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Mind from brain: physics & neuroscience

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Mind from brain: physics & neuroscience
Mind from brain:
physics & neuroscience
Włodzisław Duch
Katedra Informatyki Stosowanej,
Uniwersytet Mikołaja Kopernika, Toruń.
Google: W. Duch
Kraków, 25-26.09.2008
Plan:
How physicist may help neuroscience?
Interesting problems worth working on.
• Intro: gap between neuroscience and psychology.
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•
•
•
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From molecules to mind
Generative psychiatry: autism, brain death
Experimental psychology – priming, functions
Intuition and creativity
Psychological spaces and neurodynamics
Higher cognitive functions, categorization,
language and consciousness
• Conclusions
Cognitive Science
Cognitive science: mixture (syntopy) of cognitive psychology,
neurosciences, AI, linguistics, philosophy of mind, psychophysics,
anthropology ... No central model of mind in cognitive science.
Very few general laws in psychology (mostly psychophysical).
Psycho-logy lost the soul ?
Philosophical problems in foundations of cognitive sciences: mindbody problem, qualia, symbol grounding, Searle critique, the
binding problem, Fodor's critique of connectionist approach ...
The Central Paradox of Cognition: how can the structure and
meaning, expressed in symbols and ideas at the mental level,
result from numerical processing at the brain level?
Mind the Gap
Gap between neuroscience and psychology:
mixture (syntopy) of cognitive psychology, neurosciences, AI,
linguistics, philosophy of mind, psychophysics, anthropology ...
No central model of mind in cognitive science.
Is a satisfactory understanding of the mind possible ?
Roger Shepard, Toward a universal law of generalization for
psychological science (Science, Sept. 1987):
“What is required is not more data or more refined data but a
different conception of the problem.”
• Mind is what the brain does.
How to approximate the dynamics of the brain to get satisfactory
picture of the mind ? At which level?
Od molekuł ...
Proste organizmy: nartniki i pasikoniki w Korei Płd. (P. Jabłoński).
Quantum level?
Quantum level - explaining what?
Roger Penrose, Henry Stapp and others, brought quantum level to
discussion of consciousness and free will, but this has not contributed to
understanding of any real phenomena so far.
“ … consciousness of human agents enters into the structure of empirical
phenomena” – decoherence and quantum Darwinism deal in a much way
with interpretation of quantum mechanics.
Unlikely to have any influence on global brain states = real cognitive states.
Strongly coupled dynamical systems form a whole that cannot be easily
decomposed into parts and their interactions => quantum-like behavior.
• Synchronization as basis for brain dynamics (Haken, 2002).
• Noise leading to clusters of synchronized groups of neurons, echo states.
• Brain dynamics is best modeled by a large ensemble of coupled nonlinear
dynamical subsystems with unstable and transient dynamics.
Mind is a shadow of neurodynamics.
to mind.
Neurony pobudzające i hamujące
Kwas glutaminowy
otwiera kanały Na+,
pobudzająco,
GABA działa na
kanały Cl- hamując
pobudzanie.
Siatkówka
• Siatkówka nie jest pasywną matrycą rejestrującą obrazy.
• Kluczowa zasada: wzmacnianie kontrastów podkreślających zmiany w
przestrzeni i czasie, wzmacnianie krawędzi, jednolicie oświetlone obszary są
mniej istotne.
• Fotoreceptory w czopkach i pręcikach,
• 3-warstwowa sieć, komórki zwojowe =>LGN.
Pole recepcyjne: obszar, który
pobudza daną komórkę.
Kombinacja sygnałów w siatkówce
daje pola recepcyjne typu centrumotoczka (on-center) i odwrotnie,
wykrywa krawędzie.
Każde z pól indywidualnych komórek
można modelować gaussem, więc
takie pola otrzymuje się jako różnicę
dwóch gaussów (DOG).
Wzrok
• Z siatkówki przez ciało kolankowate boczne (część wzgórza) informacja
trafia do pierwotnej kory wrokowej V1 i stamtąd wędruje dwiema drogami.
Złożony model rozpoznawania
Prezentacja dwóch obiektów, uwzględnia LGN, V1, V2, V4/IT, V5/MT
Model ma dodatkowe dwie
warstwy:
Spat1 połączone z V1 i
Spat2 połączone z V2.
Spat1 ma pobudzenia
wewnątrz warstwy, skupia
się na obiekcie.
Przeniesienie uwagi z
jednego obiektu na drugi
jeśli wszystko dobrze działa.
Przyspieszanie symulacji:
procesory graficzne, CUDA.
Efekty ...
Brak akomodacji neuronów spowoduje trudności z przeniesieniem uwagi, a w
efekcie u dziecka:
• skupienie tylko na jednym, absorpcje
• schematyczne, powtarzalne ruchy
• niechęć do zróżnicowanej stymulacji czy zabaw
• brak kontaktu z opiekunem
• trudności językowe
• echolalię
• traktowanie ludzi tak jak przedmioty
• brak „teorii umysłu”, normalnych relacji
Co to przypomina?
Autyzm, lub podobne formy spektrum autyzmu 6:1000 dzieci.
Zaburzenia budowy kanałów upływu?
Istotnie, stwierdzono mutacje genów zarówno w kanałach potasowych (gen
CASPR2) jak i sodowych (gen SCN2A):
http://www.autismcalciumchannelopathy.com/
Psychiatria generatywna?
• Jak zmiany na poziomie genetycznym i molekularnym wpływają na dynamikę
działania mózgu?
• Jakich zaburzeń można się spodziewać przy lokalnych zaburzeniach
poszczególnych struktur?
• Jakie efekty daje brak synchronizacji pomiędzy odległymi obszarami?
Zaburzenia świadomości:
• Rola pnia mózgu (tworu siatkowatego) w utrzymaniu pobudliwości kory.
• Stan czuwania, stupor i stany obniżonej świadomości.
• Śpiączka – brak reakcji na otoczenie, stany snu.
• Stan minimalnej świadomości. pozostają proste reakcje, „wyspy aktywności”
• Stan wegetatywny, tylko ruchy spontaniczne, cykl sen-czuwanie.
• Proces umierania mózgu.
Neuroanatomia i psychologia talentu?
Wsteczne projekcje (dt-MRI) do kory zmysłowej warunkują zdolności do
wywołania „żywych” wyobrażeń.
Brain-like computing
Brain states are physical, spatio-temporal states of neural tissue.
• I can see, hear and feel only my brain states! Ex: change blindness.
• Cognitive processes operate on highly processed sensory data.
• Redness, sweetness, itching, pain ... are all physical states of brain tissue.
In contrast to computer registers,
brain states are dynamical, and thus
contain in themselves many
associations, relations.
Inner world is real! Mind is based on
relations of brain’s states.
Computers and robots do not have
an equivalent of such WM.
Priming
T.P. McNamara, Semantic priming: perspectives from memory and word
recognition, Psychology Press, 2005
Priming (David Meyer, Roger Schvaneveldt, 1971): semantically related word
pairs are recognized faster as words than nonrelated words.
Priming: improvement in performance in a perceptual or cognitive task, relative
to an appropriate baseline, produced by context or prior experience.
Spreading neural activation leads to faster activation for related stimuli.
Thousands of papers in experimental psychology.
A lot of neurophysiology and brain imaging studies, especially N400 in ERP.
Over 10 models of semantic priming, many other types of priming, but no
computational simulations to predict the latency, timings, ERP shapes etc.
Experimental psychologist urgently need help of physicist !
Symbols in the brain
Organization of the word recognition circuits in the left temporal lobe
has been elucidated using fMRI experiments (Cohen et al. 2004).
How do words that we hear, see or are thinking of, activate the brain?
Seeing words: orthography, phonology, articulation, semantics.
Lateral inferotemporal multimodal area (LIMA) reacts to auditory visual
stimulation, has cross-modal phonemic and lexical links. Adjacent visual word
form area (VWFA) in the left occipitotemporal sulcus is unimodal.
Likely: homolog of the VWFA in the auditory stream, the auditory word form area,
located in the left anterior superior temporal sulcus.
Large variability in location of these regions in individual brains.
Left hemisphere: precise representations of symbols, including phonological
components; right hemisphere? Sees clusters of concepts.
Words in the brain
Psycholinguistic experiments show that most likely categorical,
phonological representations are used, not the acoustic input.
Acoustic signal => phoneme => words => semantic concepts.
Phonological processing precedes semantic by 90 ms (from N200 ERPs).
F. Pulvermuller (2003) The Neuroscience of Language. On Brain Circuits of Words
and Serial Order. Cambridge University Press.
Action-perception
networks inferred
from ERP and fMRI
Phonological neighborhood density = the number of words that are similar in
sound to a target word. Similar = similar pattern of brain activations.
Semantic neighborhood density = the number of words that are similar in meaning
to a target word.
Semantic reps
Word w in the context: (w,Cont), distribution of brain activations.
States (w,Cont)  lexicographical meanings: clusterize (w,Cont) for all
contexts, define prototypes (wk,Cont) for different meanings wk.
Simplification: use spreading activation in semantic networks to define .
How does the activation flow? Try this algorithm on collection of texts:
• Perform text pre-processing steps: stemming, stop-list, spell-checking ...
• Discover main concepts in text, avoiding highly ambiguous results when
•
•
•
mapping text to ontologies.
Use relations between concepts to create first-order cosets (terms + all new
terms from included relations); add only those types of relations that lead to
improvement of classification results.
Reduce dimensionality of the first-order coset space, leave all original features;
use feature ranking method for this reduction, increasing concept distances.
Repeat last two steps iteratively to create second and higher-order enhanced
spaces, first expanding, then shrinking the space.
Creates vector representation of concepts; QM-like formalism possible.
Neuroimaging words
Predicting Human Brain Activity Associated with the Meanings
of Nouns, T. M. Mitchell et al., Science, 320, 1191, May 30, 2008
• Clear differences between fMRI brain activity when people read and think
about different nouns.
• Reading words and seeing the drawing invokes similar brain activations,
presumably reflecting semantics of concepts.
• Although individual variance is significant similar activations are found in
brains of different people, a classifier may still be trained on pooled data.
• Model trained on ~10 fMRI scans + very large corpus (1012) predicts brain
activity for over 100 nouns for which fMRI has been done.
Word w is represented by a vector (w,Cont), still structural info is missing,
spreading activation should give better results.
Overlaps between activation of the brain for different words may serve as
expansion coefficients for word-activation basis set.
Memory & creativity
Creative brains accept more incoming stimuli from the surrounding environment
(Carson 2003), with low levels of latent inhibition responsible for filtering stimuli
that were irrelevant in the past.
“Zen mind, beginners mind” (S. Suzuki) – learn to avoid habituation!
Complex representation of objects and situations kept in creative minds.
Pair-wise word association technique may be used to probe if a connection
between different configurations representing concepts in the brain exists.
A. Gruszka, E. Nęcka, Creativity Research Journal, 2002.
Word 1
Priming 0,2 s
Word 2
Words may be close (easy) or distant (difficult) to connect;
priming words may be helpful or neutral;
helpful words are either semantic or phonological (hogse for horse);
neutral words may be nonsensical or just not related to the presented pair.
Results for groups of people who are less/highly creative are surprising …
Creativity & associations
Hypothesis: creativity depends on the associative memory,
ability to connect distant concepts together.
Results: creativity is correlated with greater ability to associate words
susceptibility to priming, distal associations show longer latencies before decision
is made.
Neutral priming is strange!
• for close words and nonsensical priming words creative people do worse
than less creative; in all other cases they do better.
• for distant words priming always increases the ability to find association,
the effect is strongest for creative people.
Latency times follow this strange patterns.
Conclusions of the authors:
More synaptic connections => better associations => higher creativity.
Results for neutral priming are puzzling.
Paired associations
So why neutral priming for close associations and
nonsensical priming words degrades results of creative people?
High creativity = many connections between microcircuits; nonsensical words add
noise, decreasing threshold for synchronization between many circuits;
in a densely connected network adding noise creates chaos and the time needed
for decision is increased because the system has to settle in specific attractor.
If creativity is low and associations distant, noise does not help because there are
no connections, priming words contribute only to chaos.
Nonsensical words increase overall activity in the intermediate configurations.
For creative people resonance between distant microcircuits is possible:
this is called stochastic resonance, observed previously in perception.
For priming words with similar spelling, and for words that are easily associated ,
pattern representing the second word becomes more active, always increasing the
chance of connections and decreasing latency.
For distant words it will not help, as intermediate configurations are not activated.
EEG and creativity
How to increase cooperation between distant
brain areas important for creativity?
John H. Gruzelier (Imperial College), SAN President
a-q neurofeedback produced “professionally significant
performance improvements” in music and dance students.
Neurofeedback and heart rate variability (HRV) biofeedback.
benefited performance in different ways.
Musicality of violin music students was enhanced; novice singers from
London music colleges after ten sessions over two months learned
significantly within and between session the EEG self-regulation of q/a ratio.
The pre-post assessment involved creativity measures in improvisation,
a divergent production task, and the adaptation innovation inventory.
Support for associations with creativity followed improvement in creativity
assessment measures of singing performance.
Why? Low frequency waves = easier synchronization between distant
areas; parasite oscillations decrease.
… to mind.
Words: simple model
Goals:
• make the simplest testable model of creativity;
• create interesting novel words that capture some features of products;
• understand new words that cannot be found in the dictionary.
Model inspired by the putative brain processes when new words are being
invented. Start from keywords priming auditory cortex.
Phonemes (allophones) are resonances, ordered activation of phonemes will
activate both known words as well as their combinations; context + inhibition in
the winner-takes-most leaves one or a few words.
Creativity = space+imagination (fluctuations) + filtering (competition)
Imagination: many chains of phonemes activate in parallel both words and
non-words reps, depending on the strength of synaptic connections.
Filtering: associations, emotions, phonological/semantic density.
Problems requiring insights
Given 31 dominos
and a chessboard with 2 corners
removed, can you cover all board with dominos?
Analytical solution: try all combinations.
Does not work … to many combinations to try.
Logical, symbolic approach has
little chance to create proper
activations in the brain, linking
new ideas: otherwise there will
be too many associations,
making thinking difficult.
chess board
domino
n
black
white
Insight <= right hemisphere,
meta-level representations
without phonological (symbolic)
components ... counting?
m
do
o
i
phonological reps
Insights and brains
Activity of the brain while solving problems that required insight and that
could be solved in schematic, sequential way has been investigated.
E.M. Bowden, M. Jung-Beeman, J. Fleck, J. Kounios, „New approaches to
demystifying insight”. Trends in Cognitive Science 2005.
After solving a problem presented in a verbal way subjects indicated themselves
whether they had an insight or not.
An increased activity of the right hemisphere anterior superior temporal
gyrus (RH-aSTG) was observed during initial solving efforts and insights.
About 300 ms before insight a burst of gamma activity was observed,
interpreted by the authors as „making connections across distantly related
information during comprehension ... that allow them to see connections
that previously eluded them”.
Insight interpreted
What really happens? My interpretation:
•
•
•
•
•
•
•
•
LH-STG represents concepts, S=Start, F=final
understanding, solving = transition, step by step, from S to F
if no connection (transition) is found this leads to an impasse;
RH-STG ‘sees’ LH activity on meta-level, clustering concepts into
abstract categories (cosets, or constrained sets);
connection between S to F is found in RH, leading to a feeling of vague
understanding;
gamma burst increases the activity of LH representations for S, F and
intermediate configurations; feeling of imminent solution arises;
stepwise transition between S and F is found;
finding solution is rewarded by emotions during Aha! experience;
they are necessary to increase plasticity and create permanent links.
Creativity in dementia?
• Bruce L. Miller, Craig E. Hou, Emergence of Visual Creativity in Dementia. Arch
Neurol. 61, 842-844, 2004.
Miller et al (UCSF) describe a series of patients with frontotemporal dementia who
acquired new artistic abilities despite evidence of deterioration in the left anterior
temporal lobe.
Good memory is common with frontotemporal dementia (FTD). Simple copying is
typically preserved, some patients with FTD develop a new interest in painting,
their artistic productivity can increase despite progression of the dementia.
The artwork is approached in a compulsive manner and is often realistic or
surrealistic in style.
Why? Is it a disinhibition effect?
Negation of linguistic concepts that block visual creativity?
Slow “rewiring” of the cortex? Paradoxical functional compensation?
Relation to TMS & savant syndrome studies (A. Snyder, MindLab Sydney).
Some speculations
How to increase spatial coherence in the brain?
Neurofeedback, or even simpler, “mantra” meditation.
Simplifies neurodynamics, stops many weaker processes that pop-up.
Role of neurotransmiters in creativity?
Creative people store extensive specialized knowledge in temporoparietal
cortex, but may switch to divergent thinking, distant associations typical for
parietal system, by modulation of the frontal lobe - locus coeruleus
(norepinephrine) system.
Frontal lobes are involved in working memory, divergent thinking, control of
the locus coeruleus-norepinephrine system.
Low levels of norepinephrine => increase synchrony, large distributed
activations across brain areas, creation of novel concepts.
High levels of norepinephrine (mostly from locus coeruleus), more precise
memory recall, localized activations.
Computational creativity
Go to the lower level …
construct words from combinations of phonemes, pay attention to
morphemes, flexion etc.
Creativity = neural space
+ imagination (fluctuations) + filtering (competition)
Space: neural tissue providing space for infinite patterns of activations.
Imagination: many chains of phonemes activate in parallel both words and
non-words reps, depending on the strength of synaptic connections.
Filtering: associations, emotions, phonological/semantic density.
Start from keywords priming phonological representations in the auditory
cortex; spread the activation to concepts that are strongly related.
Use inhibition in the winner-takes-most to avoid false associations.
Find fragments that are highly probable, estimate phonological probability.
Combine them, search for good morphemes, estimate semantic probability.
Autoassociative networks
Simplest networks:
• binary correlation matrix,
• probabilistic p(ai,bj|w)
Major issue: rep. of symbols,
morphemes, phonology …
W
x 0 0
0 x 0
0 0 x
x x x
x x x
x x x
x x x
x x x
x x x
x 0 0
0 x 0
0 0 x
x x x
x x x
x x x
x x x
x x x
x x x
x 0 0
0 x 0
0 0 x
Phonological filter
•
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•
•
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•
•
•
•
•
•
•
•
Train the autoassociative network on words from some dictionary.
Create strings of words with “phonological probability”>threshold.
Many nice Polish words … good for science-fiction poem
ardyczulać ardychstronność
ardywialiwić ardykloność
ardywializować ardywianacje
argadolić argadziancje
arganiastość arganastyczna
arganianalność arganiczna
argasknie argasknika
argaszyczny argaszynek
argażni argulachny argatywista
argumialent argumiadać argumialenie argumialiwić
argumializować argumialność
argumowny argumofon argumował argumowalność
Words: experiments
A real letter from a friend:
I am looking for a word that would capture the following qualities: portal to new
worlds of imagination and creativity, a place where visitors embark on a journey
discovering their inner selves, awakening the Peter Pan within.
A place where we can travel through time and space (from the origin to the future
and back), so, its about time, about space, infinite possibilities.
FAST!!! I need it sooooooooooooooooooooooon.
creativital, creatival (creativity, portal), used in creatival.com
creativery (creativity, discovery), creativery.com (strategy+creativity)
discoverity = {disc, disco, discover, verity} (discovery, creativity, verity)
digventure ={dig, digital, venture, adventure} still new!
imativity (imagination, creativity); infinitime (infinitive, time)
infinition (infinitive, imagination), already a company name
portravel (portal, travel); sportal (space, sport, portal), taken
timagination (time, imagination); timativity (time, creativity)
tivery (time, discovery); trime (travel, time)
Server at: http://www-users.mat.uni.torun.pl/~macias/mambo
More experiments
• Probabilistic model, rather complex, including various linguistic
peculiarities; includes priming.
Search for good name for electronic book reader (Kindle?):
Priming set (After some stemming):
• Acquir, collect, gather , air, light, lighter, lightest, paper, pocket, portable,
anyplace, anytime, anywhere, cable, detach, global, globe, go, went,
gone, going, goes, goer, journey, move, moving, network, remote,
road\$, roads\$, travel, wire, world, book, data, informati, knowledge,
librar, memor, news, word, words, comfort, easi, easy, gentl, human,
natural, personal, computer, electronic, discover, educat, learn, read,
reads, reading, explor.
Exclusion list (for inhibition):
• aird, airin, airs, bookie, collectic, collectiv, globali, globed, papere,
papering, pocketf, travelog.
More words
Created word Word count and # domains in Google
• librazone
968
1
• inforizine
--• librable
188
-• bookists
216
-• inforld
30
-• newsests
3
-• memorld
78
1
• goinews
31
-• libravel
972
-• rearnews
8
-• booktion
49
-• newravel
7
-• lighbooks
1
-+ popular infooks , inforion, datnews, infonews, journics
Static Platonic model: motivation
Plato believed in reality of mind, ideal forms recognized by intellect.
Perceived mind content is like a shadow of ideal, real world of objects
projected on the wall of a cave.
Real mind objects: shadows of neurodynamics.
R. Shepard (BBS, 2001): psychological laws should be formulated
in appropriate psychological abstract spaces.
Physics - macroscopic properties results from microinteractions.
Description of movement - invariant in appropriate spaces:
• Galileo transformations in Euclidean 3D;
• Lorentz transformations in (3+1) pseudo-Euclidean;
• Riemannian curved space, laws invariant in accelerating frames.
Psychology - categorization, behavior, results from neurodynamics.
Neural networks: microscopic description, too difficult to use.
Find psychological spaces resulting from neural dynamics, allowing for
general behavioral laws.
P-spaces
Psychological spaces:
K. Lewin, The conceptual representation and the measurement of
psychological forces (1938), cognitive dynamic movement in
phenomenological space.
George Kelly (1955), personal construct psychology, geometry of
psychological spaces as alternative to logic.
A complete theory of cognition, action, learning and intention.
P-space: region in which we may place and
classify elements of our experience,
constructed and evolving, „a space without
distance”, divided by dichotomies.
P-spaces (Shepard 1957-2001):
• minimal dimensionality
• distances that monotonically decrease
with increasing similarity
(multi-dimensional non-metric scaling).
Some evidence
Universal law of generalization, Shepard (1987)
Tenenbaum, Griffith (2001), Bayesian framework unifying set-theoretic
approach (Tversky 1977) with Shepard.
Generalization gradients tend to fall off approximately exponentially with
distance in an appropriately scaled psychological space.
Distance - from MDS maps of perceived similarity of stimuli.
G(D) = probability of response learned to stimulus for D=0, for many
visual/auditory tasks, falls exponentially with the distance.
More evidence
Object recognition theory, S. Edelman (1997)
Second-order similarity in low-dimensional (<300) space is sufficient.
Population of columns as weak classfiers working in chorus - stacking.
Static Platonic model
Newton: introduced space-time, arena for physical events.
Mind events: need psychological spaces.
Goal: integrate neural and behavioral information in one model, connect
psychology and neuroscience, create mind model at intermediate level.
Static version: short-term response properties of the brain, behavioral
(sensomotoric) or memory-based (cognitive).
Applications: object recognition, category formation in low-dimensional
psychological spaces, models of mind.
Approach:
• simplify neural dynamics, find invariants (attractors), characterize
them in psychological spaces;
• use behavioral data, represent them in psychological space.
How to make static model?
From neural responses to stimulus spaces.
Bayesian analysis of multielectrode responses (Foldiak).
P(ri|s), i=1..N computed from multi-electrode measurements
The posterior probability P(s|r) = P(stimulus | response)
Bayes law:
N
P  s | r   P  s | r1 , r2 ..rN  
P( s ) P  ri | s 
i 1
N
 P(s ') P  r | s '
i
s'
i 1
Population analysis: visual object represented as
population of column activities.
Same for words and abstract objects (evidence from
brain imaging)
Semantic memory
Autoassociative network, developing internal
representations (McClleland-Naughton-O’Reilly,
1995).
After training distance relations between different
categories are displayed in a dendrogram, showing
natural similarities/ clusters.
MDS mappings: min S (Rij-rij)2
from internal neural activations;
from original data in the P-space - hypercube, dimensions
for predicates, ex. robin(x)  {0, 1};
from psychological experiments, similarity matrices;
show similar configurations.
From neurodynamics to P-spaces.
Modeling input/output relations with some internal parameters.
Freeman: model of olfaction in rabbits, 5 types of odors, 5 types of
behavior, very complex model in between.
Attractors of dynamics in high-dimensional space => via fuzzy symbolic
dynamics allow to define probability densities (PDF) in feature spaces.
Mind objects - created from fuzzy prototypes/exemplars.
Case-based reasoning: static model.
Geometric properties.
Geometric representation of mental events should be understandable.
Problem of all Euclidean models: similarities are non-metric.
Re-entry connections between columns are not symmetric.
Asymmetric MDS requires change of perspective for each object.
Solution: Finsler geometry (ex: time as distance)
A curve X(t) parameterized by t, distance between t1=A, t2=B depends on
the positions X(t+dt) and derivative dX(t)/dt.
B
s  A, B   min  L  X (t ), dX (t ) / dt  dt
A
where L(.) is a metric function (Lagrangian in physics).
Distance = „action” , fundamental laws of physics have such form.
To get non-symetric distance s(A,B), potential may be introduced, for
example proportional to probability density.
More neurodynamics.
Amit group, 1997-2001,
simplified spiking neuron
models of column activity
during learning.
Stage 1: single columns
respond to some feature.
Stage 2: several columns
respond to different features.
Stage 3: correlated activity of
many columns appears.
Formation of new attractors =>
formation of mind objects.
PDF: p(activity of columns,
given presented features)
Human categorization
How do we discretize percepts, creating basis for symbolic communication?
Multiple brain areas involved in different categorization tasks.
Classical experiments on rule-based category learning:
Shepard, Hovland and Jenkins (1961), replicated by Nosofsky et al. (1994).
Problems of increasing complexity; results determined by logical rules.
3 binary-valued dimensions:
shape (square/triangle), color (black/white), size (large/small).
4 objects in each of the two categories presented during learning.
Type I - categorization using one dimension only.
Type II - two dim. are relevant, including exclusive or (XOR) problem.
Types III, IV, and V - intermediate complexity between Type II - VI.
All 3 dimensions relevant, "single dimension plus exception" type.
Type VI - most complex, 3 dimensions relevant, enumerate, no simple rule.
Difficulty (number of errors made): Type I < II < III ~ IV ~ V < VI
For n bits there are 2n binary strings 0011…01; how complex are the rules
(logical categories) that human/animal brains still can learn?
Canonical dynamics.
What happens in the brain during category learning?
Complex neurodynamics <=> simplest, canonical dynamics.
For all logical functions one may write corresponding equations.
For XOR (type II problems) equations are:
1 2
2
2 2
V  x, y, z   3 xyz   x  y  z 
4
V
x -3 yz -  x 2  y 2  z 2  x
x
V
y -3 xz -  x 2  y 2  z 2  y
y
V
z -3 xy -  x 2  y 2  z 2  z
z
Corresponding feature space for relevant
dimensions A, B
Inverse based rates.
Relative frequencies (base rates) of categories are used
for classification: if C is 3 times as coomn as R, and C is
associated with (PC, I) symptoms then PC => C, I => C.
Predictions contrary to the base: inverse base rate
effects (Medin, Edelson 1988).
Although PC + I + PR => C (60%)
PC + PR => R (60%)
Basins of attractors - neurodynamics;
PDFs in P-space {C, R, I, PC, PR}.
Psychological interpretation (Kruschke 1996):
PR is attended to because it is a distinct
symptom, although PC is more common.
PR + PC activation leads more frequently to R
because the basin of attractor for R is deeper.
Feature Space Mapping.
FSM (Duch 1994) - neurofuzzy system for modeling PDFs using separable
transfer (membership) functions.
Categorization (classification), extraction of logical rules, decision support.
Set up (fuzzy) facts explicitly as dense regions in the feature space;
Initialize by clusterization - creates rough PDF landscape.
Train by tuning adaptive parameters P;
novelty criteria allow for creation of new nodes as required.
Self-organization of G(X;P) = prototypes of objects in the feature space.
g p ( X; P )   g p ,i  xi ; Pi p 
N
p
i 1
F ( X; P )  W p g p  X; P p 
n
p 1
Recognition: find local maximum of
the F(X;P) function.
Dynamic approach.
Static model - responsible for immediate, memory-based behavior.
Local maxima of PDF - potential activations of the long-term memory.
Working memory, content of mind - currently active objects.
Masking: the circle exposed for 30
ms is seen, but not if ring follows.
Mind state - in attractor, near O1, active object, it has momentum and
inertia. External stimulus pushes the mind state towards O2.
A masking stimulus O3 close to O2 blocks activation of O2; no conscious
recall of the small disk is noted; priming lowers inertia.
Platonic mind model.
Feature detectors/effectors: topographic maps.
Objects in long-term memory (parietal, temporal, frontal): local P-spaces.
Mind space (working memory, prefrontal, parietal): construction of mind
space features/objects using attentional mechanisms.
Language of thought.
Precise language, replacing folk psychology,
reducible to neurodynamics.
Mind state dynamics - gradient dynamics in mind
space, „sticking” to PDF maxima, for example:
S (0)  X inp ;


S (t )    S M ( S ; t ) 1  g  M  S ; t     (t )
where g(x) controls the „sticking” and h(t) is a
noise + external forces term.
Mind state has inertia and momentum;
transition prob. between mind objects should be
fitted to transition prob. between corresponding
attractors of neurodynamics (QM fromalism).
Primary mind objects - from sensory data.
Secondary mind objects - abstract categories.
Intuition
Intuition is a concept difficult to grasp, but commonly believed to play
important role in business and other decision making; „knowing
without being able to explain how we know”.
Sinclair Ashkanasy (2005): intuition is a „non-sequential information-processing
mode, which comprises both cognitive and affective elements and results in direct
knowing without any use of conscious reasoning”.
First tests of intuition were introduced by Wescott (1961), now 3 tests are used,
Rational-Experiential Inventory (REI), Myers-Briggs Type Inventory (MBTI) and
Accumulated Clues Task (ACT).
Different intuition measures are not correlated, showing problems in constructing
theoretical concept of intuition. Significant correlations were found between REI
intuition scale and some measures of creativity.
Intuition in chess has been studied in details (Newell, Simon 1975).
Intuition may result from implicit learning of complex similarity-based evaluation
that are difficult to express in symbolic (logical) way.
Intuitive thinking
Question in qualitative physics (PDP book):
if R2 increases, R1 and Vt are constant, what
will happen with current and V1, V2 ?
Learning from partial observations:
Ohm’s law V=I×R; Kirhoff’s V=V1+V2.
Geometric representation of facts:
+ increasing, 0 constant, - decreasing.
True (I-,V-,R0), (I+,V+,R0), false (I+,V-,R0).
5 laws: 3 Ohm’s 2 Kirhoff’s laws.
All laws A=B+C, A=B×C , A-1=B-1+C-1, have
identical geometric interpretation!
13 true, 14 false facts; simple P-space, but
complex neurodynamics.
Intuitive reasoning
5 laws are simultaneously fulfilled, all have the same representation:
5
F (Vt , R, I ,V1 ,V2 , R1 , R2 )   Fi ( Ai , Bi , Ci )
i 1
Question: If R2=+, R1=0 and V =0, what can be said about I, V1, V2 ?
Find missing value giving F(V=0, R, I,V1, V2, R1=0, R2=+) >0
Assume that one of the variable takes value X = +, is it possible?
Not if F(V=0, R, I,V1, V2, R1=0, R2=+) =0, i.e. one law is not fulfilled.
If nothing is known 111 consistent combinations out of 2187 (5%) exist.
Intuitive reasoning, no manipulation of
symbols; heuristics: select variable
giving unique answer.
Soft constraints or semi-quantitative =>
small |F(X)| values.
Mental models
Kenneth Craik, 1943 book “The Nature of
Explanation”, G-H Luquet attributed mental
models to children in 1927.
P. Johnson-Laird, 1983 book and papers.
Imagination: mental rotation, time ~ angle, about 60o/sec.
Internal models of relations between objects, hypothesized to play a major role
in cognition and decision-making.
AI: direct representations are very useful, direct in some aspects only!
Reasoning: imaging relations, “seeing” mental picture, semantic?
Systematic fallacies: a sort of cognitive illusions.
• If the test is to continue then the turbine must be rotating fast enough to
generate emergency electricity.
• The turbine is not rotating fast enough to generate this electricity.
• What, if anything, follows? Chernobyl disaster …
If A=>B; then ~B => ~A, but only about 2/3 students answer correctly..
Reasoning & models
Easy reasoning A=>B, B=>C, so A=>C
• All mammals suck milk.
• Humans are mammals.
• => Humans suck milk.
... but almost no-one can draw conclusion from:
• All academics are scientist.
• No wise men is an academic.
• What can we say about wise men and scientists?
Surprisingly only ~10% of students get it right, all kinds of errors!
No simulations explaining why some mental models are difficult?
Creativity: non-schematic thinking?
Mental models summary
The mental model theory is an alternative to the view that
deduction depends on formal rules of inference.
1. MM represent explicitly what is true, but not what is false;
this may lead naive reasoner into systematic error.
2. Large number of complex models => poor performance.
3. Tendency to focus on a few possible models => erroneous conclusions and
irrational decisions.
Cognitive illusions are just like visual illusions.
M. Piattelli-Palmarini, Inevitable Illusions: How Mistakes of Reason Rule Our
Minds (1996)
R. Pohl, Cognitive Illusions: A Handbook on Fallacies and Biases in Thinking,
Judgement and Memory (2005)
Amazing, but mental models theory ignores everything we know about
learning in any form! How and why do we reason the way we do?
I’m innocent! My brain made me do it!
Świadomość?
Tak! Np. Pentti Haikonen (Nokia) robi symulacje modeli pamięci roboczej w
których informacja sensoryczna (oparta o konkurencyjny algorytm dostępu do
pamięci) przesyłana jest do obszarów skojarzeniowych.
Właściwe pytanie:
jak szczegółowy
powinien być model by
odtwarzać istotne
cechy działania
umysłu? Jeśli
podsystem językowy
będzie komentował
stan pamięci roboczej,
to jak będzie wyglądał
ciąg jego komentarzy?
Strumień świadomości: śliczny kolor, całkiem jak morza na Capri ...
Some connections
Geometric/dynamical ideas related to mind may be found in many fields:
Philosophy: „Mind as motion”, ed. R.F. Port, T. van Gelder (MIT Press 1995)
Linguistics: G. Fauconnier, Mental Spaces (Cambridge U.P. 1994).
Mental spaces and non-classical feature spaces.
J. Elman, Language as a dynamical system (San Diego, 1997).
Stream of thoughts, sentence as a trajectory in P-space.
Psycholinguistics: T. Landauer, S. Dumais, Latent Semantic Analysis Theory,
Psych. Rev. (1997) Semantic for 60 k words corpus requires about 300 dim.
Neuroscience: Anderson, van Essen (1994): Superior Colliculus maps as PDFs
AI: problem spaces - reasoning, problem solving, SOAR, ACT-R
Folk psychology: to put in mind, to have in mind, to keep in mind, to make up
one's mind, be of one mind ... (space).
Neurocognitive informatics
Use inspirations from the brain, derive practical algorithms!
My own attempts - see the webpage, Google: W. Duch
1. Mind as a shadow of neurodynamics: geometrical model of mind
processes, psychological spaces providing inner perspective as an
approximation to neurodynamics.
2. Global trajectories from EEG.
3. Intuition: learning from partial observations, solving problems without
explicit reasoning (and combinatorial complexity) in an intuitive way.
4. Neurocognitive linguistics: how to find neural pathways in the brain.
5. Creativity & word games.
6. New model of neurons that go beyond threshold logic.
Duch W, Intuition, Insight, Imagination and Creativity,
IEEE Computational Intelligence Magazine 2(3), August 2007, pp. 40-52
Conclusions
A unified paradigm for cognitive science – simplified neurodynamics?
Relations between different levels of modeling are important.
Simplified dynamics in psychological spaces provides low-dimensional
representations of mind events => geometrical theory of mind.
Recurrent neural network, reservoir computing => psychological spaces.
Useful technical/psychological inspirations and applications, including
understanding of intuition, language, creativity and other higher functions.
Many open questions:
High-dimensional P-spaces with Finsler geometry needed for visualization of
the mind events - will the model be understandable?
Mathematical characterization of P-spaces.
Challenge: neurodynamical model => P-spaces for monkey categorization.
Large-scale simulations of models of mind are missing but ... hierarchical
approach: networks of networks in simulated environment, is coming.
At the end of the road: physics-like theory of events in mental spaces;
mind as the shadow of neurodynamics.
Conference Series
Enactivism: A new paradigm? From neurophenomenology
and social/evolutionary robotics to distributed cognition.
Toruń, 06-09.10.2008.
http://www.kognitywistyka.net/~enp/
Interdisciplinary conference following:
„Embodied and Situated Cognition: from Phenomenology and
Neuroscience to Artificial Intelligence” (Toruń 2006)
„Self, Intersubjectivity & Social Neuroscience: from Mind and
Action to Society" (Toruń 2007)
Thank
you
for
lending
your
ears
...
Google: W. Duch => Papers, Talks
Fly UP