class: bottom, inverse background-image: url(images/school_of_athens.jpeg) background-size: cover ## A Network Theory of Developmental Intelligence #### Alexander Savi, 10 July 2018 ??? * In the next twelve minutes I will introduce a new formal model for a developmental and idiographic intelligence. * Let me start with a spoiler. --- class: center, top, inverse background-image: url(images/background.png) background-size: cover <img src="images/fk_han.gif" style="height: 550px;"/> The wiring of facts and procedures, or knowledge and skills, during development. ??? * We use a network model to conceptualize intelligence as the wiring ... * These nodes represent knowledge and skills, and the edges their connections. * Colors / domains * Filled nodes / correct facts or knowledges / adequacies * Represents a single person: idiographic --- class: middle <img src="images/positivemanifold.png" style="height: 250px;"/> .footnote[ [Spearman, 1904](https://archive.org/details/jstor-1412107); [Carrol, 1993](http://www.cambridge.org/us/academic/subjects/psychology/cognition/human-cognitive-abilities-survey-factor-analytic-studies?format=PB&isbn=9780521387125) ] ??? * But that's not where today's story starts * If we discuss intelligence, there's one phenomenon that must be addressed * Reflected in this table, published by Spearman in 1904 * Correlations between different scholastic / cognitive abilities * You'll see high correlations between languages --> __hierarchy__ * But most important: you should observe is that __all correlations are positive__ * This is a phenomenon that we call the __positive manifold__ * Stress it is __not a spurious finding__, John B. Carroll (former president psychometric society) found it in 461 datasets --- class: center <img src="images/factor.png" style="height: 400px;"/> .footnote[ [Spearman, 1927](https://archive.org/details/abilitiesofman031969mbp); _g_ = general factor; x<sub>i</sub> = score on a cognitive test ] ??? * The most famous explanation is the formative _g_ factor model of general intelligence * One single factor / common cause that influences all mental tasks, hence their positive correlations * The question __'what is g'__ remains a mystery as of today * It's certainly not (only) genes * As of today, __the most popular model of intelligence__ actually is a factor model * And we asked ourselves: how does development fit into a theory of intelligence --- class: center, middle ## "[o]ne of the most intractable problems in evaluating the relationship between education and _g_ is the problem of development and age. As near as we can tell, _g_ theories have failed to provide any account of development across the lifespan." .footnote[ [Ackerman & Lohman, 2003](https://doi.org/10.1016/B978-008043793-4/50052-0) ] ??? * So _g_ theory is not where we should be looking * Where should we? * There are __2 important contemporary explanations__ of the positive manifold --- .pull-left[ <img src="images/mutualism.png" style="height: 400px;"/> ] .footnote[ [van der Maas et al.](https://dx.doi.org/10.1037/0033-295x.113.4.842); x<sub>i</sub> = cognitive process ] ??? * First is van der Maas' __mutualism model__ * As you can see, this is a __network model__ * __Explain model__ * Two things to notice * 1. "The __positive manifold emerges purely by positive beneficial interactions__ between cognitive processes during development" * 2. __No single underlying _g_ factor__ * ? The processes are not further specified, but assumed to be measurable by tests -- .pull-right[ <br><font size="5">"Reciprocal causal relations are well known in the psychological literature. For instance, better short-term memory helps to develop better cognitive strategies, and better strategies make it possible to increase the efficiency of short-term memory. Similar examples are the relations between cognition and meta-cognition, between action and perception, and between performance and motivation."</font> ] ??? * The authors defend their model by explaining the following: * __Interesting mechanism but simplistic__ * __No clear roles for genes and the environment__: in K factor * __No actual growth dynamics__ (everything is in there from the start): unclear what drives the actual development / reciprocal relations --- .pull-left[ <img src="images/multiplier.png" style="height: 400px;"/> ] .footnote[ .pull-left[ <br>[Dickens & Flynn, 2001](https://dx.doi.org/10.1037/0033-295x.108.2.346); G = genetic endowment, m<sub>i</sub> = intelligence measure at moment i, e = environment at moment i ] ] ??? * The second is Dickens and Flynn's __multiplier effect model__ * They explicitly model genes and the environment (__gene-environment interaction__ model) * __Explain model__ * __Positive manifold emerges__ from the reciprocal relations of IQ with the environment * This multiplier effect is a very powerful idea, beautifully described by Stanovich * ? Self-reinforcement, state-dependence, cumulative advantage, preferential attachment * ? Explain heritability increase -- .pull-right[ <br><font size="5">"The very children who are reading well and who have good vocabularies will read more, learn more word meanings, and hence read even better. Children with inadequate vocabularies – who read slowly and without enjoyment – read less, and as a result have slower development of vocabulary knowledge, which inhibits further growth in reading ability."</font> ] .footnote[ .pull-left[ [Dickens & Flynn, 2001](https://dx.doi.org/10.1037/0033-295x.108.2.346); G = genetic endowment, m<sub>i</sub> = intelligence measure at moment i, e = environment at moment i ] .pull-right[ [Stanovich, 1986](http://www.jstor.org/stable/747612) ] ] ??? * This mechanism can be generalized: * The children who are reading well __will also receive better education__, __make friends with people__ that also have a higher ability, etc. * Now let me show you a powerful mechanisms for this multiplier effect, that does not rely on genetical differences. --- class: center, middle background-image: url(images/background.png) background-size: cover .pull-left[ <img src="images/polya_net_0.png" style="width: 300px;"/> <img src="images/background.png" style="width: 300px;"/> ] .pull-right[ <img src="images/background.png" style="width: 300px;"/> <img src="images/background.png" style="width: 300px;"/> ] .footnote[ [Eggenberger & Pólya, 1923](https://dx.doi.org/10.1002/zamm.19230030407) ] ??? * This model is known as __Polya's urn__ * Assume the urn represents a person, let's call her Ann * Then the balls represent her cognitive abilities: blue for cognitive abilities and yellow for cognitive disabilities * Now we use one very simple growth mechanism: pick a random ball and put 2 of the same color back * Another way of looking at this is that: * The urn is Ann's IQ, which is at timepoint 0 fully determined by her __genetic endowment__ * The growth mechanism is the __environment__ * Let's take an example: * E.g., table tennis example backhand versus forehand * Now do this in a network framework, let's see if it works live * Balls of the same color get connected * We start with an initial network, and at each trial we add a node to it * We attach it to a random node in the network and give it the color of that node --- class: center, middle background-image: url(images/background.png) background-size: cover .pull-left[ <img src="images/polya_net_0.png" style="width: 300px;"/> <img src="images/polya_net_1.png" style="width: 300px;"/> ] .pull-right[ <img src="images/polya_net_2.png" style="width: 300px;"/> <img src="images/polya_net_3.png" style="width: 300px;"/> ] ??? * As you can see the proportion of blue balls, or cognitive ability as we called it, starts to vary greatly --- class: center, middle .pull-left[ <img src="images/matthew.png"/> ] .pull-right[ <img src="images/compensation.png"/> ] ??? * If we observe many copies of Ann on the long run, this is what we see * __Explain figure__ * p(blue) is our measure of cognitive ability * What we see is also called the __Matthew effect__: poor get poorer and rich get richer * Widening gap (increasing achievement gap) * Observed in many complex systems: citations, internet, ..., and also in IQ * Polya works with __identical genetic endowment__ * For the moment, we have only consider the influence of the environment on IQ * If we would model the full multiplier effect: the urn rule would dependent on what's in the urn * Even stronger effect! * But, Matthew effect is not undisputed! * A closing gap (decreasing achievement gap), called the compensation effect, is also observed * To obtain this, I gave all Anns formal education * Rather than adding two balls, I added three balls with p=.5 * __Let me pause for a moment__ * Our simple toy model of a multiplier effect just explained __two of the most important phenomena in the development of intelligence__ (Matthew and compensation effect) * These phenomena were previously unexplained * We know that this type of mechanism can explain the positive manifold --- class: middle .pull-left[ ## Idiographic theory ## Nodes represent items ## Positive manifold ] .pull-right[ ## Hierarchical structure ## Matthew & compensation ## Growth & decline ] .footnote[ [Molenaar, 2009](https://doi.org/10.1207/s15366359mea0204_1); A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever ] ??? * This is what we're working on * Each person is described as a network * Nodes are on the level of items * Intelligence is hierarchical, clusters may represent that * And we want both growth and decay * __Preferential attachment__ is a multiplier-like mechanism for networks * But may also include forgetting, by removing nodes or edges * __Show wiring cognition 2.0 alpha__ --- ## ⚔ Idiographic theory .pull-left[ <img src="images/fk.png"/> <img src="images/nodes.png"/> <img src="images/edges.png"/> ] .pull-right[ <img src="images/connie.png" /> ] .footnote[ <a href="http://dx.doi.org/10.1016/0031-8914(72)90045-6">Fortuin & Kasteleyn, 1972</a> ] ??? * Nodes may represent skills, knowledge, or items, such as `\(9\times9=81\)` (an adequacy) or `\(9\times9=18\)` (an inadequacy) * Edges represent relations between skills, knowledge, or items --- ## ⚔ Positive manifold & hierarchical structure .pull-left[ <img src="images/communities.png"/> <img src="images/positivemanifold.png"/> ] .pull-right[ <img src="images/fk_heatmap.png" /> ] ??? * Model we use is the Fortuin Kasteleyn model * Describes the distribution of the nodes and edges (__omega__) * Gives us a random network, nodes and edges are allowed to differ across individuals * Satisfies our requirement of idiography * The beauty of the model is that it, by definition, satisfies the positive manifold * ? θ is a parameter of the model that describes the probability that any two skills become connected * ? δ(a, b) is known as Kronecker’s delta (1 if a=b) (0 if a!=b) * ? Erdos-Renyi versus Fortuyn-Kastelein: random versus preference for clusters (among other things) * To get the hierarchical structure, we add communities of nodes * Within-community connections have a higher probability than between-community connections --- ## ⚔ Increasing pos.man. & Matthew effect / bifurcation .pull-left[ <img src="images/fk_heatmaps.png"/> ] .pull-right[ <img src="images/fk_matthew_all_160.png" style="height: 225px;"/> <img src="images/fk_bifurc_all_300.png" style="height: 225px;"/> ] --- ## Growth & decline mechanisms ### (Conditional) developmental phenomena * Matthew / compensation effect * Age differentiation / dedifferentiation * ... ### Developmental mechanisms * Preferential attachment * Multiplier effect * ... --- class: center, top, inverse background-image: url(images/background.png) background-size: cover <img src="images/fk_han.gif" style="height: 550px;"/> The wiring of facts and procedures, or knowledge and skills, during development. ??? * An example of a growing network * Including multiple domains / communities * And forgetting --- class: bottom, inverse background-image: url(images/fk_network.png) background-size: cover # Thank you [Gunter Maris](mailto:Gunter.Maris@act.org), ACTNext<br> [Maarten Marsman](mailto:M.Marsman@uva.nl), University of Amsterdam<br> [Han van der Maas](mailto:H.L.J.vanderMaas@uva.nl), University of Amsterdam<br> [Alexander Savi](mailto:O.A.Savi@gmail.com), University of Amsterdam Preprint available soon @ [alexandersavi.nl/publications](https://www.alexandersavi.nl/publications/)<br> Slides available now @ [alexandersavi.nl/talks](http://www.alexandersavi.nl/talks/)