability
Wilimzig, Schöner, 2006
opposite to that predicted for input-driven detection instabilities:
metrically close choices show larger effect of probability
0 100 200 300-20246
time, t
max
imal
activ
atio
n
0 100 200 300
parameter, x0
1
2
3
parameter, x
S(x)
time, ttime, t0 100 200 300
more probablechoice
less probablechoice
more probablechoice
less probablechoice
0
10
20
30
40
% e
rror
s
more probablechoice
less probablechoice
parameter, x
same metrics, different probability different metrics, same probability
Behavioral evidence for preshapemovement preparation is graded and continuous in time starting out from preshaped representations
timemove on 4th to tone
imperative stimulus
imposed SR interval
timed movement initiation paradigm
[Ghez and colleagues, 1988 to 1990’s]
Behavioral evidence for preshape
[Favilla et al. 1989]
\
Behavioral evidence for preshape
0
20
40
60
0
20
40
60
125 75 25
0
20
40
60
0
20
40
60
0
20
40
60
125 75 25
0
20
40
60
Peak Force (N)
Dis
trib
ution o
f P
eak F
orc
es
Experimental results of Henig et al
short
SR
interval
medium
SR
interval
short
SR
interval
Dynamic Field Theory (DFT)
[Erlhagen, Schöner. 2002, Psychological Review 109, 545–572 (2002)]
theoretical account: movement parameters are represented in dynamic neural activation fields
0
100
200
0
100
200
0
100
200
0
100
200
0
100
200
0
100
200
0
100
200
0
100
200
Amplitude value
Num
ber
of tr
ials
theoretical account for Henig et al.
zero
SR
interval
short
SR
interval
medium
SR
interval
long
SR
interval
0
20
40
60
0
20
40
60
125 75 25
0
20
40
60
0
20
40
60
0
20
40
60
125 75 25
0
20
40
60
Peak Force (N)
Dis
trib
ution o
f P
eak F
orc
es
Experimental results of Henig et al
short
SR
interval
medium
SR
interval
short
SR
interval
place with minimal changes in the hand paths. Table 1shows the means and standard errors of curvature andlinearity indices (see Materials and methods) across sub-jects (n = 5) for predictable targets and for each time in-terval for unpredictable targets. Small increases in curva-ture of 1°–2° and reductions in linearity occur amongmovements initiated between 80 and 200 ms after targetpresentation. However, all values are well within therange of normal values for linearity in reaching move-ments (e.g. Atkeson and Hollerbach 1985; Georgopoulos1988a, b; Georgopoulos and Massey 1988; Gordon et al.1994b). Moreover, as can be noted among the hand pathsillustrated in Fig. 5, change in direction associated withcurvature did not appreciably reduce the directional errorat the end point. Similarly, the improvement in accuracywas not achieved through variations in movement time.
Those data will, however, be considered in greater detailbelow when the systematic effects of target separation onmovement time are described (see Fig. 10).
Threshold target separationfor discrete directional specification
Figure 7 shows the distributions of initial movement di-rections in one subject at five target separations andsmoothed for clarity. Data from the same three succes-sive S-R time interval bins used in earlier figures areshown in different line types. For the 30° degree targetseparation, at S-R intervals ≤ 80 ms (dotted line and his-togram to show effect of smoothing) initial directions aredistributed unimodally around the midpoint of the range
224
Fig. 7 Experiment 2. Distribu-tions of movement directions atthe time of peak acceleration inone subject for five target sepa-rations. In each plot, distribu-tions were fitted with a smoothline using a cosine function(Chambers et al. 1983). The ar-rows on the x-axis point to therequired direction for each tar-get separation. In the top plot,the actual histogram for re-sponses with S-R intervals≤ 80 ms is displayed to demon-strate the relationship of the fit-ted line to the actual distribu-tion. On the right side of eachplot, the actual target locationsare displayed for reference &/fig.c:
[Ghez et al 1997]
infer width of preshape peaks in field
behavioral evidence for preshape
behavioral evidence for preshape
0
50
100
0
50
100
0
50
100
0
50
100
0
50
100
0
50
100
Num
ber
of t
rial
s
parameter, x
0
50
100
0
50
100
0
50
100
0
50
100
0
50
100
0
50
100
rare frequent rare frequentprobability in timed movement initiation
short SR interval: observe preshape
long SR interval: observe stimulus-defined
movement plan
rare frequentGhez et al, 1997
Neural evidence for preshape
[Bastian, Riehle, Schöner: Europ J Neurosci 18: 2047 (2003)]
movementdirection
precue
responsesignal
PS250
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time [ms]
movement direction
activ
atio
n
completeprecue0 60 120 180 240 300 360
activ
atio
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movement direction required in this trial
movement direction
Distribution of population activation =tuning curve * current firing rate
neurons
[after Bastian, Riehle, Schöner, submitted]
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FEMU <- H0&+(0) )3 *-4
[Bastian, Schöner, Riehle 2003]
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FEMU <- H0&+(0) )3 *-4
DPA reflects prior information
[Bastian, Schöner, Riehle 2003]
DPA reflects prior information
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PS 200 400 600 800 RS 200 MVT 2000
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//
//complete information2 target information3 target information
PS 200 400 600 800 RS 200 MVT 2000
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//
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[Bastian, Schöner, Riehle 2003]
preshape correlates with RT
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500 250 MVT 250
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nB fast RTs
slow RTs
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[Bastian, Schöner, Riehle 2003]
DPA experiment DFT model
an estimation procedure through which a distribu-tion of activation over the movement parameter‘direction’ can be constructed. (2) The notion ofpreshaping of neural representations is employed tosearch for specific use of prior information. Byextrapolating the estimation procedure for popula-tion representations into periods in which incompleteinformation about movement direction is available,the preshaping of these representations can beobserved. (3) To detect experimentally suchpreshaping, the amount and metric range of priorinformation is varied by precueing either one, twoor three adjacent movement targets.
Materials and Methods
A monkey (Macaca mulatta) was trained to performpointing movements. It was cared for in the mannerdescribed in the Guiding Principles in the Care and
Use of Animals of the American Physiological Society.The animal sat in a primate chair in front of a verticalpanel on which seven touch sensitive light emittingdiodes (LED) were mounted, one in the center andsix equidistantly on a circle around the center. A trialstarted when the center target was illuminated. Theanimal had to touch the center target and wait forthe preparatory signal (PS), consisting of the illumi-nation of one or several targets in green. After apreparatory period (PP) of 1 s, one of the greentargets turned red, thus providing a response signal(RS), which instructed the animal to release the centerbutton and to point at the specified target. Threedifferent types of prior information were presented:(i) complete information in which a single target wasilluminated; (ii) partial information with two adjacenttargets illuminated; (iii) partial information with threeadjacent targets illuminated. Each of the three typesof prior information was presented in a separate blockof about 120 trials. Within each block, all possiblemovement directions were presented randomly.
After training, the animal was prepared forsurgery. A circular recording chamber was placedunder halothane anesthesia (< 0.5% in air) over thedorsal premotor cortex contralaterally to the taskperforming arm. A T-bar was fixed on the skull in order to immobilize the animal’s head during the experimental session. A multi-electrode micro-drive (Reitboeck device, Uwe Thomas Recording,Marburg) was used to transdurally insert sevenindependently driven micro-electrodes (impedance1–4 M! at 1 kHz) into the motor cortex. Actionpotentials of single neurons were recorded extracel-lularly and isolated using a window discriminator.Only neurons that changed significantly (one-factoranalysis of variance) their activity as a function ofmovement direction during reaction time (time fromthe occurrence of the RS until the initiation of move-ment observed as the release of the center button),or during movement time (time from the initiationof movement until the hand touches the target) wereselected for the further analysis at the populationlevel. The activity of 40 of 56 neurons (71%) recordedin the condition of complete information, 46 of 57neurons (81%) recorded in the condition of partialinformation with a precue of two targets, and 41 of49 neurons (84%) recorded in the condition of partialinformation with a precue of three targets reachedstatistical significance.
The construction of a population representation of movement direction is technically similar to the
A. Bastian et al.
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316 Vol 9 No 2 26 January 1998
FIG. 1. The dynamic field model of movement preparation repre-sents the movement parameter ‘direction’ ("), by an activation field,u("). Peaks of activation represent the parameter value at whichthey are localized. The field evolves continuously in time as governedby a dynamic system:
#uu. (",t) = – u(",t) + !w(" – ") f (u(",t)) d"$+v(t) + h(t) + S(",t)
#vv.(t) = – v(t) + c!f(u(",t))d"
Sensory information associated with the preparatory signal, PS, andthe response signal, RS, is modelled as localized excitatory input,S(",t) and global excitatory input, h(t). Interaction within the field(local excitation, global inhibition, w(" – ")) stabilizes a single local-ized peak of activation as the target state of the field. The activa-tion induced by input stimulation is transiently suppressed again byan inhibitory process, v(t). The figure shows the temporal evolutionof the activation field in two cases. (A) When the preparatory signalspecifies completely the movement direction (at target 3), the corre-sponding input preshapes the field at the specified location. Theresponse signal drives this localized peak transiently to higher levelsof activation. (B) When, by contrast, the preparatory signal speci-fies two neighboring targets (at targets 3 and 4) the field is morebroadly preshaped and its maximum is centered on the average ofthe two precued movement directions. The response signal nowleads not only to an increase of activation, but also to a shift of thepeak location toward the specified target (target 3) and a sharpeningof the distribution.
methods used by Georgopoulos and colleagues9 toconstruct the population code, although the goalpersued with this construction is different. Inquiriesinto population code typically ask which movementparameters are represented by populations of neuronsin motor cortex. Although movement direction isclearly coded for in motor cortex, neural firing mayalso depend on parameters such as movement extent,arm configuration, or shoulder joint angle.10–12 Wesimply conclude from the tuning of single neuronsto movement direction that motor cortical neuronscontribute to the represention of that parameter,among the potentially many other representationsthat they might contribute to. To inquire aboutmovement direction, we projected from thispotentially high-dimensional space onto the axisrepresenting movement direction, !. This can be done by constructing a population distribution ofactivation defined over the space of movement direc-tions. The distribution was built from basis functions,which we chose as the tuning curves of each neuron.By weighting (multiplying) the tuning curve with thecurrent firing rate, population representations wereconstructed for the various experimental conditionsand at different points in time. Specifically, for eachof the three types of prior information (complete,two-target, three-target), a population representationwas constructed for each value of the preparatory andresponse signal, that is, for each possible direction.The combination of targets presented as preparatoryand response signal is designated in the formula as‘configuration’.
The mathematical definition reads
uconfiguration(!,t) = " tuningi(!)#firingrateconfiguration(i,t)neurons i
where the index i indicates the individual neurons inthe population. The firing rate of neuron i in a partic-ular configuration was obtained by averaging withina time slice beginning at time t. Thus, the populationrepresentation could be estimated as a function oftime. A normalization factor was introduced tosmooth the density at which the parameter ‘move-ment direction’ was sampled by the preferred direc-tions of the cells. The tuning curves were obtainedfrom neural firing rates averaged over the reactiontime interval. Note that computing the populationrepresentation during the reaction time interval isthus somewhat tautological, but extrapolating thisestimator into other periods is not.
Means were computed from the populationrepresentation by treating it as a probability distrib-ution and using circular statistics.13 The width of thepopulation representation was obtained by using theconcentration measure of circular statistics. Becausethe population representation is unnormalized, the
concentration was calculated after the areas under the population distributions at different configura-tions were all equaled by adding or subtractingappropriate constants.
Population representations of movement directionwere computed on the basis of the recorded activityof 40 neurons for the condition of complete infor-mation and 22 neurons for each of the two condi-tions of partial information.
ResultsThe temporal evolution of the population represen-tation is shown for the condition of completeinformation (Fig. 2A) and for the condition of twotarget information (Fig. 2B). The following state-ments hold true for all movement directions: (1)Neuronal activation increased in response to thepreparatory signal and in response to the responsesignal. After a first maximum of activity following
Representation of movement direction in motor cortex
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Vol 9 No 2 26 January 1998 317
FIG. 2. The population representation of movement direction asconstructed from neural responses of a population of motor corticalcells is shown when complete prior information (A, target 3 wasprecued at PS and specified at RS) and two target prior information(B, targets 3 and 4 were precued at PS and target 3 was specifiedat RS) is provided. The time slices for the computation of the popu-lation distribution are 100 ms. Note how the population distributionis preshaped in response to the preparatory signal. Location andwidth of activation reflect the range and contents of prior informa-tion. If complete information is provided (A) the activation peak islocalized over the precued target during the preparatory period andthe distribution increases in activation and sharpens subsequent tothe RS. At two target prior information (B), the preshaped distribu-tion is centered broadly on the precued range, whereas after presen-tation of the RS its peak shifts towards the specified value whilesharpening.
[Bastian, Riehle, Erlhagen, Schöner, 98]