A Processing Ghost in a
Tank Machine
Mario Fifić
Grand Valley State University, Michigan
Midwestern Cognitive Science Conference
May, 2014
Working memory (WM) under
consideration
•
•
•
•
•
Processing order
Capacity status
Subdivision by modalities
Dual or one system
Status of mental representations & resource
allocation
Resource allocation models of WM
• The discrete-slot model proposes that WM operates on
the ALL-OR-NONE principle: holding only highresolution item representations stored in a limited
number of memory slots.
– The slots+averaging model is variant of the discrete-slot
model assuming that more than one slot could be
allocated to a single item representation
• the variable-resources model WM operates on the ALLGET-SOME principle: a pool of limited resources is
dynamically allocated across a set of memorized items
representations.
Resource allocation in model of WM
ALL-OR-NONE
Discrete slots model
Slots+Averiging
Equal distribution
ALL-GET-SOME
A continuous resource
model
discrete-slot
model
slots+averaging
model
Lim f(x)
n->Infinity
variable-resources
model
Evidence supporting Discrete Slots
Model
•
•
•
•
Zhang & Luck 2008
Cowan (2001) The magical number 4 in short-term memory
Rouder, Morey, Cowan, Zwilling, Morey, & Pratte (2008).
Donkin, Nosofsky, Gold, & Shiffrin, (2013).
Evidence supporting
the Variable-resource model
• Van den Berg, Shin, Chou, George, & Ma, (2012)
• Bays & Husain (2008)
van den Berg, et al. (2012). Appendix..
Unresolved question(s)
(what’s under the All-or-none carpet)
or
“Why I am not an enthusiast “
• (1) We argue that the above research
advances have been downplaying the
experimental approaches to directly
manipulate the allocation of resources across
item representations held by WM.
– Our study showed that, when instructed, subjects
adaptively allocated a limited amount of resources
and shared them across memorized item
representations.
Unresolved question(s)
(what’s under the carpet)
• (2) The exact mechanism of resource
allocation has not been specified.
Specific Research Questions
How are the resources allocated in WM? (HalfHalf rule)
What is the status of mental representations
in WM?
How are the capacity resources
allocated?
0.30
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
0.30
Ascending Descending
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
Propotion of Allocated Capacity
Equal
Propotion of Allocated Capacity
Propotion of Allocated Capacity
Attentional gating function in WM
0.30
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
How are the capacity resources
distributed?
The Half-Half Optimal Rule
• The optimal solution for allocation of a limited amount of
resources: one Half of resources should be allocated to
memorized items and another Half to a target.
N -1
arg max[ Target  Itemi ]
Target
i
N -1
 Target  Item
i
N -1
 Target  Itemi  Target (TotalCapacity - Target) 
i
i
Target  TotalCapacity - Target 2
d
[Target  TotalCapacity - Target 2 ]  TotalCapacity - 2  Target
dTarget
TotalCapacity - 2  Target  0
Target 
1
TotalCapacity
2
The Target Locking Hypothesis
Propotion of Allocated Capacity
• Implication for non-optimal strategies,
after the Half-Half rule→
Attentional gating should aim to allocate
more capacity resources to the target than
to memorized items.
Ascending
0.30
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
The model
The Exemplar-Based STM Retrieval Model EBRW and the ItemTarget Product Rule
Capacity
Distributed via
Attentional Gating
N  number of items stored in STM  Target
2 (Intercept  N - TotalCap)
Item Capacity(Target Capacity)  f ( N)  
N (1  N)
Assuming limited capacity   f ( N , Intercept )  TotalCap
N
1
EBRW
r r
K
dij   wk xik - x jk  ,
 k 1

Distance
dij  fixed value distance (free paramter)
dij  0 , on positive match
Activation*
sij  exp  c  dij  Item Capacityi  Target Capacity j
Similarity
Stepping
Probability
pi 
 si,old
s
i ,old
Capacity via Attentional Gating

OLD
Random
Walk
RTx1
NEW
Time
e.g. Nosofsky, Little ,Donkin, & Fific, 2011
New Method
The attention-to-position paradigm
• Rapid short-term memory paradigm
• Focal set : To pay special attention to certain item positions
in the memorized list, called a “focal set”. This means that if
a target item was a member of a focal set, a response
decision had to be extremely fast, and accurate
• Peripheral set: The rest items not contained in a focal set.
Focal set
Peripheral set
“First Three”
“Last Three”
Serial Position (1-6)
“All Fast”
TARGET
(N=6)
5
4
9
1
2
8
5
Ti me
RT (ms) & Accuracy
The data
Serial Position (1-6)
TARGET
“All Fast”
(N=6)
5
4
9
1
2
8
RT (ms) & Accuracy
5
Time
1.2
580
1.0
560
0.8
P(Correct)
Mean RT (ms)
600
540
520
500
0.6
0.4
OLD
NEW
OLD
NEW
Old Predicted
New Predicted
480
Old Predicted
New Predicted
0.2
0.0
460
0
1
2
3
4
5
Serial Position
6
Lure
0
1
2
3
4
5
6
Lure
Serial Position
• This is a typical RT pattern observed in the STM research, the primacy and
recency
(1) Equal-precision
(2) ALL-OR-NONE
(3) The decay-representation WM model
(4) Fluid-resource model
(5) Slots+averaging model
The data
“First Three”
1.2
600
OLD
580
Old Predicted
New Predicted
1.0
NEW
P(Correct)
Mean RT (ms)
620
560
540
520
500
0.8
0.6
0.4
OLD
NEW
0.2
Old Predicted
New Predicted
480
0.0
460
0
1
2
3
4
5
6
Lure
Serial Position
• Not typical strong primacy RT effect
(1) Equal-precision
(2) ALL-OR-NONE
(3) Decay-representation WM model
(4) Fluid-resource model
(5) Slots+averaging model
0
1
2
3
4
5
Serial Position
6
Lure
Comparison
620
600
580
RT(ms)
560
540
520
500
480
All Fast
First Three
-
460
1
• Implications
2
3
4
5
6
Lure
Serial Position of a target item
– A discontinuous serial position effect -> Dual WM
systems
– The principle of resource conservation-> Strictly fixed
capacity
The data – further validation of
resource allocation
“Last Three”
600
1.2
1.0
560
P(Correct)
Mean RT (ms)
580
540
520
500
OLD
NEW
Old Predicted
New Predicted
480
1
2
0.6
0.4
OLD
NEW
Old Predicted
New Predicted
0.2
460
0
0.8
3
4
5
Serial Position
6
Lure
0.0
0
1
2
3
4
5
Serial Position
6
Lure
Comparison
620
600
580
RT(ms)
560
540
520
500
480
All Fast
First Three
Last Trhee
460
1
2
3
4
5
6
Serial Position of a target item
Lure
1 2 3 4 5 6 78
Equal
Descending
0.30
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
0.30
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
1 2 3 4 5 6 78
Propotion of Allocated Capacity
1 2 3 4 5 6 78
Propotion of Allocated Capacity
Propotion of Allocated Capacity
The proposed resource allocation
model :The Tilted Water Tank
Ascending
0.30
Memorized Items
Target
0.25
0.20
0.15
0.10
0.05
0.00
1
2
3
4
5
Item Serial Position
6
7
Model fitting: the linear distribution
function of resource allocation
Estimated Capacity Allocations
600
Mean RT (ms)
0.18
All Fast
First Three
Last Trhee
560
540
520
500
OLD
NEW
480
Old Predicted
New Predicted
460
0
1
2
3
4
5
6
Lure
6
Lure
6
Lure
Serial Position
0.16
600
Mean RT (ms)
580
0.14
560
540
520
500
OLD
NEW
Old Predicted
New Predicted
480
460
0.12
0
1
2
3
4
5
Serial Position
620
0.10
1
2
3
4
5
6
Item's Position in the Set
7
Mean RT (ms)
Capacity Proportion Allocated
580
600
OLD
580
Old Predicted
New Predicted
NEW
560
540
520
500
480
460
0
1
2
3
4
5
Serial Position
discrete-slot
model
slots+averaging
model
×
Lim f(x)
n->Infinity
?
variable-resources
model
How many boxes?
• Conduct data fitting of the EBRW model that
can freely allocate fixed amount of resources
across memorized items, including the
parameter which defines a number of possible
memory slots (boxes).
• In other words: find the number of possible
resource allocation units (slots, boxes) that
maximizes the goodness of fit of the model for
resource allocation.
How many boxes?
Params
Free resource parameter-EBRW
mode
First
All Fast
Three
Last
Three
c
acrit
bcrit
scale
mu
listbase
dscale
m1
m2
m3
m4
m5
m6
0.959
2.52
3.936
44.706
175.816
0.175
2.705
0.145
0.131
0.132
0.161
0.201
0.231
1.6
11.378
17.164
1.901
256.035
0.42
0.65
0.128
0.131
0.128
0.176
0.208
0.229
boxes
801
𝑚𝑖 = 1
2.383
3.556
43.592
4.576
137.859
0.261
0.979
0.161
0.166
0.167
0.170
0.172
0.164
670
𝑚𝑖 = 1
711
𝑚𝑖 = 1
Conclusions




New method for testing WM, attention by instruction
Support for the variable-resources model WM, all-get-some
Falsification of all-or-none approaches, discrete representations
We specified a likely mechanism of resource allocation (Target locking)
and provided rationale
 The ghost is likely to reside in a tilted tank!
Further Implications:
 Linear distribution function of resources could serve as a proxy to the
Attentional Gating mechanism.
 Falsification of Dual system WM view: the last item position advantage
 A joint fit of mean RT and choice probabilities.[EBRW]
 A STM capacity resources are strictly limited (the conservation of
resources principle)
fificm@gvsu.edu
research: http://faculty.gvsu.edu/fificm/index.html
Free allocation of fixed capacity model
Resource Distribution Function
2D Graph 1
0.22
0.20
0.18
0.16
0.14
All Fast
First Three
Last Trhee
0.12
0.10
1
2
3
4
5
6
Serial Position of a target item
Tests & methods
A Short-Term Memory (STM)
Retrieval Task
Serial Position (1-6)
TARGET
Memorized Set (N=1-6)
5
4
9
1
2
8
1
3
5
7
9
5
0
6
4
1
5
4
3
8
5
1
5
5
7
5
5
Time
Response RT (ms) & Accuracy
•The variant of the Sternberg task:
Set size (1-6)
•Fast presentation rate (250msec)
•No target cuing
Tests & methods
Attention to Location Method
Manipulate subjects' temporal distribution of attention across
items in the list
Focus on the first items in the list
Focus on all items in the list
Serial Position (1-6)
4
9
1
2
8
1
3
5
7
9
5
0
6
4
1
5
4
3
8
5
1
5
5
7
5
5
Time
Response RT (ms) & Accuracy
Memorized Set (N=1-6)
TARGET
5
The data
Attentional Gating and Set Size Effect
“No Target Cuing”
750
Serial Position (1-6)
5
0
6
4
1
5
4
3
8
5
1
5
5
7
5
5
1.0
P(Correct)
8
9
650
600
550
0.8
0.6
0.4
OLD
Time
OLD
NEW
NEW
Old Predicted
New Predicted
500
0
1
2
3
4
5
6
Old Predicted
New Predicted
0.2
0.0
7
0
Set Size
1
2
3
4
5
6
7
4
5
6
7
Set Size
“First two items”
750
1.2
1.0
700
P(Correct)
2
7
650
600
0.8
0.6
0.4
OLD
NEW
OLD
550
NEW
Old Predicted
Set Size vs New Predicted
0.2
Old Predicted
Set Size vs New Predicted
500
0.0
0
1
2
3
4
Set Size
5
6
7
0
1
0.18
No Target Cues
Attention to first positions
0.16
0.14
0.12
0.10
1
2
3
2
3
Set Size
Estimated Capacity Allocations
Capacity Proportion Allocated
1
5
Mean RT (ms)
9
3
Mean RT (ms)
Memorized Set (N=1-6)
4
1
Response RT (ms) & Accuracy
5
1.2
700
TARGET
4
5
6
Item's Position in the Set
7
Relationship between
Short-term memory and Attention
Ahw & Jonides, 2001
Oberauer & Kliegl, 2006
Oberauer 2001; 2002; 2003
Garavan, 1998;
Reeves & Sperling, 1986
Relationship between
Short-term memory and Attention
• External Search: when search items in a visual
field attention uses short-term memory to
mark the important spatial locations.
The idea:
• Internal search: when search items in memory
(STM), the search mechanism uses attention
to allocate processing resources to “mark”, or
to lock, important memory locations.
Why status of mental representations
in WM?
• Resource allocation.
• If representations are ALL-OR-NONE, and the
system’s capacity is limited, then when there
is information overload an operator must
guess.
• Sophisticated guessing?
• Neural system’s implications.
New Method
The attention-to-position paradigm
• To prevent interference of extraneous variables with
the process of resource allocation the subjects were
instructed to pronounce each item in a set, without
accentuation, and with a monotonic prosody
• Two measures: mean response time (RT) and
accuracy.