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. • 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: mind-body 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.

Kwas glutaminowy otwiera kanały Na+, pobudzająco, GABA działa na kanały Cl- hamując pobudzanie. Neurony pobudzające i hamujące

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 centrum-otoczka (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 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. Prezentacja dwóch obiektów, uwzględnia LGN, V1, V2, V4/IT, V5/MT

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 (genSCN2A): 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 lobehas 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 occipitotemporalsulcus 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 win 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 wis 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 synapticconnections => 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. chess board domino n 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. Insight <= right hemisphere, meta-level representations without phonological (symbolic) components ... counting? o m black white i d o 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 Science2005. 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 …

Phonological filter • 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 argumiadaćargumialenie 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.comcreativery (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 nameportravel (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: 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=Bdepends on the positions X(t+dt) and derivative dX(t)/dt. 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: 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. Recognition: find local maximum of the F(X;P) function.

Mind from brain: physics & neuroscience