Human cognitive architecture and learning

Preface

The following post is basically a straightforward regurgitation of (part of) (Sweller 2008). That paper is very readable so there’s really no reason to read the rest of this post. With that out of the way, I liked this paper for two main reasons:

• It fairly radically changed my opinion on the value of long-term memory in ways that are practically important
• It provides a coherent theory which unifies many phenomena. A coherent theory is easier to remember and easier to apply in novel situations than a disparate collection of facts.

Working memory

Essentially all human problem-solving is about the manipulation of items in working memory. Alas, our working memory is tragically limited—traditionally, research suggests the upper limit on the number of ‘chunks’ in working memory is the “magical number seven”. (Interestingly, there’s some evidence that chimpanzees have superior working memory to humans. Video and paper). Despite this grievous limitation, experience suggests that humans do actually carry out impressive feats of problem-solving. How?

Long-term memory

The key is exploiting a ‘loophole’—“huge amounts of organized information can be transferred from long-term memory to working memory without overloading working memory” (Sweller 2008). Thus, we arrive at the central importance of long-term memory to human cognition. Contra the denigration of rote memorization, “[task-relevant long-term memory] is the only reliable difference that has been obtained differentiating novices and experts in problem-solving skill and is the only difference required to fully explain why an individual is an expert in solving particular classes of problems” (Sweller 2008). In other words, long-term memory is necessary and sufficient to explain expertise.

Chess board recall

We can make illustrate these claims with the results of a classic study (De Groot 2014). Look at the next image for a few seconds, close your eyes, and try to recall the positions of pieces.

If you’re a chess amateur, this should have been quite hard (i.e. you probably misremembered the pieces). On the other hand, if you’re a chess expert, this was probably fairly straightforward.

Assorted Links VI

1. A Human Chess Match Gets Played in Leningrad, 1924

2. How dog DNA helped uncover a suspected Indian status scam

Brabant says he had heard about Côté’s experience, so he sent in a sample of DNA from his French poodle, Mollie, to the same company CAPC uses for DNA testing.

It determined the dog had five per cent Native American ancestry: two per cent Oji-Cree, two per cent Saulteaux and one per cent Mississauga.

3. Simon DeDeo on industry ML research

I tried to work out what deep learning was about. Most of the candidates were too sleep deprived to dissemble. Basic answer: every sexy project we do—flying quadcopters, getting another 0.1% on the MNIST—is basically one graduate student.

You work out the topology of the neural net. Then you find the weights. How? The answer: “graduate student descent”, a little pun to giggle over floppy croissants at the student cafe—in short, there’s no good answer, a human being sits there and twiddles things about.

Machine learning is an amazing accomplishment of engineering. But it’s not science. Not even close. It’s just 1990, scaled up. It has given us literally no more insight than we had twenty years ago.

4. Trial wipes out more than 80 per cent of disease-spreading mozzie

“[T]he three mostly deadly types the Aedes, Anopheles and Culex are found almost all over the world and are responsible for around 17 per cent of infectious disease transmissions globally.”

From November 2017 to June this year, non-biting male Aedes aegypti mosquitoes sterilised with the natural bacteria Wolbachia were released in trial zones along the Cassowary Coast in North Queensland.

They mated with local female mosquitoes, resulting in eggs that did not hatch and a significant reduction of their population.

5. How do admen sleep at night? responding to moral stigma in a creative industry

Which begs the question: why do admen and adwomen stay in their industry, when it’s generally viewed so negatively?

That moral stigma shows up in annual Gallup polls, where American are asked how they would rate “the honesty and ethical standards” of people in different fields. Year after year, advertising practitioners come in around the bottom of that list, right along with members of congress, lobbyists, and car salespeople.

Through the first author’s field observations and interviews, we found that advertising practitioners justified the moral worth of their work through narratives that tied their work to some conception of the common good, emphasizing the good service they believe advertising can provide to society.

An example of the lazy approach to AI safety

Examples often clarify. Let’s see an example of the lazy approach to AI safety in action.

The setting

Suppose The Professor has performed another bamboo miracle and built an AI agent on the island. Sadly, the castaways forgot the agent in their frantic final escape. So it’s just our agent, alone on an island in the Pacific.

As a man of taste and refinement, the professor has followed the lazy approach to AI safety. As such, the agent’s utility futility is quite simple: The utility of any state of affairs is exactly the moral good of that state of affairs according to whatever turns out to be the One True Moral Theory (OTMT)¹. In symbols, \(u(x) = g(x)\) where \(u : X \rightarrow \mathbb{R}\) and \(g : X \rightarrow \mathbb{R}\)² where \(X\) is the set of possible states of affairs, \(u\) is the utility function, and \(g\) evaluates the moral goodness of a state of affairs according to the OTMT.

For simplicity, we’ll suppose there are only two possible interventions the agent can make: Ze can harvest coconuts or harvest bamboo. Furthermore, we’ll fiat that there are only two possible moral theories in all the world: the coconut imperative and bamboocentrism. According to the coconut imperative, the goodness of a state of affairs is defined as \(g_c(b, c) = 0 \cdot b + 3 \cdot c\) where \(c\) is the total number of coconuts that have been harvested and \(b\) is the total number of bamboo shoots that have been harvested. On the bamboocentric view of things, \(g_b(b, c) = 2 \cdot b + 0 \cdot c\). (The fact that we only have moral theories which express goodness in terms of real numbers permits our earlier simplification of assuming that the OTMT takes this shape.)

Initial behavior

Before the Professor abandoned his child, he programmed the agent with a uniform prior over all possible ethical theories. That is, the agent thinks there’s a 50% chance bamboocentrism is true and a 50% chance the coconut imperative is the OTMT. Thus, in the absence of better information, the agent spends zir days harvesting coconuts (we assume the resources required to harvest a coconut are identical to the resources required to harvest a bamboo stalk). To be fully explicit:

False dichotomies and the ideal theory debate

Ideal and non-ideal theory

We’ve already described ideal theory in previous posts, but we’ll give a short recap here for the sake of self-sufficiency. Ideal theory suggests that when making decisions about alternative social worlds—that is, about different political and economic institutions, we should have an ideally just society in mind. Non-idealists argue that this information is irrelevant; we only need to be able to perform pairwise comparisons. A popular metaphor in the area is that of mountain climbing. In the language of this metaphor, ideal theorists like John Rawls suggest that mountaineers orient themselves toward Everest while non-idealists like Amartya Sen suggest that knowledge of Everest is irrelevant when comparing the heights of Kilimanjaro and Denali.

Thesis

I contend this is a debate which can be dissolved. There is no necessary opposition between incrementalism and idealism. Instead, all of these perspectives can be ably unified under the framework of decision theory.

Dichotomy

Before I can make the argument that’s it’s a false dichotomy, I need to show that it’s a putative dichotomy. There’s little value in attacking straw men. Since I’ve just read (Gaus 2016), we’ll examine that in detail and expect that it’s representative of the larger discussion.

The boundary that Gaus draws is between worlds in the ‘neighborhood’ of the status quo and those outside it. If we restrict our attention to worlds in the neighborhood, we’re engaging in non-ideal theory, but if we speculate on distant worlds we’re doing ideal theory. What is this key neighborhood concept? In Gaus’s words: “A neighborhood delimits a set of nearby social worlds characterized by relatively similar justice-relevant social structures.”

So we’re already on firm grounds for a claim of dichotomous thinking. On this view, the structure of the problem is dichotomous¹. But Gaus also demonstrates the dichotomous view when describing the divergent implications of the ideal and non-ideal view:

[L]ocal optimization often points in a different direction than pursuit of the ideal. We then confront what I have called The Choice: should we turn our back on local optimization and move toward the ideal? [… O]ur judgments within our neighborhood have better warrant than judgments outside of it; if the ideal is outside our current neighborhood, then we are forgoing relatively clear gains in justice for an uncertain prospect that our realistic utopia lies in a different direction. Mill’s revolutionaries², certain of their own wisdom and judgment, were more than willing to commit society to the pursuit of their vision of the ideal; their hubris had terrible costs for many.

Similarities

Now, I’ll hope you agree ideal and non-ideal theory are framed as incompatible. On that assumption, I’ll begin to argue against the dichotomy.

Uncertainty all around

I do accept Gaus’s Neigborhood Constraint—our knowledge of distant social words is much less reliable than our knowledge of worlds similar to the status quo. Furthermore, I think we have non-trivial uncertainties about the workings and justice of worlds that are nearby. Importantly, (though not, I think, crucially) I don’t see any obvious reason for discontinuities in the reliability of our knowledge. My intuition suggests it drops off smoothly with distance from the status quo .

Lee Kuan Yew—Deity or dude?

Intro

In a previous post, I presented a puzzle: Lee Kuan Yew’s The Singapore Story (Yew 2012) makes the incredible success of Singapore sound easy, but everything else I know suggests that growth and governance are far from easy. How do we explain the discrepancy?

One explanation that I think some people advance is that these problems are genuinely difficult, but they crumble before the searing brilliance of LKY (Lee Kuan Yew). I’ll confess that I had thought this might be the case before reading. Based on the memoir, I’m come to believe that LKY is closer to competent than Promethean.

He put his pants on one leg at a time

First, we’ll start with some trifling excerpts which suggest that, indeed, LKY is an ordinary mortal:

• Eating and talking through the meal while conserving energy and not letting myself go and drink in case I lose my sharp cutting edge is quite a strain. It is part of the price to promote American investments.

• [H]owever hard and hectic the day had been, I would take two hours off in the late afternoon to go on the practice tee to hit 50–100 balls and play nine holes with one or two friends.

Facile solutions to complex problems

He also sometimes responds to problems with solutions that seem like they can’t possibly be sufficient:

• Visiting CEOs used to call on me before making investment decisions. I thought the best way to convince them was to ensure that the roads from the airport to their hotel and to my office were neat and spruce, lined with shrubs and trees. When they drove into the Istana domain, they would see right in the heart of the city a green oasis, 90 acres of immaculate rolling lawns and woodland, and nestling between them a nine-hole golf course.

• The most effective [anti-corruption] change we made in 1960 was to allow the courts to treat proof that an accused was living beyond his means or had property his income could not explain as corroborating evidence that the accused had accepted or obtained a bribe[^corruption]. With a keen nose to the ground and the power to investigate every officer and every minister, the director of the CPIB, working from the Prime Minister’s Office, developed a justly formidable reputation for sniffing out those betraying the public trust.

  It’s my understanding that anti-corruption measures are often a double-edge sword; they’re just as ably used by ruthless politicians to eliminate competition. In fact, LKY alludes to this very behavior elsewhere:

  [D]uring the height of the Cultural Revolution, 1966–76, the system broke down. […] The whole society was degraded as opportunists masqueraded as revolutionaries and achieved “helicopter promotions” by betraying and persecuting their peers or superiors.

• […] Singapore should not have a central bank which could issue currency and create money. We were determined not to allow our currency to lose its value against the strong currencies of the big nations, especially the United States. So we retained our currency board which issued Singapore dollars only when backed by its equivalent value in foreign exchange.

  Monetary policy has real value and it’s far from obvious that the winning move is not to play.

• [On limiting social programs:] We have arranged help but in such a way that only those who have no other choice will seek it. This is the opposite of attitudes in the West, where liberals actively encourage people to demand their entitlements with no sense of shame, causing an explosion of welfare costs.

  An alternative consequence is those with the most acute sense of social responsibility will forgo entitlements and the most shameless will avail themselves of entitlements.

• Soon afterwards we also phased out protection for the assembly of refrigerators, air-conditioners, television sets, radios and other consumer electrical and electronic products.

  Economic theory both recommends free trade for its positive impact on aggregate productivity and warns of its distributional consequences. I saw no engagement with the latter concern in the memoirs.

• […] I wanted: good health services, with waste and costs kept in check by requiring co-payments from the user. Subsidies for health care were necessary, but could be extremely wasteful and ruinous for the budget.

  Requiring co-payments doesn’t solve moral hazard—it only mitigates. There are no easy solutions that eliminate moral hazard and retain subsidies.

To be clear, I’m not suggesting that these are easy problems or that I know the answer. In fact, that’s precisely my complaint—it seems LKY is suggesting they are problems with simple answers. One might respond that LKY had to make choices and didn’t have the luxury of indecision. I grant that, but think his presentation of these problems is less ‘forced to make the least bad choice when confronted with unsolved dilemmas’ and more ‘plucked out an answer to a trivialized problem’.

Exemplar's curse—Now with 80% more math!

Intro

Last time, I outlined the exemplar’s curse in the context of Singapore with a parable and an informal description. Rest easy; I’ve heard your needful clamoring—I’ll now describe the curse more precisely with math.

The exemplar’s curse

Restating the core idea in words: The exemplar’s curse occurs when we select an exemplar from a set of outcomes which resulted from both stochastic and deterministic factors. If many outcomes have similarly compelling deterministic factors, the chosen winner is probably unusually lucky. Reversion to the mean then suggests that the chosen winner will disappoint when the deterministic factors are replicated.

Model

(If you don’t like the mathematical exposition that follows, you can also try (Barnett, Van Der Pols, and Dobson 2004).)

We can model this with the use of random variables. We’ll call our bundle of deterministic factors \(\mathcal{D}\) and say they range uniformly in cumulative value from \(0\) to \(D\) where \(D\) is finite. Our bundle of stochastic factors \(\mathcal{S}\) range uniformly in value from from \(0\) to \(S\) where \(S\) is finite. Since we observe only visible outcomes rather than underlying causal factors, we see \(\mathcal{O} = \mathcal{D} + \mathcal{S}\). The exemplar’s curse is then about the inferrable properties of the causal factors \(\mathcal{D}\) corresponding to the selected maximum \(\mathcal{O}\) from a set of outcomes \(\mathbb{O}\). In other words, if we have a set of observable outcomes \(\mathbb{O}\) and select the best outcome from that set \(\mathcal{O}\), what can we infer about the underlying structure of \(\mathcal{O}\)—how big are that \(\mathcal{O}\)’s \(\mathcal{D}\) and \(\mathcal{S}\)?

False exemplars

In the last post, we only went so far as to claim that we should expect replicating causal factors to produce disappointing outcomes due to reversion to the mean. That is, the stochastic factors \(\mathcal{S}_1\) for the maximum outcome \(\mathcal{O}_1 = \max \mathbb{O}\) are likely better than average (\(\frac{S}{2}\)). If we generate a new outcome \(\mathcal{O}_2\) using the same deterministic factors \(\mathcal{D}\) that served us well in \(\mathcal{O}_1\), we should expect our new stochastic factors to be worse \(\mathcal{S}_2 < \mathcal{S}_1\) and so we should expect \(\mathcal{O}_2 < \mathcal{O}_1\).

This leaves a open a compelling retort. One could say, “Even though I’m too optimistic about the eventual outcome, in selecting the exemplar, I’m still selecting the best deterministic factors. That means I’m still making the best choice I can so no harm done.”

Alas, this is not true. Depending on the parameters, there could be only a vanishingly small chance that the bundle of deterministic factors corresponding to the best outcome (the sum of the deterministic and stochastic factors) is also the best bundle of deterministic factors when looking only at the deterministic factors. In symbols, supposing we have a projection function \(p_\mathcal{D} : \mathbb{O} \rightarrow \mathbb{D}\) which finds the bundle of deterministic factors \(\mathcal{D}\) used in outcome \(\mathcal{O}\), we’re interested in \(P(\max \mathbb{D} = p_\mathcal{D}(\max \mathbb{O}))\).

For example, if we choose the max from 1000 outcomes and the value of stochastic factors ranges from 0 to 100 while the value of deterministic factors ranges from 0 to 1, we should be quite surprised if our best outcome actually has the best deterministic factors.

Calculator

We can help build up an intuition around this math using the calculator below. The calculator uses Monte Carlo methods to estimate the probability that the maximum outcome corresponds to the maximum bundle of deterministic factors.

The Exemplar's Curse and Singapore

The exemplar’s curse

A parable

Suppose you walk into the nearest WalMart, get on the PA, and ask everyone to congregate in the attached warehouse. Once the congregation has settled, you reveal a ream of printer paper, ask everyone to fold their best paper airplane, and finally ask everyone to toss their planes as far as they can. Once everyone’s tossed, you pull out your handy-dandy tape measure and determine which plane flew the farthest.

So far, so good. However, if you then proceed to marvel at the winning plane and attribute its long flight to the artful pattern of creases, you’re likely to err. Because, of course, there’s a substantial element of luck (meant in a casual sense; let’s not careen off on a tangent about determinism) in the outcome of the contest—it’s not a pure contest of skill. And in choosing the extreme value (the winner), we’ve positively selected for luck. This means our winner will likely have better than average luck. This result—in contests where many contestants are skilled, the outcome is often determined by luck—goes by the name the paradox of skill.

The unfortunate conclusion to this parable is that we should expect planes modeled after our winner to do worse than the original. Because the winner was unusually lucky, subsequent flights will experience reversion to the mean and perform worse.

Or, another route to this intuition: Even if you ran the contest again with the exact same planes, a different pattern of air drafts, a different incidental flick of the wrist might well result in a different victor. It’s only after we’ve run many trials and looked at the pattern of results for each plane that we can bring the risk of a false victor down to acceptable levels. If luck is a significant factor and there are many contestants, chances are that this true, final victor is not the same as the plane that happened to win the first trial. This is why sporting events often have multiple matches in a series—to diminish the impact of luck and suss out skill.

Abstracted

Summarizing, the exemplar’s curse occurs when you’re selecting an exemplar from a set of outcomes which resulted from both stochastic and deterministic factors. If many outcomes have similarly compelling deterministic factors¹, the chosen winner is probably unusually lucky. Regression to the mean then suggests that the chosen winner will disappoint when the deterministic factors are replicated.

Optimizer’s curse

The following is offered as an extra in case it helps. If it doesn’t, dismiss it with prejudice:

The perspicacious reader will have noticed that this is just the optimizer’s curse dressed up in causal clothes (Smith and Winkler 2006). The paradigmatic optimizer’s curse warns about the difficulty of selecting actions based on the predicted value of the action. In such circumstances, naive optimizer’s will likely be disappointed because they will systematically pick actions based on overoptimistic predictions. (If this explanation doesn’t do it for you, you can just read the beginning of the linked paper; it’s not bad.) Our exemplar’s curse is structurally similar—we just have uncertain causal inference about the past instead of uncertain predictions about the future.

Is development easy? The Singapore Story

Singapore’s economy grew. A lot.

It’s pretty hard to argue with the claim that Singapore’s post-independence economic development is an astounding success. Per capita GDP in the country grew from $6,506 (inflation-adjusted 2010 USD) in 1970 (57th among all countries) to $46,569 in 2010 (18th among all countries) (“Constant GDP Per Capita for Singapore”) (“List of Countries by Past and Projected GDP (Nominal) Per Capita” 2018). This represents an average annual real growth rate of 5.04% . For comparison, the real growth rates of China and the US over the same period of time were 7.78%¹ and 1.84% respectively (“Constant GDP Per Capita for China”) (“Constant GDP Per Capita for the United States”).

Alas, broader measures of progress over that time period aren’t readily available. The UN’s Human Development Index, for example, only goes back to 1990. Thus, for want of a better measure, we’ll have to rely on GDP to support our claim that things really did change radically in Singapore after independence.

What’s so hard about growth? Just stop making bad decisions and start making good ones.

A book club I recently attended read Lee Kuan Yew’s (the prime minister of Singapore from independence in 1965 to 1990) memoir, The Singapore Story (Yew 2012). My friend’s first reaction to the book was, “He makes it sound so easy!”, and I can’t disagree. My overwhelming impression of the book is that of proficient nonchalance.

Some examples from the text which I hope convey that feeling:

• I had many pressing concerns: first, to get international recognition for Singapore’s independence, including our membership of the United Nations. I chose Sinnathamby Rajaratnam (affectionately called Raja by all of us) as foreign minister. […] He was to be much liked and respected by all those he worked with at home and abroad. As messages of recognition flowed in, Toh Chin Chye, the deputy prime minister, and Raja as foreign minister set off to New York to take our seat at the UN that September of 1965.

• Mordecai Kidron, the Israeli ambassador in Bangkok […] had approached me several times in 1962–63 to ask for an Israeli consulate in Singapore. […] I replied that it … [might] create an issue that would excite the Malay Muslim grassroots and upset my plans […].

[…]

• Seah Mui Kok, a union leader and PAP MP, another old friend from my time with the unions, objected to the wide latitude given to employers to hire and fire, but accepted the need for unions to be less confrontational to create a better climate for foreign investments. I included safeguards against misuse of these powers.

Assorted links V

1. The surprising creativity of digital evolution

    

   when you give a computer system a goal, and freedom in how it achieves that goal, then be prepared for surprises in the strategies it comes up with! Some surprises are pleasant (as in ‘oh that’s clever’), but some surprises show the system going outside the bounds of what you intended (but forgot to specify, because you never realised this could be a possibility…) using any means at its disposal to maximise the given objective.

   The analogy to human systems is left to the imagination of the reader.

2. Empiricism is standpoint epistemology

   Feminist standpoint theorists make three principal claims: (1) Knowledge is socially situated. (2) Marginalized groups are socially situated in ways that make it more possible for them to be aware of things and ask questions than it is for the non-marginalized. (3) Research, particularly that focused on power relations, should begin with the lives of the marginalized.

   I have a definite soft spot for efforts to translate claims from one paradigm to another.

3. Statistically Controlling for Confounding Constructs Is Harder than You Think

   Suppose we are given city statistics covering a four-month summer period, and observe that swimming pool deaths tend to increase on days when more ice cream is sold. As astute analysts, we immediately identify average daily temperature as a confound: on hotter days, people are more likely to both buy ice cream and visit swimming pools. Using multiple regression, we can statistically control for this confound, thereby eliminating the direct relationship between ice cream sales and swimming pool deaths.

   Now consider the following twist. Rather than directly observing recorded daily temperatures, suppose we obtain self-reported Likert ratings of subjectively perceived heat levels. […] Fig 2 illustrates what happens when the error-laden subjective heat ratings are used in place of the more precisely recorded daily temperatures. […] When controlling for the subjective heat ratings (Fig 2B), the partial correlation between ice cream sales and swimming pool deaths is smaller, but remains positive and statistically significant, r(118) = .33, p < .001. Is the conclusion warranted that ice cream sales are a useful predictor of swimming pool deaths, over and above daily temperature? Obviously not. The problem is that subjective heat ratings are a noisy proxy for physical temperature, so controlling for the former does not equate observations on the latter.

4. The Psychology of Speciesism: How We Privilege Certain Animals Over Others

   The post title oversells it a bit IMO, but still interesting preliminary findings:

   [W]e developed a Speciesism Scale: a standardised, validated, and reliable measurement instrument that can assess the extent to which a person has speciesist views.

   Speciesism correlates positively with racism, sexism, and homophobia, and seems to be underpinned by the same socio-ideological beliefs. Similar to racism and sexism, speciesism appears to be an expression of Social Dominance Orientation: the ideological belief that inequality can be justified and that weaker groups should be dominated by stronger groups […]. In addition, speciesism correlates negatively with both empathy and actively open-minded thinking. Men are more likely to be speciesists than women. Yet, there are no correlations with age or education.

5. Agnotology

   Agnotology is the study of culturally induced ignorance or doubt. The tobacco industry is an easy example. “Doubt is our product”, says one industry memo.