dynamic field theory: memory - rub

Dynamic Field Theory:Memory

Gregor Schö[email protected]

mailto:[email protected]

Recall from last lecture …

input

input

saccadic end-point

targets

targets

saccadic end-point

activation field

activation fieldactivationfield

[after Kopecz, Schöner: Biol Cybern 73:49 (95)]

bistable

initial fixation

visualtargets

[after: Ottes et al., Vis. Res. 25:825 (85)]

reaction time (RT) paradigm

time

imperative signal=go signal

response

RT

task set

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

this supports categorical behavior

when preshape dominates

[Wilimzig, Schöner, 2006]

Behavioral evidence for the graded and continuous evolution of decision

timemove on 4th to tone

imperative stimulus

imposed SR interval

timed movement initiation paradigm

[Ghez and colleagues, 1988 to 1990’s]

[Erlhagen, Schöner. 2002, Psychological Review 109, 545–572 (2002)]

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Amplitude value

Num

ber o

f tria

lstheoretical account for Henig et al.

zeroSR interval

shortSR interval

mediumSR interval

longSR interval

0

20

40

60

0

20

40

60

125 75 250

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125 75 250

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60

Peak Force (N)

Dis

tribu

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of P

eak

Forc

es

Experimental results of Henig et al

shortSRinterval

mediumSRinterval

shortSRinterval

long

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

Neural evidence for preshape

[Bastian, Riehle, Schöner: Europ J Neurosci 18: 2047 (2003)]

movementdirection

precue

responsesignal

PS250

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45

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time [ms]

movement direction

activ

atio

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completeprecue0 60 120 180 240 300 360

activ

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movement direction required in this trial

movement direction

Distribution of population activation =tuning curve * current firing rate3

neurons

[after Bastian, Riehle, Schöner, submitted]

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DPA reflects prior information

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preshape correlates with RT

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500 250 MVT 250

L

PS 250 500 750 RS 12500

0.2

0.4

0.6

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entra

tion

A

500 250 MVT 250

J

PS 250 500 750 RS 12500

0.2

0.4

0.6

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ncen

tratio

nB fast RTs

slow RTs

!"#$ II< !"( 123/ )($( 7-87:8-'(% /(,-$-'(85 +*$ '$#-8/ )#'" +-/' $(-7'#*0 '#6(/ B/*8#% 8#0(/C -0% /8*) $(-7'#*0 '#6(/ B%*''(% 8#0(/C& -4($-9(% *4($ -88 '"$(( '-/.7*0%#'#*0/ +*$ 6*0.(5 ] B#0 3C& -0% '"( ')* ,-$'#-8 #0+*$6-'#*0 7*0%#'#*0/ #0 6*0.(5 ^ B#0 \C< D$*6 '"(/(& '"( 7*07(0'$-'#*0 6(-/:$( #/ /"*)0 -/ - +:07'#*0 *+ '#6(B>#0/! I__6/C< 3' '"( 8(+'& %-'- )($( -8#90(% '* /#90-8 *77:$$(07( -0% -' '"( $#9"' '* 6*4(6(0' *0/('< (̀$'#7-8 8#0(/ #0%#7-'( '"( *77:$$(07(/ *+ '"( ,$(,-$-'*$5 /#90-8B2RC -0% '"( $(/,*0/( /#90-8 BHRC -/ )(88 -/ 6*4(6(0' *0/(' BT`!C< !#6( #/ #0 6/<

! a__W D(%($-'#*0 *+ b:$*,(-0 =(:$*/7#(07( R*7#('#(/& )$&*+(", -*$&,"% *. /($&*'01(,0(& !"& a_YPca_XV

d*$'#7-8 $(,$(/(0'-'#*0/ *+ 6*4(6(0' ,$(,-$-'#*0 a_XP

[Bastian, Schöner, Riehle 2003]

Pre-shape and memory trace

how does pre-structuring of representations arise?

in some cases, from the perceptual layout, the environment…

but in other cases, from experience…. memory trace

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

memory trace reflects history of decisions formation

020

4060

805

1015

200

20

020

4060

805

1015

00.20.4

memorytrace

dimension

activation

time

dimension

time

(Working) memory instability

h

dimension0

h

dimension0 input

self-excited

peak

input

self-excited

peak

h

dimension0

sub-threshold attractorh

dimension0

self-sustained

peak

Working memory as sustained peaks

WM is marginally stable state: it is not asymptotically stable against drift within the low-dimensional space

=> empirically real.. ?

“space ship” task probing spatial working memory

Metric�Working�Memory�Tasks10 sec delay2000 ms Ready, Set, Go!

+++

-40°

[Schutte, Spencer, JEP:HPP 2009]1977; Compte et al., 2000, for neural network models that usesimilar dynamics).

Considered together, the layers in Figure 3 capture the real-timeprocesses that underlie performance on a single spatial recall trial.At the start of the trial, the only activation in the perceptual fieldis at the location associated with the perceived reference axis (seehighlighted reference input in Figure 3a). This is a weak input andis not strong enough to generate a self-sustaining peak in theSWM field, though it does create an activation peak in theperceptual field (PFobj). Note that this input to the model isassumed to be generated by relatively low-level neural pro-cesses that extract symmetry using the visible edges of the taskspace (for evidence that symmetry axes are perceived as weaklines, see Li & Westheimer, 1997). We have not included thevisible edges in simulations of the model because they are quitefar from the target locations probed in our experiments. Giventhat neural interactions in the DFT depend on metric separation,these additional inputs far from the targets would have negli-gible consequences.

The next event in the simulation in Figure 3a is the targetpresentation. This event creates a strong peak in PFobj (see targetinput in Figure 3a) which drives up activation at associated sites inthe SWM field (SWMobj). When the target turns off, the targetactivation in PFobj dies out, but the target-related peak of activationremains active in SWMobj. In addition, activation from the refer-ence axis continues to influence PFobj because the reference axis issupported by readily available perceptual cues (see peak in PFobj

during the delay).Central to the DFT account of geometric biases is how the

reference-related perceptual input affects neurons in the workingmemory field during the delay. Figure 3c shows a time slice of theSWMobj field at the end of the delay. As can be seen in the figure,the working memory peak has slightly lower activation on the leftside. This lower activation is due to the strong inhibition aroundmidline created by the reference-related peak in PFobj (see high-

lighted reference input in Figures 3a & 3c). The greater inhibitionon the left side of the peak in SWM effectively “pushes” the peakaway from midline during the delay, that is, the maximal activityin SWM at the end of the trial is shifted to the right of the actualtarget location (for additional behavioral signatures of these inhib-itory interactions, see Simmering et al., 2006). Note that workingmemory peaks are not always dominated by inhibition as in Figure3c. For instance, if the working memory peak were positioned veryclose to or aligned with midline (location 0), it would be eitherattracted toward or stabilized by the excitatory reference input.This hints at how the DFT accounts for developmental changes ingeometric biases.

A simulation of the model with “child” parameters is shown inFigure 3b. This simulation is the same as the adult simulation inFigure 3a, except the interaction among neurons within each fieldand the projections between the fields have been scaled accordingto the spatial precision hypothesis: the neural interactions withinthe SWMobj and PFobj fields are weaker (relative to the adultparameters), the widths of the projections between the fields arebroader, and the excitatory and inhibitory projections areweaker (for a more detailed discussion see below). As can beseen in Figure 3b, these changes in interaction result in abroader peak in the SWMobj field. Additionally, the referenceinput is broader and weaker to reflect young children’s diffi-culty with reference frame calibration, that is, their ability tostably align and realign egocentric and allocentric referenceframes (see Spencer et al., 2007). The result of these changes isthat neural interactions in PFobj are not strong enough to builda reference-related peak during the delay. Consequently,SWMobj is only influenced by the broad excitatory input fromdetection of midline in the task space and the SWMobj peakdrifts toward the reference axis instead of away from the axis.

The simulations in Figure 3 demonstrate that the spatial preci-sion hypothesis and the DFT can capture the general pattern ofgeometric biases in early development and later development, but

Figure 4. Apparatus used for spaceship task. Inset shows sample target locations relative to the starting point.Targets are projected onto the table from beneath and responses are recorded using an Optotrak movementanalysis system. Note that the lights in the room are turned on for the photograph. During the experiment thelights were dimmed, and the table appeared black.

1702 SCHUTTE AND SPENCER

1977; Compte et al., 2000, for neural network models that usesimilar dynamics).

Considered together, the layers in Figure 3 capture the real-timeprocesses that underlie performance on a single spatial recall trial.At the start of the trial, the only activation in the perceptual fieldis at the location associated with the perceived reference axis (seehighlighted reference input in Figure 3a). This is a weak input andis not strong enough to generate a self-sustaining peak in theSWM field, though it does create an activation peak in theperceptual field (PFobj). Note that this input to the model isassumed to be generated by relatively low-level neural pro-cesses that extract symmetry using the visible edges of the taskspace (for evidence that symmetry axes are perceived as weaklines, see Li & Westheimer, 1997). We have not included thevisible edges in simulations of the model because they are quitefar from the target locations probed in our experiments. Giventhat neural interactions in the DFT depend on metric separation,these additional inputs far from the targets would have negli-gible consequences.

The next event in the simulation in Figure 3a is the targetpresentation. This event creates a strong peak in PFobj (see targetinput in Figure 3a) which drives up activation at associated sites inthe SWM field (SWMobj). When the target turns off, the targetactivation in PFobj dies out, but the target-related peak of activationremains active in SWMobj. In addition, activation from the refer-ence axis continues to influence PFobj because the reference axis issupported by readily available perceptual cues (see peak in PFobj

during the delay).Central to the DFT account of geometric biases is how the

reference-related perceptual input affects neurons in the workingmemory field during the delay. Figure 3c shows a time slice of theSWMobj field at the end of the delay. As can be seen in the figure,the working memory peak has slightly lower activation on the leftside. This lower activation is due to the strong inhibition aroundmidline created by the reference-related peak in PFobj (see high-

lighted reference input in Figures 3a & 3c). The greater inhibitionon the left side of the peak in SWM effectively “pushes” the peakaway from midline during the delay, that is, the maximal activityin SWM at the end of the trial is shifted to the right of the actualtarget location (for additional behavioral signatures of these inhib-itory interactions, see Simmering et al., 2006). Note that workingmemory peaks are not always dominated by inhibition as in Figure3c. For instance, if the working memory peak were positioned veryclose to or aligned with midline (location 0), it would be eitherattracted toward or stabilized by the excitatory reference input.This hints at how the DFT accounts for developmental changes ingeometric biases.

A simulation of the model with “child” parameters is shown inFigure 3b. This simulation is the same as the adult simulation inFigure 3a, except the interaction among neurons within each fieldand the projections between the fields have been scaled accordingto the spatial precision hypothesis: the neural interactions withinthe SWMobj and PFobj fields are weaker (relative to the adultparameters), the widths of the projections between the fields arebroader, and the excitatory and inhibitory projections areweaker (for a more detailed discussion see below). As can beseen in Figure 3b, these changes in interaction result in abroader peak in the SWMobj field. Additionally, the referenceinput is broader and weaker to reflect young children’s diffi-culty with reference frame calibration, that is, their ability tostably align and realign egocentric and allocentric referenceframes (see Spencer et al., 2007). The result of these changes isthat neural interactions in PFobj are not strong enough to builda reference-related peak during the delay. Consequently,SWMobj is only influenced by the broad excitatory input fromdetection of midline in the task space and the SWMobj peakdrifts toward the reference axis instead of away from the axis.

The simulations in Figure 3 demonstrate that the spatial preci-sion hypothesis and the DFT can capture the general pattern ofgeometric biases in early development and later development, but

Figure 4. Apparatus used for spaceship task. Inset shows sample target locations relative to the starting point.Targets are projected onto the table from beneath and responses are recorded using an Optotrak movementanalysis system. Note that the lights in the room are turned on for the photograph. During the experiment thelights were dimmed, and the table appeared black.

1702 SCHUTTE AND SPENCER

a source of excitatory input, S n 0, then the resulting stable

state of the activation dynamics

!d,(><t)?dt = p,(><t) + h + S(>)

is ,(>) = h + S(>), the level at which positive and negative

rates of change balance so that d,?dt = 0. Note that ! is a

parameter that fixes the time scale of the activation field.

When the rate of change of activation at a field site, >,

depends not only on the activation level, ,(><t)< and current

inputs, S(>), but also on the activation levels, ,(>A< t), at

other field sites, >A, then the activation dynamics are

interactive. Locally excitatory interaction is described by a

kernel, 5(>->A), such that

!d,(><t)?dt = p,(><t) + h + S(><t) + ! d>A5(>p

>A)!(,(>A<t))

Only sufficiently activated sites, >A, contribute to interaction.

This is expressed by passing activation level through a

sigmoidal function:

!(,) = 1/(1 + exp(p",))

Such threshold functions are necessarily non-linear and are

the basis for the bi-stability that structures the activation

dynamics. Because cortical neurons never project both

excitatorily and inhibitorily onto targets, the inhibitory

lateral interaction must be mediated through an ensemble of

interneurons. A generic formulation (Amari & Arbib, 1977)

is to introduce a second, inhibitory activation field, v(><t),

which receives input from the excitatory activation field,

,(><t), and in turn inhibits that field:

!, d,(><t)?dt = p,(><t) + h, + S(><t) + ! d>A5(>p

>A)!(,(>A<t)) pc ! d>A5i(>p>A)!(v(>A<t))

!v dv(><t)?dt = pv(><t) + hv + ! d>A5(>p>A)!(,(>A<t))

Stabilizing the contents of working memory via

spatial categories. The set of equations above describes a

neurally-plausible bi-stable network for SWM. Although

sustained activation peaks in this network are stably in the

“on” state, they are inherently unstable with respect to the

metric information they represent. One manifestation of this

metric instability is the “drift” of sustained peaks under the

influence of noisy inputs that are common in the nervous

system (Compte et al., 2000). Peak drift can also be induced

by small, localized input gradients into the excitatory layer

of the field which attract sustained peaks if they are

positioned sufficiently close to the gradient (Amari & Arbib,

1977). Conversely, small localized inputs into the inhibitory

layer cause peaks to drift away from the input gradient.

How might such gradients arise? A specific mechanism

is through long-term memory traces of activation patterns.

Whenever and wherever above threshold activation is

present in WM, traces of activation can be slowly built up.

This can be modeled through a simple linear activation

dynamics of an additional set of fields—the LTM fields—

which receive inputs from the corresponding layers of WM.

Conversely, LTM traces feed back as excitatory inputs into

the corresponding layers of WM:

!traced,trace?dt = p,trace + !(,);

!tracedvtrace?dt = pvtrace + !(v);

!,d,?dt = s + c,<trace,trace + noise

!vd,?dt = s + cv<tracevtrace + noise

A LTM trace of the excitatory layer will generate a

small source of input that stabilizes WM peaks near the

locations at which peaks have been activated earlier. Such

excitatory memory traces form the neural substrate of

spatial categories. Conversely, LTM traces of the inhibitory

layer will generate a source of input that repels memory

items from field sites that have been activated earlier. Such

traces provide long-term discriminative information,

amplifying activation differences based on past experiences.

If excitatory memory traces are the substrate from which

spatial categories are built, then inhibitory memory traces

maximize the differences between categories.

Spdating and re-establishing reference frames. To

this point, we have described a neural mechanism for SWM

and spatial categories but have remained vague on the

-2

0

2

4

6

8

10

0 5 10 15 20

0

1

2

3

4

5

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7

0 5 10 15 20

delay (s)

-2

0

2

4

6

8

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0 5 10 15 20

mean

co

nsta

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err

or

(°)

center

20 degrees

40 degrees

60 degrees

80 degrees

0

1

2

3

4

5

6

7

0 5 10 15 20

delay (s)

mean

vari

ab

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rro

r (°

)

Participants Model

!y

Figure 1. The DNFT. Figure 2. Simulations of data from Spencer & Hund (2003)

2182

[Spencer, Schöner, 2006]

repulsion from mid-line

DFT account of repulsion: inhibitory interaction with peak representing landmark

DFT�$ Spatial�Recall

PF

SWM

Inhib

Act

ivat

ion

Location (°)

Time

midlinetarget

target

drift�away�from�midline

Simmering,�Schutte,�&�Spencer�(2007)�Brain�Research[Simmering, Schutte, Spencer: Brain Research, 2007]

has limited capacity

based on the number of objects…

about 4

probed by change detection, free recall

[Luck, Vogel, 1997]

visual working memory

Nature © Macmillan Publishers Ltd 1997

letters to nature

280 NATURE | VOL 390 | 20 NOVEMBER 1997

observers were instructed to look for an orientation change. In thethird and critical condition, either colour or orientation could vary,and the observers were required to remember both features of eachobject. In this last condition, accurate performance with a set size offour objects would require the observer to retain eight features (fourcolours and four orientations), whereas only four features would berequired for accurate performance in the simple feature conditions.Performance was essentially identical for the feature and conjunc-tion conditions despite the greater total number of features that hadto be retained in the conjunction condition (Fig. 1c). This indicatesthat visual working memory stores integrated object percepts ratherthan individual features, just as verbal working memory can storehigher-order ‘chunks’15. This is also analogous to findings fromvisual attention experiments, which have shown that attention isdirected to entire objects rather than to individual features and that,consequently, two features of a given object can be reported asaccurately as a single feature16.

Because the stimulus arrays shown in Fig. 1c always varied inboth colour and orientation, it is possible that the subjects wereunable to avoid encoding both features even when only one featurewas relevant. To rule out this potential explanation of the similarresults obtained for the feature and conjunction conditions, asecond version of this experiment was conducted in which theirrelevant feature dimension was held constant in the single-featureconditions (all of the rectangles were black when the subjectswere required to remember orientation and all were verticalwhen the subjects were required to remember colour). The resultswere virtually identical to those shown in Fig. 1c, with statisticallyindistinguishable performance in the feature and conjunctionconditions.

To extend these findings, we conducted an experiment in which

the objects were defined by a conjunction of four features: colour,orientation, size and the presence or absence of a gap. Performancewas just as good in this quadruple conjunction condition as it was inthe individual feature conditions (Fig. 1d), indicating that 16features distributed across 4 objects can be retained as accuratelyas 4 features distributed across 4 objects.

The surprisingly good performance for conjunctions could beexplained by the use of separate, independent memory systems foreach feature type rather than the storage of integrated objectrepresentations. To rule out this possibility, we examined colour–colour conjunctions in which each object consisted of a large squareof one colour and a small inner square of a different colour.Observers were just as accurate with these colour–colour conjunc-tions as they were with either the large outer squares or the smallinner squares presented alone (Fig. 1e). Thus, eight colours dis-tributed across four objects can be retained as accurately as fourcolours distributed across four objects. Because both features ofeach object consisted of colours, the high accuracy observed in theconjunction condition cannot be explained by the existence ofindependent memory systems for different features.

These results indicate that integrated object percepts are stored invisual working memory, leading to a large capacity for retainingindividual features as long as the features are confined to a smallnumber of objects. Although there may be limits on the number offeatures that can be linked together in a single object representation,our results indicate that at least four features can be joined in thismanner with no cost in terms of storage capacity.

The present findings have important implications for both thenature of the input to, as well as the contents of, visual workingmemory. Specifically, studies of selective attention indicate thatattentional processes are used to combine the features of an object

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Figure 1 Example stimulus arrays (not drawn to scale) and performance on the

sequential comparison task. All set size effects shown here were statistically

significant at the P , 0:001 level (ANOVA). No other effects approached the

P , 0:05 level of significance. a, Performance with and without a verbal load for

simple colour stimuli. b, Comparison of 100-ms and 500-ms sample durations for

simple colour stimuli (with a verbal load and no cue box). Also shown is the

performance in a similar experiment with a cue box that indicated the one item

that might have changed colour (100-ms sample duration and no verbal load).

c, Comparison of performance when the observers were instructed to detect a

colour change, an orientation change or a change in either feature (conjunction

task). d, Comparison of performance for each of four simple features and the

conjunction of all four features. e, Comparison of performance for colour–colour

conjunctions versus the individual large and small squares.

DFT account of WM capacity

fundamentally caused by accumulation of inhibitory interaction across peaks

=> generic to DFT

WM capacity depends on interaction

capacity increases across development

consistent with “spatial precision hypothesis”… interaction becomes more excitatory/local over development

this task and higher cognition, suggesting that it could tap the processes ofinterest when trying to explain fundamental cognitive skills.

To assess developmental changes in visual working memory capacity,the change detection task has been modified for use with children betweenthe ages of 3 and 12 years by reducing the number of trials and extending theduration of the memory array (Cowan et al., 2005; Cowan, Fristoe, et al., 2006;Riggs, McTaggart, Simpson, & Freeman, 2006; Simmering, 2012). Figure 2shows results across these studies, with estimates increasing from about two tofive items during childhood. As this figure shows, capacity increases steadilyacross this age range (see Simmering, 2012, for discussionofdiffering estimatesin 5-year-olds). Of the theories described in the working memory sectionabove, only Cowan’s embedded process model has been applied specifically tochange detection performance. According to that perspective, the controllednature of the change detection task leaves only increases in capacity (i.e., thescope of attention) to account for developmental improvements (Cowan et al.,2005; see also, Cowan, AuBuchon, Gilchrist, Ricker, & Saults, 2011). However,as noted above, this model does not include a specific mechanism by whichcapacity increases (Cowan, 2013). Riggs, Simpson, and Potts (2006) proposedthat developmental changes in neural synchrony could account for thiscapacity increase (discussed further in Chapter 2).

Memory array (100-500 ms)

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different

FIGURE 1.—Sample trial of the change detection task in set size three (not drawn to scale).Different patterns represent different colors.

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FIGURE 2.—Capacity estimates from the change detection task with children. References:1¼Cowan et al. (2005), these estimates were approximated from figures, precise values werenot reported in text; 2¼Cowan, Fristoe, et al. (2006); 3¼Riggs et al. (2006); 4¼ Simmering(2012) “card” task; 5¼ Simmering (2012) standard task.

20

[Simmering 2010]

Change detection

the standard probe of working memory

[Johnson, et al. 2009]

Simmering and Perone Capacity development

In our view, capacity in the classic sense (e.g., the “slots”metaphor) does not work. In the laboratory, we derive capacityestimates that are the emergent product of multiple, highly com-plex, coupled cognitive and behavioral systems operating withinthe task context. If we want to understand why capacity estimatesappear limited and why they differ across individuals, develop-ment, and task contexts we must understand the dynamics of thesesystems (i.e., how the components of a system interact throughtime). We illustrate this claim below by reviewing two case studiesfrom our own work. Our proposal stands in contrast to the histor-ical approach to understanding capacity and its development. Forinstance, Cowan et al. (2010) emphasized the role of processing(e.g., strategy) in explaining cross-task performance differences,while contending that storage remains relatively constant acrosstasks. Though we agree that both processing and storage must beconsidered to understand performance across tasks, we disagreewith both the characterization of storage as a separable componentof the system as well as the notion that storage is constant acrosstasks. In our view, storage capacity cannot be “tapped.” Storage isa process in and of itself that cannot be considered in isolationfrom the processes that contribute to (e.g., encoding, chunking)and operate upon (e.g., rehearsal, retrieval) stored information.

Below, we present two case studies illustrating how a systemsapproach can be applied to WM capacity development. Thesestudies have tested specific predictions derived from the imple-mentation of visual WM into a computational model, which allowsfor direct testing of how changes in a given set of processes maysimulate developmental improvements in performance. Theseexamples demonstrate how the specific details of the behavioraltasks designed to measure WM capacity influence the processes bywhich WM representations are formed and used in service of thetasks,and reveal that capacity may vary within the same participants

depending on the manner in which information is presented andcapacity is measured. Importantly, we do not consider these differ-ences across tasks to be “noise” in our estimates, but rather believethis cross-task variation informs our understanding of how thisdynamic cognitive and behavioral system operates and develops.

CASE STUDY 1: INFANT VISUAL WORKING MEMORYOur first case study centers on a series of neural network sim-ulations reported by Perone et al. (2011). Perone et al. showedthat a single, complex system can produce remarkable variationin performance across contexts. More specifically, they tested theprediction that a single neuro-dynamical systems model of infantlooking and memory could produce variation in infants’ capacityestimates across task conditions. They simulated infants’ perfor-mance in a change preference task designed by Ross-Sheehy et al.(2003) to estimate visual WM capacity. Figure 1A shows this task,in which infants viewed two displays of colored squares blinkingon and off in synchrony. On a “no-change” display, all of the colorsremained the same with each blink/delay. On a “change” display,one randomly selected color changed to a new color. Infants’ look-ing time to the two displays was compared, and a robust preferencefor the change display was interpreted as memory for the numberof items per display (i.e., set size). Across set sizes, Ross-Sheehyet al. found that 6-month-olds showed a robust change prefer-ence only at set size one, whereas 10-month-olds showed change

A B

FIGURE 1 | Schematic illustrations of tasks used to assess visual

working memory in (A) infants versus (B) children and adults; both

present examples of set size three.

preferences up to set size four. They concluded that infants’ visualWM capacity increases from one to four items between 6 and10 months.

Perone et al. (2011) simulated infants’ performance in this taskusing a model of infant looking and memory. The model con-sists of a neurocognitive system that encodes object details (e.g.,color) and a fixation system that is biased to sustain looking duringencoding. Encoding leads to WM formation of the colors in thedisplays; once a robust WM is formed, inhibition biases the sys-tem to look away from remembered items and explore items thatmay be novel. The model exhibited a change preference throughrecognition of the items on the no-change display and detectionof novelty on the change display. This preference emerged throughreal-time interactions between looking, encoding, and WM forma-tion. Critically, Perone et al. found that a preference for the changedisplay did not require memory for all items in the display, that is,the model exhibited a higher capacity estimate (measured throughlooking time) than the number of items maintained in WM.

This example highlights how multiple processes workingtogether give rise to behavioral estimates of capacity. Critically,the challenge remains to understand how such processes give riseto variation in performance like that shown in Tables 1–4. Withinsystems approaches, such variation is viewed as a signature of asystem that organizes in real-time in response to the current taskcontext. Perone et al. (2011) illustrated this concept by simulat-ing a second experiment by Ross-Sheehy et al. (2003) in whichthey removed the delay to insure that young infants’ performancereflected a limitation in memory, not perception or attention.Indeed, young infants exhibited change preferences for set sizes upto three in this condition. This manipulation changed the task intwo important ways. First, “blinks” on the change and no-changedisplays were no longer present, that is, there were no transientonsets within each presentation of the items. Second, it introduceda “flicker” associated only with the changing item on the changedisplay. Perone et al. showed that these minor manipulations dra-matically influenced looking behavior. In the DNF model, lookingand memory are reciprocally coupled components of a larger cog-nitive and behavioral system. Manipulations of looking influenced

Frontiers in Psychology | Developmental Psychology January 2013 | Volume 3 | Article 567 | 12

DFT account for change detection

separation between perceptual and memory function

3 layer model

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=> simulations


=> account for how working memories arise from percepts, how percepts may detect change and update memories…


generate the categorical “answer” by two competing nodes

based on the “hidden” go-signal in the task

(1998) on the basis of studies of cortical neurophysiology. The

model consists of an excitatory perceptual field, an excitatoryworking memory field (VWM), and a shared inhibitory field. As

its name suggests, the perceptual field is the main target ofafferent input to the network. VWM also receives direct stimulus

input, but its primary excitatory input comes from the perceptualfield. Both the perceptual field and VWM provide excitatoryinput to and receive broad inhibitory feedback from the inhib-

itory field. Additionally, nearby neurons within both the per-ceptual and the working memory fields interact via local

excitatory connections. This pattern of excitatory and inhibitoryconnectivity gives rise to a ‘‘Mexican hat’’ form of interaction

common in neural models of cortical function (Durstewitz,Seamans, & Sejnowski, 2000). With the right balance of exci-tation and inhibition, multiple peaks of activation can be sus-

tained in the absence of input. (Videos S1 and S2 in thesupporting information available on-line show the three-layer

model operating, respectively, in a self-stabilized mode, in whichpeaks of activation form in response to input but die out when

input is removed, and in a self-sustained mode, in which peaks of

activation are sustained in the absence of input; see p. XXX.)Thus, this form of interaction represents a plausible neural basis

for the sustained activation proposed to underlie workingmemory (Compte et al., 2000; Fuster & Alexander, 1971).

Finally, to capture performance in change-detection tasks, wehave added a response layer containing two nodes: a differentnode, which receives summed excitatory activation from the

perceptual field, and a same node, which receives summed ex-citatory activation from VWM (see Fig. 2b). The nodes are

equipped with self-excitatory connections and are mutuallyinhibitory, competing for control of response output when a ‘‘go’’

signal arrives (following the presentation of the test display).Visual comparison is made possible in this architecture

through excitatory and inhibitory interactions among the mod-

el’s layers. Consider the simulations shown in Figure 3, whichcapture performance in the one-shot variant of the change-de-

tection task (Fig. 1). We focus on this variant of the task becauseof its relative simplicity, which minimizes the impact of factors

ExcitatoryLayer

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Fig. 2. Two- and three-layer dynamic neural field models of visual working memory (VWM). The thin, solidhorizontal line in each field marks the activation threshold (conventionally set to be 0), the point at whichinteractions among neurons within and between layers become engaged. The two-layer model (a) consists ofa single population of feature-selective excitatory neurons coupled to a similarly tuned population of in-hibitory neurons. This simulation depicts the formation of a peak of activation following localized input tothe excitatory layer. Input takes the form of a Gaussian distribution that is centered at a particular fieldlocation and has a specified strength and width. Once activation goes above threshold (i.e., 0) in the ex-citatory layer, activation is passed to the inhibitory layer, which, in turn, passes broad inhibition back to theexcitatory layer. Locally excitatory interactions among neurons in the excitatory layer (solid, curved arrow)keep neurons in a highly active state, whereas inhibitory feedback from the inhibitory layer keeps excitationlocalized by preventing the diffusion of activation throughout the field. The three-layer model (b) containstwo populations of excitatory neurons (perceptual and VWM fields) reciprocally coupled to a single pop-ulation of inhibitory neurons (inhibitory field). Input is applied to both excitatory fields, but input to theperceptual field is much stronger than input to the VWM field. Once activation in the perceptual field goesabove 0, strong activation is propagated to both the inhibitory and the VWM fields. The VWM field alsoprojects excitatory activation to the inhibitory field, which projects inhibition to both the perceptual andthe VWM fields. The model also contains a response layer consisting of two nodes: one that receives summedexcitatory input from the perceptual field and is responsible for generating ‘‘different’’ (‘‘Diff’’) responses,and a second that receives summed excitatory input from VWM and is responsible for generating ‘‘same’’responses. The nodes in the response layer have self-excitatory connections and are mutually inhibitory.Note that only above-threshold activation (i.e., activation> 0) in the perceptual field or VWM is propagatedto the response nodes at test.

Volume ]]]—Number ]] 3

J.S. Johnson et al.



1) working memory is created


contributing to failures of change detection when real-world

scenes are used as stimuli (see, e.g., Hollingworth, 2003; Hol-lingworth et al., 2001).

The simulations in Figure 3 demonstrate how ‘‘same’’ and

‘‘different’’ responses arise in the model. Each column shows thepattern of activation in the excitatory layers of the model at a

given point in time during a trial in the change-detection task.

Note that, for simplicity, the inhibitory layer is not shown. At the

beginning of the trial (Fig. 3a), the model is presented with threeinputs: two nearby inputs representing very similar, or ‘‘close,’’colors and a third input representing a distinct, or ‘‘far,’’ color.

When input is turned on, strong activation is applied to theperceptual field, and weaker activation is applied to VWM.

Once activation in the perceptual field reaches a given threshold

Feature-SpecificSuppression viaInhibitory Layer

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Fig. 3. Simulation showing the generation of ‘‘same’’ and ‘‘different’’ responses in the dynamic neural field model of visual working memory (VWM)and change detection. For simplicity, only the two excitatory layers of the model are shown here, although the inhibitory layer plays a critical role in theformation and maintenance of peaks and in the model’s ability to detect changes at test. Following the presentation of a sample input representing twosimilar colors and one distinctive color (a), three peaks of activation form very quickly in the perceptual field and more slowly in VWM (because input tothe perceptual field is stronger). Once activation goes above threshold (0) in the perceptual field, strong activation is transmitted to the inhibitory andVWM layers, and three above-threshold peaks are established in VWM. When the input is removed during the delay interval (b), the peaks die out inthe perceptual field, but are sustained in VWM. Inhibitory feedback from VWM to the perceptual field via the inhibitory layer suppresses the firing ofneurons in the perceptual field that code for the same features being held in VWM. When a close (c) or far (e) item is probed at test and the inputmatches one of the remembered features, inhibitory feedback to the perceptual field prevents a new peak from forming. Thus, input to the responsenodes comes exclusively from the VWM field, and a ‘‘same’’ (S) response is generated. In contrast, when one of the close items is changed to a new valueat test (d), input comes in at a relatively uninhibited region of the perceptual field, allowing a new peak to be established and activation to flow to the‘‘different’’ (D) node, which wins the competition when a sufficiently strong peak is present in the perceptual field at test. However, when the far item ischanged by an identical amount at test (f), input again comes in at a relatively uninhibited region of the perceptual field, but activation is unable to goabove threshold, and the model incorrectly responds ‘‘same.’’ Strong laterally inhibitory interactions between close peaks in VWM result in theinhibitory projection to the perceptual field being stronger for far than for close items (compare inhibition in the perceptual field during the delayinterval for close vs. far items). The higher level of inhibition makes it more difficult to detect changes to far items.

4 Volume ]]]—Number ]]

Neural Field Model of Visual Working Memory


2) change detection in “same” trial












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predict better change detection when items are metrically closer !


Fig. 6.Metric interactions in WM leading to enhanced change-detection for close features: (A) time-slice through the FWM field during the delay interval of a change detection task showing WMpeaks representing two far color targets separated by 160 units. Relatively broad and high-energy peaks in WM produce correspondingly broad and deep inhibition in PF (B) viainhibitory feedback. (C) With close colors, peaks are narrower and somewhat lower energy,which produces narrower and shallower inhibition in PF (D), making it easier for peaks to buildin PF when a new item is presented at test. See text for details.

Johnson et al. Page 25

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predict better change detection when items are metrically closer !


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Fig. 4. Illustration of the trial sequences in the experiments and results from the experiments and model simulations. Experiment 1a (a) used astandard one-shot change-detection task. A test display of three colors was followed by a delay and then a test display of a single color. Experiment 1b(b) tested change detection when the color stimuli to be remembered were presented sequentially, rather than simultaneously. In these illustrations,different fill patterns represent different solid colors. Experiment 2 (c) followed the procedure for Experiment 1b, but using orientation stimuli. Thegraph (d) shows performance (d0) for close and far targets separately for each experiment and the simulations. Note that for the orientationexperiment, results are shown only for trials on which the close-orientation separation was 201. Error bars represent 95% confidence intervals.



Multi-object tracking

[Pylyshyn]

Seeing and Visualizing: It’s not what you think Zenon Pylyshyn

9/27/2002 5-15

Figure 5-5. Illustration of a typical Multiple Object Tracking experiment. A display of eight identical objects is shown (t=1) and a subset of 4 are briefly flashed to make them distinctive (t=2). Following this the objects stop flashing so the “target” set becomes indistinguishable from the other objects. All objects then move in a random fashion for about 10 seconds (t=3). Then the motion stops (t=4) and one of the objects is flashed. The observer’s task is to say whether the flashed object was one of the objects that had been initially flashed. In other experiments the observer has to indicate all the tracked objects by clicking on each one using a computer mouse.

If there had only been one object to track the answer would be relatively straighforward: Observers could simply track it with their eyes, or perhaps they could track the moving object using attention scanning (such error-driven tracking systems have been common since the development of feedback control theory and servo-mechanisms). But how do observers do this task with 4 objects moving along independent random trajectories, interspersed among 4 other randomly-moving identical “distractor” objects that must be ignored. One possibility is that observers record and use the locations of each target object and visit them serially. After the initial recording of target locations they simply go to the location in the list that they have stored and look around for the nearest object, taking that to be the target they are tracking and updating its location code in the list using the following algorithm:

1. While the targets are visually distinct, scan attention to each target and encode its location

on a list. Then, when targets begin to move;

2. For n=1 to 4; Check the n’th position in the list and retrieve the location Loc(n) listed there.

3. Scan attention to location Loc(n). Find the closest object to Loc(n).

4. Update the n’th position on the list with the actual location of the object found in #3. This becomes the new value of Loc(n).

5. Move attention to the location encoded in the next list position, Loc(n+1).

6. Repeat from #2 until elements stop moving.

7. Go to each Loc(n) in turn and report elements located there.

So long as attention moves fast enough from one object to another in relation to the speed of the objects themselves, and so long as targets are sufficiently far from nontargets to prevent frequent mistakes, such a strategy of serial attending and updating a list of locations could explain how observers could track multiple objects. In (Pylyshyn & Storm, 1988), however, we were able to show that the motion and dispersion parameters of our original experiments were such that tracking could not have been accomplished using such a serial strategy. The performance of the above algorithm when it is applied to the actual displays used in the Pylyshyn & Storm study results in the performance shown in Figure 5-6 below.


[Spencer et al]

34


[Spencer et al]

37

Combining working memory and the memory trace

in a case study that invokes all dynamic instabilities of DFT as well…

Piaget’s A not B paradigm: “out-of-sight -- out of mind”

A trial

delay

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A B

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A B

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delay

A not B error

Toyless variant of A not B task

toy to be hidden [24]. Directing attention to an in-viewobject (A) heightens activation at the location and, in theexperiment, infants reach to that continually in-viewobject. Subsequently, when the experimenter directsattention to a different nearby in-view object (B), infantswatch, but then reach back to the original object (A).

Experimenters have also made the error vanish bymaking the reaches on the B trials different in some wayfrom the A trial reaches. In the model, these differencesdecrease the influence of the A trial memories on theactivations in the field. One experiment achieved this by

shifting the posture of the infant [24]. An infant who satduring the A trials would then be stood up, as shown inFig. 3, to watch the hiding event at B, during the delay andduring the search. This posture shift causes even 8- and10-month-old infants to search correctly, just like12-month-olds. In another experiment, we changed thesimilarity of reaches on A and B trials by putting on andtaking off wrist weights [25]. Infants who reached with‘heavy’ arms onA trials but ‘light’ ones on B trials (and viceversa) did not make the error, again performing as if theywere 2–3 months older. These results suggest that therelevant memories are in the language of the body andclose to the sensory surface. In addition, they underscorethe highly decentralized nature of error: the relevantcauses include the covers on the table, the hiding event,the delay, the past activity of the infant and the feel of thebody of the infant.

This multicausality demands a rethinking of what ismeant by knowledge and development. Do 10-month-old infants know something different when they makethe error compared with when they do not? The answeris ‘yes’ if we conceptualize knowledge and knowing asemergent, that is, made at a precise moment frommultiple components in relation to the task and to theimmediately preceding activity of the system. What do12-month-olds know that 10-month-olds do not? Therecan be no single cause, no single mechanism and noone knowledge structure that distinguishes 10-month-olds from 12-month-olds because there are manycauses that make the error appear and disappear.Instead, both 10-and 12-month-olds can be regarded ascomplex systems that self-organize in the task. How-ever, just as trial dynamics are nested in taskdynamics, so are task dynamics nested in develop-mental dynamics.

Developmental dynamicsThe A-not-B error has been important to developmentaltheory because it is tightly linked to a few months ininfancy. However, the neural field model suggests that thedynamics that create the error in infants are basicprocesses involved in goal-directed actions at all ages.Indeed, by changing the task, researchers can makeperseverative errors come and go in older children andadults, just as in infants. Recently, Spencer and colleagues

Fig. 2. (a) The time evolution of activation in the planning field on the first A trial.The activation rises as the object is hidden and, owing to self-organizing propertiesin the field, is sustained during the delay. (b) The time evolution of activation inthe planning field on the first B trial. There is heightened activation at A before thehiding event, owing to memory for prior reaches. As the object is hidden at B, acti-vation rises at B, but as this transient event ends, owing to the memory propertiesof the field, activation at A declines and that at B rises.

TRENDS in Cognitive Sciences

BA

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Opinion TRENDS in Cognitive Sciences Vol.7 No.8 August 2003346

http://tics.trends.com

[Smith, Thelen et al.: Psychological Review (1999)]

Toyless variant of A not B task reveals that A not B is essentially a

decision task!

A trial

delay

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[Smith, Thelen et al.: Psychological Review (1999)]

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[Dineva, Schöner, Dev. Science 2007]

activationfield

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A B

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after the delay

boost-induced detection

Instabilities

detection: forming and initiating a movement goal

selection: making sensori-motor decisions

(learning: memory trace)

boost-driven detection: initiating the action

memory instability: old infants sustain during the delay, young infants do not

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movementdirection

A B

A B

memorytrace

afterdelay

movementdirection

A B

interaction-based sustained activation

young

old

DFT of infant perseverative reaching

[Dinveva, Schöner, Dev. Science 2007]



memory trace



perseverativeerrors

in spontaneous errors, activation arises at B on an A trial

which leads to correct reaching on B trial

because reaches to B on A trials leave memory trace at B

spontaneouserror correct on B!



=> DFT is a neural process model

that makes the decisions in each individual trial, by amplifying small differences into a macroscopic stable state

and that’s how decisions leave traces, have consequences

Decisions have consequences

66 E. DINEVA AND G. SCHÖNER

21 3 4 5 60

.5

1 infantsDFT, repeatedinfants, repeated

DFT

spontaneous errors

trial [T]

prob

abili

ty

Figure 7. Estimates from experiment (solid lines) and DFT simulations (broken lines) of the rate of spon-taneous errors across A-trials (black lines). The grey lines show the conditional probability that a reachagain goes to B on a given A-trial given that the first spontaneous reach to B has just occurred on theprevious trial.

number of spontaneous errors [n]

distribution of error frequencies

1 2 3 6 5 4

infantsDFT

Figure 8. Estimates from infant experiments (solid line) and DFT simulations (broken line) for theprobability to make exactly n spontaneous errors as a function of n.

According to this hypothesis, the overall rate of spontaneous errors reflects the distribu-tion of the side bias across babies and is, therefore, constant across A trials. This hypothesispredicts that the conditional probability of repeating a spontaneous error after a previouserror should be high (close to one in the limit case of completely deterministic decisions).In fact, this limit case predicts that babies with a bias to B should repeat spontaneous errorsacross the entire A-trials phase of the paradigm.

This prediction is tested in Figure 8 showing the probability that an infant/simulationmakes exactly n spontaneous errors as a function of n (Equation (3)). The deterministicaccount predicts that this probability should have a U-shape: Some infants should system-atically make no spontaneous errors, while the biased babies should make a large numberof spontaneous errors. Intermediate numbers of spontaneous errors should not be fre-quent, as these reflect stochastic decision making. The data clearly refute this hypothesis.The monotonic decrease of the probability of n spontaneous errors with the number n isconsistent with a stochastic contribution to sensorimotor decision making.

[Dineva, Schöner: Connection Science 2018]

a spontaneous error doubles probability to make the spontaneous error again

Conclusions

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

dynamic field theory: memory - rub

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