Short-term memory tasks coupled with online chunking: a straight

Embryologie
d’un
groupement
d’informa4on
et
sa
rela4on
avec
l’intelligence
générale
Fabien
Mathy
Collaborateurs
:
Mustapha
Chekaf,
Caroline
Jacquin,
Nicolas
Gauvrit,
Alessandro
Guida
http://fabien.mathy.free.fr/
1
MSHS Sud-Est 2014, Symposium du 14 Nov.
Extraction de régularités et de connaissances
1
Context and outline
► learning
and memory are inextricably intertwined
► the extraction of regularities domain is twofold:
implicit learning (based on exploited statistics;
Saffran, Aslin & Newport, 1996), which forms long-term
memories
vs.
explicit learning (based on detected regularities;
Cowan, Chen, & Rouder, 2004), which can be
immediate and conscious.
learning can be manipulated in span tasks to study
the STM/WM constructs and their relationships to
intelligence.
►
2
Background
► Individuals have a tendency to group/chunk information (Gobet
et al, 2001; Miller, 1956; Simon, 1974) and chunking makes
memory more efficient by breaking up long sequences of
information (Feigenson & Halberda, 2008; Rabinovitch et al. 2014)
E - G - U - S - A- F - R
►
5-8-1-9-8-4-2
Chunking runs counter a rigorous estimation of the span (Cowan,
2001)
3
Background
►
Chunking is generally hindered in memory span tasks by…
- change detection paradigms, using rapid
presentations (Luck & Vogel, 1997)
4
Background
►
Chunking is generally hindered in memory span tasks by…
- change detection paradigms, using rapid
presentations (Luck & Vogel, 1997)
4
Background
►
Chunking is generally hindered in memory span tasks by…
- change detection paradigms, using rapid
presentations (Luck & Vogel, 1997)
4
5
- complex span tasks, using concurrent tasks (Baddeley, 1986)
6
STM, WM, ChunkingM
► STM
►
: 7+/- 2 items in simple span tasks (Miller, 1956).
WM : 4 +/- 1 items in complex span tasks (Cowan, 2001)
and change detection paradigms (Luck & Vogel, 1997))
►
CM : 4 +/- 1 chunks in chunking span tasks (Mathy & Feldman, 2012),
but 4 items or more can be unpacked from the chunks.
4 is the capacity reached AFTER chunking
For similar ideas, see Alvarez & Cavanagh (2004) and Brady, Konkle
& Alvarez (2009), Exp. 2.
7
Digits
(2012
study)
8
8
► In our tasks, we encourage chunking/grouping
ON THE FLY,
and we predict the expansion of capacity …
9
9
Result
Digits
Chunks
Nota Bene:
Error bars are
+/- 1 SE
in all plots
Prop.
Correct
3 chunks
9
7 digits
Mathy & Feldman (2012). Cognition
10
Janus
3 chunks
7 digits
9
Mathy & Feldman (2012). Cognition
11
Present study - Key idea
In simple memory span tasks (e.g., digit span), both
storage and processing are uncontrolled
►
In complex memory span tasks (e.g., dual tasks),
processing is separated from storage and thus
controlled, but processing is not dedicated to the storage
process. Working memory does not work on memorizing
but works on something else (concurrent task) !
►
In chunking memory span tasks, processing is still
controlled while fully supporting storage.
►
This paradigm allows us to study the optimization of
storage thanks to ...
►
Storage × Processing
12
Storage × Processing
2 slots
2 slots
4 slots
4 slots
etc.
*
*
*
*
2 items/slot
4 items/slot
2 items/slot
4 items/slot
= 4 items
= 8 items
= 8 items
= 16 items
13
Compressibility
=
Algorithmic complexity
=
Kolmogorov complexity
High complexity = noncompressible sequence
14847398376382761958 : PRINT“14847398376382761958”
Low complexity = compressible sequence
0000000000...0000000000 : FOR i=1 TO 200, PRINT “0”
6
(Kolmogorov, 1965; Li & Vitányi, 1993, 1997, 2008)
14
Compression
Lossless versus Lossy
Exploits regularity
(.png, .gzip)
7
Exploits resolution
(.jpeg, .mpeg)
15
Algorithmic
complexity
for
short
strings
16
6
5
4
3
2
1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Gauvrit, Zenil, Delahaye, & Soler-Toscano (2014). Beh. Res. Methods
Soler-Toscano, Zenil, Delahaye, & Gauvrit (2014). PloS ONE
17
Soler-Toscano, Zenil, Delahaye, & Gauvrit (2014). PloS ONE
“There are 26 559 922 791 424* Turing machines
with 5 states ...”
* twenty-six trillion five hundred fifty-nine billion
nine hundred twenty-two million seven hundred
ninety-one thousand four hundred twenty-four **
** google convert numbers into words
18
Studies inspired of SIMON®
Note: The real SIMON game shows a normal
distribution around 7 colors (Gendle et Ransom, 2006)
Note that our experiment
was nonspatial, and that
sequences did not resume
like in the original game.
19
Method
- N = 183 young adults aged ~ 20
- Random sequences accross participants; Pace: 1 second
per item.
- Long task : 50 sequences, 25 minutes total.
- Not progressive
20
Method (next)
- Working Memory Capacity battery (WMCB)
(N = 112):
- one memory updating task (MU)
- two complex span tasks: operation span (OS) and
sentence span (SS)
- one spatial short-term memory span task (SSTM)
- Raven’s APM (N = 111)
21
Hypothesis
Chunking can be used as an estimate of the
Storage × Processing construct in working memory.
►
Performance at the Simon should best correlate with
the memory updating task (MU) and Raven
►
22
Result
Performance was
related to
complexity...
Note. The scoring method was based on the all-or-nothing method;
23
24
25
Correlations
SIMON
WM
MU
OS
SS
SSTM
RAVEN
.428**
.437**
.545**
.297**
.326**
.406**
SIMON
_
.531**
.572**
.457**
.376**
.515**
WM
MU
OS
SS
Performance
at.630**
the Simon
estimated
a
_
.767**
.824** by
.630**
logistic regression for each subject to find the critical decrease in
performance that occurs half-way down the logistic curve (i.e., the
inflection point). This simply
that participants
more
_ means
.499**
.466** failed
.506**
than 50% of the time on sequences where complexity was above
the inflection point.
_
.651**
.374**
_
.345**
Note. Memory updating task (MU), operation-span tasks (OS), sentence-span task (SS), spatial short-term memory task (SSTM). **, p < .01; *, p < .05.
26
Correlations
SIMON
WM
MU
OS
SS
SSTM
RAVEN
.428**
.437**
.545**
.297**
.326**
.406**
SIMON
_
.531**
.572**
.457**
.376**
.515**
_
.630**
.767**
.824**
.630**
_
.499**
.466**
.506**
_
.651**
.374**
_
.345**
WM
MU
OS
SS
Note. Memory updating task (MU), operation-span tasks (OS), sentence-span task (SS), spatial short-term memory task (SSTM). **, p < .01; *, p < .05.
26
Resulting component plot in rotated space for Exp. 1 from the
exploratory factor analysis using PCA and Oblimin
27
Text
r = .64, corresponding
to 41% of shared
variance
Chi-square = 2.82
Degrees of freedom = 7
Probability level = .90
28
Table 1
Correlations Between WMC and Gf/Reasoning Factors Derived From Confirmatory Factor Analyses of Data From Latent-Variable
Studies With Young Adults
Study
Kyllonen & Christal (1990)
Study 2: n ! 399
WMC tasks
Gf/reasoning tasks
r(95% CI)
ABC numerical assignment, mental
arithmetic, alphabet recoding
Arithmetic reasoning, AB grammatical reasoning,
verbal analogies, arrow grammatical reasoning,
number sets
Arithmetic reasoning, AB grammatical reasoning,
ABCD arrow, diagramming relations,
following instructions, letter sets, necessary
arithmetic operations, nonsense syllogisms
Arithmetic reasoning, verbal analogies, number
sets, 123 symbol reduction, three term series,
calendar test
Raven, Cattell culture fair
.91 (.89, .93)
Study 3: n ! 392
Alphabet recoding, ABC21
Study 4: n ! 562
Alphabet recoding, mental math
Engle, Tuholski, et al. (1999; N
! 133)
Miyake et al. (2001; N ! 167)
Ackerman et al. (2002; N !
135)
Conway et al. (2002; N ! 120)
Süß et al. (2002; N ! 121a)
Hambrick (2003; N ! 171)
Mackintosh & Bennett (2003;
N ! 138b)
Colom et al. (2004)
Study 1: n ! 198
Study 2: n ! 203
Study 3: n ! 193
Kane et al. (2004; N ! 236)
Operation span, reading span,
counting span, ABCD, keeping
track, secondary memory/
immediate free recall
Letter rotation, dot matrix
ABCD order, alpha span, backward
digit span, computation span,
figural-spatial span, spatial span,
word-sentence span
Operation span, reading span,
counting span
Reading span, computation span,
alpha span, backward digit span,
math span, verbal span, spatial
working memory, spatial shortterm memory, updating
numerical, updating spatial,
spatial coordination, verbal
coordination
Computation span, reading span
Mental counters, reading span,
spatial span
Mental counters, sentence
verification, line formation
Mental counters, sentence
verification, line formation
Mental counters, sentence
verification, line formation
Operation span, reading span,
counting span, rotation span,
symmetry span, navigation span
.79 (.75, .82)
.83 (.80, .85)
.60 (.48, .70)
Tower of Hanoi, random generation, paper
folding, space relations, cards, flags
Ravens, number series, problem solving,
necessary facts, paper folding, spatial analogy,
cube comparison
.64 (.54, .72)
.66 (.55, .75)
Raven, Cattell culture fair
.54 (.40, .66)
Number sequences, letter sequences,
computational reasoning, verbal analogies,
fact/opinion, senseless inferences, syllogisms,
figural analogies, Charkow, Bongard, figure
assembly, surface development
.86 (.81, .90)
Raven, Cattell culture fair, abstraction, letter sets
Raven, mental rotations
.71 (.63, .78)
1.00
Raven, surface development
.86 (.82, .89)
Surface development, cards, figure classification
.73 (.66, .79)
Surface development, cards, figure classification
.41 (.29, .52)
Raven, WASI matrix, BETA III matrix, reading
comprehension, verbal analogies, inferences,
nonsense syllogisms, remote associates, paper
folding, surface development, form board,
space relations, rotated blocks
.67 (.59, .73)
r = ~ .70
Kane et al. 2005
Note. WMC ! working memory capacity; Gf ! general fluid intelligence; 95% CI ! the 95% confidence interval around the correlations; WASI !
29
Chi-square = 1.22
Degrees of freedom = 3
Probability level = .75
30
nd
2
Study : SIMON
400 ms
600 ms
400 ms
Tim
e
600 ms
400 ms
600 ms
31
Method
- N = 107
- Same sequences accross participants; Pace: 1second per
item. Quick task : 5 minutes total.
- progressive difficulty: 2 colors, 3 colors, ...
- 3 trials per length until failing
- Two conditions counterbalanced :
moderately easy (thus chunkable)
vs hard (nonchunkable)
based on the algorithmic complexity metric
32
Method (next)
- WAIS-IV: digit span subtests (N = 107):
- Digit Span Forward: DSF
- Digit Span Forward: DSB
- Digit Span Sequencing: DSS
- Raven’s APM (N = 95)
33
Hypotheses
- The simple task estimates Storage × Processing
The difficult task estimates Storage
- The simple Simon task (allowing more
chunking) better predicts the Raven than the
difficult Simon task.
- We can estimate:
processing = (Storage × Processing) / Storage
34
Result
Again, performance
was related to
complexity.
Note. The scoring method was based on the all-or-nothing method;
35
36
COMPL
SIMPL
COMPL
DSF
DSB
.422**
DSF
DSB
DSS
RAV
.294**
.337**
.157
.413**
.229*
.353**
.310**
.385**
.473**
.273**
.290**
.476**
.446**
.297**
DSS
Correlation RAVEN-Processing = -.04 !
Correlation Compl-Processing = -.59 !
37
S
S*P
P
4
7
1,8
S
5
6
1,2
S*P
5
7
1,4
7
7
1,0
S*P
P
.13
‐.90
.29
38
39
Chi-square = 3.2
Degrees of freedom = 7
Probability level = .87
40
Conclusion
- Chunking opportunity is favored by the compressibility of a set of objects.
(different from Luck & Vogel, 1997 Brady, Konkle, & Alvarez, 2009, in which grouping
occurs within objects; closer to Brady, Konkle, & Alvarez, 2009, in their Exp 2, who also
suggest that chunking can be used as an approximation of psychological compression)
-Chunking performance can be used as an estimate of the
▶
processing component in working memory, in situations where processing
directly supports storage.
-Originality : processing demand not linearly dependant on the
number of items to be stored
- Take-away message : The birth of a chunk can take place in working memory.
41
Main reference
Chekaf, M., Gauvrit, N., Guida, A. & Mathy, F. (in prep.). The capacity of
memory span while processing is fully dedicated to storage.
Other references on chunking processes
Chekaf, M., & Mathy, F. (submitted). Chunking of categorizable objects on
the fly.
Haladjian, H. H., & Mathy, F. (in revision). Snapshot encoding of spatial
information: Location memory for visual-short-term- and short-termmemory exposures.
Mathy, F., & Varré, J. S.. (2013). Retention-error patterns in complex
alphanumeric serial-recall tasks. Memory, 21, 945-968.
4
Mathy, F., & Feldman, J. (2012). What’s magic about magic numbers?
Chunking and data compression in short-term memory. Cognition, 122,
346-362.
42
_____________________________________________
Merci !
_____________________________________________
http://fabien.mathy.free.fr/
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