class: bottom, inverse background-image: url(images/school_of_athens.jpeg) background-size: cover ## A Network Approach to the Development of Intelligence #### Alexander Savi, 14 December 2017 ??? * Welcome everyone * In this talk I will shortly discuss efforts to model intelligence and its development * The painting you're looking at is the [School of Athens](http://www.museivaticani.va/content/museivaticani/en/collezioni/musei/stanze-di-raffaello/stanza-della-segnatura/scuola-di-atene.html), where you can see philosophers like Plato teach their pupils --- class: bottom, inverse background-image: url(images/uva.jpg) background-size: cover <font color="#56B4E9">Alexander Savi</font><br> PhD candidate at University of Amsterdam<br> Department of Psychological Methods <font color="#E69F00">Supervised by</font><br> Gunter Maris<br> Han van der Maas <font color="#D55E00">Involved with</font><br> Experimental interventions in online learning<br> Formal models for the development of intelligence ??? * For all of you that don't know me * Gunter is currently at ACT Next, the think-tank of a large educational testing company in the US * __Commonly known as A/B tests__, will present a poster on work in that field later today * This talk is about the development of intelligence * First an important __disclaimer__: * The talk will be on a __very high conceptual level__ * __Two reasons__ * 1. I like that level * 2. We haven't work out many of the details, it really is work in progress * __No math involved, but will discuss quite a few models__ * I want to ask you to try to get a conceptual understanding of what we aim to do --- 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) ] ??? * If we discuss intelligence, there's one main finding 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 might we look? * 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: * An __interisting mechanism but simplistic__ * For one, __no explicit roles for genes and the environment__ * And __no actual growth dynamics__ (everything is in there from the start) --- .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. * Yet again, __no actual growth mechanism__ * Now let me take you to __our first step in building a network approach__ * We will __use the multiplier effect to grow a network__ * Let me __explain this through an urn example__ --- background-image: url(images/polya.jpg) background-size: cover .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 --- 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;"/> ] ??? * 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 <img src="images/matthew.png" style="height: 500px;"/> ??? * 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 --- class: center, middle <img src="images/compensation.png" style="height: 500px;"/> ??? * 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 * This is roughly where the project is right now * I want you to dream with me about what we would want from a developmental network model of intelligence --- class: middle .pull-left[ ## Random network ## Nodes represent items ] .pull-right[ ## Hierarchy ## Growth & decay ] ??? * 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__ --- background-image: url(images/fk_network.png) background-size: cover ??? * Here's a network that does all of that * Preferably in a formal framework * Maarten Marsman received a Veni for seeking formal frameworks for growth mechanisms * Erdos-Renyi versus Fortuyn-Kastelein: random versus preference for clusters (among other things) * Need to find growth mechanisms that retain properties of the model --- class: bottom, inverse background-image: url(images/fk_network.png) background-size: cover # Thank you .pull-left[ More information Alexander Savi<br> University of Amsterdam<br> Psychological Methods Dept.<br> Contact: [o.a.savi@gmail.com](mailto:o.a.savi@gmail.com)<br> Slides: [alexandersavi.nl/talks](http://www.alexandersavi.nl/talks/)<br> ] .pull-right[ Collaborators & contributors Han van der Maas<br> Gunter Maris<br> Maarten Marsman<br> Abe Hofman<br> Frederik Coomans<br> ]