## Probabilities Small Enough To Ignore: An attack on Pascal's Mugging

19 16 September 2015 10:45AM

Summary: the problem with Pascal's Mugging arguments is that, intuitively, some probabilities are just too small to care about. There might be a principled reason for ignoring some probabilities, namely that they violate an implicit assumption behind expected utility theory. This suggests a possible approach for formally defining a "probability small enough to ignore", though there's still a bit of arbitrariness in it.

This post is about finding a way to resolve the paradox inherent in Pascal's Mugging. Note that I'm not talking about the bastardized version of Pascal's Mugging that's gotten popular of late, where it's used to refer to any argument involving low probabilities and huge stakes (e.g. low chance of thwarting unsafe AI vs. astronomical stakes). Neither am I talking specifically about the "mugging" illustration, where a "mugger" shows up to threaten you.

Rather I'm talking about the general decision-theoretic problem, where it makes no difference how low of a probability you put on some deal paying off, because one can always choose a humongous enough payoff to make "make this deal" be the dominating option. This is a problem that needs to be solved in order to build e.g. an AI system that uses expected utility and will behave in a reasonable manner.

Intuition: how Pascal's Mugging breaks implicit assumptions in expected utility theory

Intuitively, the problem with Pascal's Mugging type arguments is that some probabilities are just too low to care about. And we need a way to look at just the probability part component in the expected utility calculation and ignore the utility component, since the core of PM is that the utility can always be arbitrarily increased to overwhelm the low probability.

Let's look at the concept of expected utility a bit. If you have a 10% chance of getting a dollar each time when you make a deal, and this has an expected value of 0.1, then this is just a different way of saying that if you took the deal ten times, then you would on average have 1 dollar at the end of that deal.

More generally, it means that if you had the opportunity to make ten different deals that all had the same expected value, then after making all of those, you would on average end up with one dollar. This is the justification for why it makes sense to follow expected value even for unique non-repeating events: because even if that particular event wouldn't repeat, if your general strategy is to accept other bets with the same EV, then you will end up with the same outcome as if you'd taken the same repeating bet many times. And even though you only get the dollar after ten deals on average, if you repeat the trials sufficiently many times, your probability of having the average payout will approach one.

Now consider a Pascal's Mugging scenario. Say someone offers to create 10^100 happy lives in exchange for something, and you assign them a 0.000000000000000000001 probability to them being capable and willing to carry through their promise. Naively, this has an overwhelmingly positive expected value.

But is it really a beneficial trade? Suppose that you could make one deal like this per second, and you expect to live for 60 more years, for about 1,9 billion trades in total. Then, there would be a probability of 0,999999999998 that the deal would never once have paid off for you. Which suggests that the EU calculation's implicit assumption - that you can repeat this often enough for the utility to converge to the expected value - would be violated.

Our first attempt

This suggests an initial way of defining a "probability small enough to be ignored":

1. Define a "probability small enough to be ignored" (PSET, or by slight rearranging of letters, PEST) such that, over your lifetime, the expected times that the event happens will be less than one.
2. Ignore deals where the probability component of the EU calculation involves a PEST.

Looking at the first attempt in detail

To calculate PEST, we need to know how often we might be offered a deal with such a probability. E.g. a 10% chance for something might be a PEST if we only lived for a short enough time that we could make a deal with a 10% chance once. So, a more precise definition of a PEST might be that it's a probability such that

(amount of deals that you can make in your life that have this probability) * (PEST) < 1

But defining "one" as the minimum times we should expect the event to happen for the probability to not be a PEST feels a little arbitrary. Intuitively, it feels like the threshold should depend on our degree of risk aversion: maybe if we're risk averse, we want to reduce the expected amount of times something happens during our lives to (say) 0,001 before we're ready to ignore it. But part of our motivation was that we wanted a way to ignore the utility part of the calculation: bringing in our degree of risk aversion seems like it might introduce the utility again.

What if redefined risk aversion/neutrality/preference (at least in this context) as how low one would be willing to let the "expected amount of times this might happen" fall before considering a probability a PEST?

Let's use this idea to define an Expected Lifetime Utility:

ELU(S,L,R) = the ELU of a strategy S over a lifetime L is the expected utility you would get if you could make L deals in your life, and were only willing to accept deals with a minimum probability P of at least S, taking into account your risk aversion R and assuming that each deal will pay off approximately P*L times.

ELU example

Suppose that we a have a world where we can take three kinds of actions.

- Action A takes 1 unit of time and has an expected utility of 2 and probability 1/3 of paying off on any one occasion.
- Action B takes 3 units of time and has an expected utility of 10^(Graham's number) and probability 1/100000000000000 of paying off one any one occasion.
- Action C takes 5 units of time and has an expected utility of 20 and probability 1/100 of paying off on an one occasion.

Assuming that the world's lifetime is fixed at L = 1000 and R = 1:

ELU("always choose A"): we expect A to pay off on ((1000 / 1) * 1/3) = 333 individual occasions, so with R = 1, we deem it acceptable to consider the utility of A. The ELU of this strategy becomes (1000 / 1) * 2 = 2000.

ELU("always choose B"): we expect B to pay off on ((1000 / 3) * 1/100000000000000) = 0.00000000000333 occasions, so with R = 1, we consider the expected utility of B to be 0. The ELU of this strategy thus becomes ((1000 / 3) * 0) = 0.

ELU("always choose C"): we expect C to pay off on ((1000 / 5) * 1/100) = 2 individual occasions, so with R = 1, we consider the expected utility of C to be ((1000 / 5) * 20) = 4000.

Thus, "always choose C" is the best strategy.

Defining R

Is R something totally arbitrary, or can we determine some more objective criteria for it?

Here's where I'm stuck. Thoughts are welcome. I do know that while setting R = 1 was a convenient example, it's most likely too high, because it would suggest things like not using seat belts.

General thoughts on this approach

An interesting thing about this approach is that the threshold for a PEST becomes dependent on one's expected lifetime. This is surprising at first, but actually makes some intuitive sense. If you're living in a dangerous environment where you might be killed anytime soon, you won't be very interested in speculative low-probability options; rather you want to focus on making sure you survive now. Whereas if you live in a modern-day Western society, you may be willing to invest some amount of effort in weird low-probability high-payoff deals, like cryonics.

On the other hand, whereas investing in that low-probability, high-utility option might not be good for you individually, it could still be a good evolutionary strategy for your genes. You yourself might be very likely to die, but someone else carrying the risk-taking genes might hit big and be very successful in spreading their genes. So it seems like our definition of L, lifetime length, should vary based on what we want: are we looking to implement this strategy just in ourselves, our whole species, or something else? Exactly what are we maximizing over?

## [link] FLI's recommended project grants for AI safety research announced

17 01 July 2015 03:27PM

http://futureoflife.org/misc/2015awardees

You may recognize several familiar names there, such as Paul Christiano, Benja Fallenstein, Katja Grace, Nick Bostrom, Anna Salamon, Jacob Steinhardt, Stuart Russell... and me. (the \$20,000 for my project was the smallest grant that they gave out, but hey, I'm definitely not complaining. ^^)

15 25 June 2015 12:06PM

Summary: Utilitarianism is often ill-defined by supporters and critics alike, preference utilitarianism even more so. I briefly examine some of the axes of utilitarianism common to all popular forms, then look at some axes unique but essential to preference utilitarianism, which seem to have received little to no discussion – at least not this side of a paywall. This way I hope to clarify future discussions between hedonistic and preference utilitarians and perhaps to clarify things for their critics too, though I’m aiming the discussion primarily at utilitarians and utilitarian-sympathisers.

http://valence-utilitarianism.com/?p=8

I like this essay particularly for the way it breaks down different forms of utilitarianism to various axes, which have rarely been discussed on LW much.

For utilitarianism in general:

Many of these axes are well discussed, pertinent to almost any form of utilitarianism, and at least reasonably well understood, and I don’t propose to discuss them here beyond highlighting their salience. These include but probably aren’t restricted to the following:

• What is utility? (for the sake of easy reference, I’ll give each axis a simple title – for this, the utility axis); eg happiness, fulfilled preferences, beauty, information(PDF)
• How drastically are we trying to adjust it?, aka what if any is the criterion for ‘right’ness? (sufficiency axis); eg satisficing, maximising[2], scalar
• How do we balance tradeoffs between positive and negative utility? (weighting axis); eg, negative, negative-leaning, positive (as in fully discounting negative utility – I don’t think anyone actually holds this), ‘middling’ ie ‘normal’ (often called positive, but it would benefit from a distinct adjective)
• What’s our primary mentality toward it? (mentality axis); eg act, rule, two-level, global
• How do we deal with changing populations? (population axis); eg average, total
• To what extent do we discount future utility? (discounting axis); eg zero discount, >0 discount
• How do we pinpoint the net zero utility point? (balancing axis); eg Tännsjö’s test, experience tradeoffs
• What is a utilon? (utilon axis) [3] – I don’t know of any examples of serious discussion on this (other than generic dismissals of the question), but it’s ultimately a question utilitarians will need to answer if they wish to formalise their system.

For preference utilitarianism in particular:

Here then, are the six most salient dependent axes of preference utilitarianism, ie those that describe what could count as utility for PUs. I’ll refer to the poles on each axis as (axis)0 and (axis)1, where any intermediate view will be (axis)X. We can then formally refer to subtypes, and also exclude them, eg ~(F0)R1PU, or ~(F0 v R1)PU etc, or represent a range, eg C0..XPU.

How do we process misinformed preferences? (information axis F)

(F0 no adjustment / F1 adjust to what it would have been had the person been fully informed / FX somewhere in between)

How do we process irrational preferences? (rationality axis R)

(R0 no adjustment / R1 adjust to what it would have been had the person been fully rational / RX somewhere in between)

How do we process malformed preferences? (malformation axes M)

(M0 Ignore them / MF1 adjust to fully informed / MFR1 adjust to fully informed and rational (shorthand for MF1R1) / MFxRx adjust to somewhere in between)

How long is a preference relevant? (duration axis D)

(D0 During its expression only / DF1 During and future / DPF1 During, future and past (shorthand for  DP1F1) / DPxFx Somewhere in between)

What constitutes a preference? (constitution axis C)

(C0 Phenomenal experience only / C1 Behaviour only / CX A combination of the two)

What resolves a preference? (resolution axis S)

(S0 Phenomenal experience only / S1 External circumstances only / SX A combination of the two)

What distinguishes these categorisations is that each category, as far as I can perceive, has no analogous axis within hedonistic utilitarianism. In other words to a hedonistic utilitarian, such axes would either be meaningless, or have only one logical answer. But any well-defined and consistent form of preference utilitarianism must sit at some point on every one of these axes.

See the article for more detailed discussion about each of the axes of preference utilitarianism, and more.

## Are consequentialism and deontology not even wrong?

15 02 June 2015 07:49AM

I was stunned to read the accounts quoted below. They're claiming that the notion of morality -  in the sense of there being a special category of things that you should or should not do for the sake of the things themselves being inherently right or wrong - might not only be a recent invention, but also an incoherent one. Even when I had read debates about e.g. moral realism, I had always understood even the moral irrealists as acknowledging that there are genuine moral attitudes that are fundamentally ingrained in people. But I hadn't ran into a position claiming that it was actually possible for whole cultures to simply not have a concept of morality in the first place.

I'm amazed that I haven't heard these claims discussed more. If they're accurate, then they seem to me to provide a strong argument for both deontology and consequentialism - at least as they're usually understood here - to be not even wrong. Just rationalizations of concepts that got their origin from Judeo-Christian laws and which people held onto because they didn't know of any other way of thinking.

-----
As for morally, we must observe at once – again following Anscombe – that Plato and Aristotle, having no word for “moral,” could not even form a phrase equivalent to “morally right.” The Greek thik aret means “excellence of character,” not “moral virtue”; 2 Cicero's virtus moralis, from which the English phrase descends directly, is simply the Latin for thik aret. This is not the lexical fallacy; it is not just that the word ‘moral’ was missing. The whole idea of a special category called “the moral” was missing. Strictly speaking, the Aristotelian phrase ta thika is simply a generalizing substantive formed on th, “characteristic behaviors,” just as the Ciceronian moralia is formed on mores. To be fully correct – admittedly it would be a bit cumbersome – we should talk not of Aristotle's Nicomachean Ethics but of his Studies-of-our-characteristic-behaviors Edited-by-Nicomachus.

Plato and Aristotle were interested – especially Plato – in the question how the more stringent demands of a good disposition like justice or temperance or courage could be reasonable demands, demands that it made sense to obey even at extreme cost. It never occurred to them, as it naturally does to moderns, to suggest that these demands were to be obeyed simply because they were demands of a special, magically compulsive sort: moral demands.

Their answer was always that, to show that we have reason to obey the strong demands that can emerge from our good dispositions, we must show that what they demand is in some way a necessary means to or part of human well-being (eudaimonia). If it must be classified under the misconceived modern distinction between “the moral” and “the prudential,” this answer clearly falls into the prudential category. 4 When modern readers who have been brought up on our moral/ prudential distinction see Plato's and Aristotle's insistence on rooting the reasons that the virtues give us in the notion of well-being, they regularly classify both as “moral egoists.” But that is a misapplication to them of a distinction that they were right not to recognize.

When we turn from the Greeks to Kant and the classical utilitarians, we may doubt whether they shared the modern interest in finding a neat definition of the “morally right” any more than Plato or Aristotle did. Kant proposed, at most, a necessary (not necessary and sufficient) condition on rationally permissible (not morally right5) action for an individual agent – and had even greater than his usual difficulty expressing this condition at all pithily. The utilitarians often were more interested in jurisprudence than in individual action, and where they addressed the latter – as J. S. Mill often does, but Bentham usually does not – tended, in the interests of long-term utility, to stick remarkably close to the deliverances of that version of “common-sense morality” that was recognized by high-minded Victorian liberals like themselves. When Kant and the utilitarians disagreed, it was not about the question “What are the necessary and sufficient conditions of morally right action?” They weren't even asking that question.

[Timothy Chappell: Virtue ethics in the twentieth century. In The Cambridge Companion to Virtue Ethics (Cambridge Companions to Philosophy) (pp. 151-152). Cambridge University Press. Kindle Edition.]

How did things change so much? Here's a quote from G.E.M. Anscombe's Modern Moral Philosophy (1958), attributing the development to the influence of Christianity:

The terms "should" or "ought" or "needs" relate to good and bad: e.g. machinery needs oil, or should or ought to be oiled, in that running without oil is bad for it, or it runs badly without oil. According to this conception, of course, "should" and "ought" are not used in a special "moral" sense when one says that a man should not bilk. (In Aristotle's sense of the term "moral" [...], they are being used in connection with a moral subject-matter: namely that of human passions and (non-technical) actions.) But they have now acquired a special so-called "moral" sense — i.e. a sense in which they imply some absolute verdict (like one of guilty/not guilty on a man) on what is described in the "ought" sentences used in certain types of context: not merely the contexts that Aristotle would call "moral" — passions and actions — but also some of the contexts that he would call "intellectual."

The ordinary (and quite indispensable) terms "should," "needs," "ought," "must" — acquired this special sense by being equated in the relevant contexts with "is obliged," or "is bound," or "is required to," in the sense in which one can be obliged or bound by law, or something can be required by law.

How did this come about? The answer is in history: between Aristotle and us came Christianity, with its law conception of ethics. For Christianity derived its ethical no- tions from the Torah. [...]

In consequence of the dominance of Christianity for many centuries, the concepts of being bound, permitted, or excused became deeply embedded in our language and thought. The Greek word "aiu,avravav," the aptest to be turned to that use, acquired the sense "sin," from having meant "mistake," "missing the mark," "going wrong." The Latin peccatum which roughly corresponded to aiu,avriiu,a was even apter for the sense "sin," because it was already associated with "culpa" — "guilt" — a juridical notion. The blanket term "illicit," "unlawful," meaning much the same as our blanket term "wrong," explains itself. It is interesting that Aristotle did not have such a blanket term. He has blanket terms for wickedness — "villain," "scoundrel"; but of course a man is not a villain or a scoundrel by the performance of one bad action, or a few bad actions. And he has terms like "disgraceful," "impious"; and specific terms signifying defect of the relevant virtue, like "unjust"; but no term corresponding to "illicit." The extension of this term (i.e. the range of its application) could be indicated in his terminology only by a quite lengthy sentence: that is "illicit" which, whether it is a thought or a consented-to passion or an action or an omission in thought or action, is something contrary to one of the virtues the lack of which shows a man to be bad qua man. That formulation would yield a concept co-extensive with the concept "illicit."

To have a law conception of ethics is to hold that what is needed for conformity with the virtues failure in which is the mark of being bad qua man (and not merely, say, qua craftsman or logician) — that what is needed for this , is required by divine law. Naturally it is not possible to have such a conception unless you believe in God as a law-giver; like Jews, Stoics, and Christians. But if such a conception is dominant for many centuries, and then is given up, it is a natural result that the concepts of "obligation," of being bound or required as by a law, should remain though they had lost their root; and if the word "ought" has become invested in certain contexts with the sense of "obligation," it too will remain to be spoken with a special emphasis and special feeling in these contexts.

It is as if the notion "criminal" were to remain when criminal law and criminal courts had been abolished and forgotten. A Hume discovering this situation might conclude that there was a special sentiment, expressed by "criminal," which alone gave the word its sense. So Hume discovered the situation which the notion "obligation" survived, and the notion "ought" was invested with that peculiar for having which it is said to be used in a "moral" sense, but in which the belief in divine law had long since been abandoned: for it was substantially given up among Protestants at the time of the Reformation.2The situation, if I am right, was the interesting one of the survival of a concept outside the framework of thought that made it a really intelligible one.

## Concept Safety: World-models as tools

6 09 May 2015 12:07PM

I'm currently reading through some relevant literature for preparing my FLI grant proposal on the topic of concept learning and AI safety. I figured that I might as well write down the research ideas I get while doing so, so as to get some feedback and clarify my thoughts. I will posting these in a series of "Concept Safety"-titled articles.

The AI in the quantum box

In the previous post, I discussed the example of an AI whose concept space and goals were defined in terms of classical physics, which then learned about quantum mechanics. Let's elaborate on that scenario a little more.

I wish to zoom in on a certain assumption that I've noticed in previous discussions of these kinds of examples. Although I couldn't track down an exact citation right now, I'm pretty confident that I've heard the QM scenario framed as something like "the AI previously thought in terms of classical mechanics, but then it finds out that the world actually runs on quantum mechanics". The key assumption being that quantum mechanics is in some sense more real than classical mechanics.

This kind of an assumption is a natural one to make if someone is operating on an AIXI-inspired model of AI. Although AIXI considers an infinite amount of world-models, there's a sense in which AIXI always strives to only have one world-model. It's always looking for the simplest possible Turing machine that would produce all of the observations that it has seen so far, while ignoring the computational cost of actually running that machine. AIXI, upon finding out about quantum mechanics, would attempt to update its world-model into one that only contained QM primitives and to derive all macro-scale events right from first principles.

No sane design for a real-world AI would try to do this. Instead, a real-world AI would take advantage of scale separation. This refers to the fact that physical systems can be modeled on a variety of different scales, and it is in many cases sufficient to model them in terms of concepts that are defined in terms of higher-scale phenomena. In practice, the AI would have a number of different world-models, each of them being applied in different situations and for different purposes.

Here we get back to the view of concepts as tools, which I discussed in the previous post. An AI that was doing something akin to reinforcement learning would come to learn the kinds of world-models that gave it the highest rewards, and to selectively employ different world-models based on what was the best thing to do in each situation.

As a toy example, consider an AI that can choose to run a low-resolution or a high-resolution psychological model of someone it's interacting with, in order to predict their responses and please them. Say the low-resolution model takes a second to run and is 80% accurate; the high-resolution model takes five seconds to run and is 95% accurate. Which model will be chosen as the one to be used will depend on the cost matrix of making a correct prediction, making a false prediction, and the consequence of making the other person wait for an extra four seconds before the AI's each reply.

We can now see that a world-model being the most real, i.e. making the most accurate predictions, doesn't automatically mean that it will be used. It also needs to be fast enough to run, and the predictions need to be useful for achieving something that the AI cares about.

World-models as tools

From this point of view, world-models are literally tools just like any other. Traditionally in reinforcement learning, we would define the value of a policy $\pi$ in state s as the expected reward given the state s and the policy $\pi$,

$V^{\pi}(s)=E[R|s,\pi]$

but under the "world-models are tools" perspective, we need to also condition on the world-model m,

$V^{\pi}(s,m)=E[R|s,\pi,m]$ .

We are conditioning on the world-model in several distinct ways.

First, there is the expected behavior of the world as predicted by world-model m. A world-model over the laws of social interaction would do poorly at predicting the movement of celestial objects, if it could be applied to them at all. Different predictions of behavior may also lead to differing predictions of the value of a state. This is described by the equation above.

Second, there is the expected cost of using the world-model. Using a more detailed world-model may be more computationally expensive, for instance. One way of interpreting this in a classical RL framework would be that using a specific world-model will place the agent in a different state than using some other world-model. We might describe by saying that in addition to the agent choosing its next action a on each time-step, the agent also needs to choose the world-model m which it will use to analyze its next observations. This will be one of the inputs for the transition function $\delta$ to the next state.

$\delta:s\times(a,m)\rightarrow\(s,m)$

Third, there is the expected behavior of the agent using world-model m. An agent with different beliefs about the world will act differently in the future: this means that the future policy $\pi_{f}$ actually depends on the chosen world-model.

$P(\pi_{f})=P(\pi|m)$

Some very interesting questions pop up at this point. Your currently selected world-model is what you use to evaluate your best choices for the next step... including the choice of what world-model to use next. So whether or not you're going to switch to a different world-model for evaluating the next step depends on whether your current world-model says that a different world-model would be better in that step.

We have not fully defined what exactly we mean by "world-models" here. Previously I gave the example of a world-model over the laws of social interaction, versus a world-model over the laws of physics. But a world-model over the laws of social interaction, say, would not have an answer to the question of which world-model to use for things it couldn't predict. So one approach would be to say that we actually have some meta-model over world-models, telling us which is the best to use in what situation.

On the other hand, it does also seem like humans often use a specific world-model and its predictions to determine whether to choose another world-model. For example, in rationalist circles you often see arguments to the line of, "self-deception might give you extra confidence, but it introduces errors into your world-model, and in the long term those are going to be more harmful than the extra confidence is beneficial". Here you see an implicit appeal to a world-model which predicts an accumulation of false beliefs with some specific effects, as well as predicting the extra self-esteem with its effects. But this kind of an analysis incorporates very specific causal claims from various (e.g. psychological) models, which are models over the world rather than just being part of some general meta-model over models. Notice also that the example analysis takes into account the way that having a specific world-model affects the state transition function: it assumes that a self-deceptive model may land us in a state where we have a higher self-esteem.

It's possible to get stuck in one world-model: for example, a strongly non-reductionist model evaluating the claims of a highly reductionist one might think it obviously crazy, and vice versa. So it seems that we do need something like a meta-evaluation function. Otherwise it would be too easy to get stuck in one model which claimed that it was the best one in every possible situation, and never agreed to "give up control" in favor of another one.

One possibility for such a thing would be a relatively model-free learning mechanism, which just kept track of the rewards accumulated when using a particular model in a particular situation. It would then bias the selection of the model towards the direction of the model that had been the most successful so far.

Human neuroscience and meta-models

We might be able to identify something like this in humans, though this is currently very speculative on my part. Action selection is carried out in the basal ganglia: different brain systems send the basal ganglia "bids" for various actions. The basal ganglia then chooses which actions to inhibit or disinhibit (by default, everything is inhibited). The basal ganglia also implements reinforcement learning, selectively strengthening or weakening the connections associated with a particular bid and context when a chosen action leads to a higher or lower reward than was expected. It seems that in addition to choosing between motor actions, the basal ganglia also chooses between different cognitive behaviors, likely even thoughts

If action selection and reinforcement learning are normal functions of the basal ganglia, it should be possible to interpret many of the human basal ganglia-related disorders in terms of selection malfunctions. For example, the akinesia of Parkinson's disease may be seen as a failure to inhibit tonic inhibitory output signals on any of the sensorimotor channels. Aspects of schizophrenia, attention deficit disorder and Tourette's syndrome could reflect different forms of failure to maintain sufficient inhibitory output activity in non-selected channels. Conseqently, insufficiently inhibited signals in non-selected target structures could interfere with the output of selected targets (expressed as motor/verbal tics) and/or make the selection system vulnerable to interruption from distracting stimuli (schizophrenia, attention deficit disorder). The opposite situation would be where the selection of one functional channel is abnormally dominant thereby making it difficult for competing events to interrupt or cause a behavioural or attentional switch. Such circumstances could underlie addictive compulsions or obsessive compulsive disorder. (Redgrave 2007)

Although I haven't seen a paper presenting evidence for this particular claim, it seems plausible to assume that humans similarly come to employ new kinds of world-models based on the extent to which using a particular world-model in a particular situation gives them rewards. When a person is in a situation where they might think in terms of several different world-models, there will be neural bids associated with mental activities that recruit the different models. Over time, the bids associated with the most successful models will become increasingly favored. This is also compatible with what we know about e.g. happy death spirals and motivated stopping: people will tend to have the kinds of thoughts which are rewarding to them.

The physicist and the AI

In my previous post, when discussing the example of the physicist who doesn't jump out of the window when they learn about QM and find out that "location" is ill-defined:

The physicist cares about QM concepts to the extent that the said concepts are linked to things that the physicist values. Maybe the physicist finds it rewarding to develop a better understanding of QM, to gain social status by making important discoveries, and to pay their rent by understanding the concepts well enough to continue to do research. These are some of the things that the QM concepts are useful for. Likely the brain has some kind of causal model indicating that the QM concepts are relevant tools for achieving those particular rewards. At the same time, the physicist also has various other things they care about, like being healthy and hanging out with their friends. These are values that can be better furthered by modeling the world in terms of classical physics. [...]

A part of this comes from the fact that the physicist's reward function remains defined over immediate sensory experiences, as well as values which are linked to those. Even if you convince yourself that the location of food is ill-defined and you thus don't need to eat, you will still suffer the negative reward of being hungry. The physicist knows that no matter how they change their definition of the world, that won't affect their actual sensory experience and the rewards they get from that.

So to prevent the AI from leaving the box by suitably redefining reality, we have to somehow find a way for the same reasoning to apply to it. I haven't worked out a rigorous definition for this, but it needs to somehow learn to care about being in the box in classical terms, and realize that no redefinition of "location" or "space" is going to alter what happens in the classical model. Also, its rewards need to be defined over models to a sufficient extent to avoid wireheading (Hibbard 2011), so that it will think that trying to leave the box by redefining things would count as self-delusion, and not accomplish the things it really cared about. This way, the AI's concept for "being in the box" should remain firmly linked to the classical interpretation of physics, not the QM interpretation of physics, because it's acting in terms of the classical model that has always given it the most reward.

There are several parts to this.

1. The "physicist's reward function remains defined over immediate sensory experiences". Them falling down and breaking their leg is still going to hurt, and they know that this won't be changed no matter how they try to redefine reality.

2. The physicist's value function also remains defined over immediate sensory experiences. They know that jumping out of a window and ending up with all the bones in their body being broken is going to be really inconvenient even if you disregarded the physical pain. They still cannot do the things they would like to do, and they have learned that being in such a state is non-desirable. Again, this won't be affected by how they try to define reality.

We now have a somewhat better understanding of what exactly this means. The physicist has spent their entire life living in the classical world, and obtained nearly all of their rewards by thinking in terms of the classical world. As a result, using the classical model for reasoning about life has become strongly selected for. Also, the physicist's classical world-model predicts that thinking in terms of that model is a very good thing for surviving, and that trying to switch to a QM model where location was ill-defined would be a very bad thing for the goal of surviving. On the other hand, thinking in terms of exotic world-models remains a rewarding thing for goals such as obtaining social status or making interesting discoveries, so the QM model does get more strongly reinforced in that context and for that purpose.

Getting back to the question of how to make the AI stay in the box, ideally we could mimic this process, so that the AI would initially come to care about staying in the box. Then when it learns about QM, it understands that thinking in QM terms is useful for some goals, but if it were to make itself think in purely QM terms, that would cause it to leave the box. Because it is thinking mostly in terms of a classical model, which says that leaving the box would be bad (analogous to the physicist thinking mostly in terms of the classical model which says that jumping out of the window would be bad), it wants to make sure that it will continue to think in terms of the classical model when it's reasoning about its location.

## Concept Safety: What are concepts for, and how to deal with alien concepts

11 19 April 2015 01:44PM

I'm currently reading through some relevant literature for preparing my FLI grant proposal on the topic of concept learning and AI safety. I figured that I might as well write down the research ideas I get while doing so, so as to get some feedback and clarify my thoughts. I will posting these in a series of "Concept Safety"-titled articles.

In The Problem of Alien Concepts, I posed the following question: if your concepts (defined as either multimodal representations or as areas in a psychological space) previously had N dimensions and then they suddenly have N+1, how does that affect (moral) values that were previously only defined in terms of N dimensions?

I gave some (more or less) concrete examples of this kind of a "conceptual expansion":

1. Children learn to represent dimensions such as "height" and "volume", as well as "big" and "bright", separately at around age 5.
2. As an inhabitant of the Earth, you've been used to people being unable to fly and landowners being able to forbid others from using their land. Then someone goes and invents an airplane, leaving open the question of the height to which the landowner's control extends. Similarly for satellites and nation-states.
3. As an inhabitant of Flatland, you've been told that the inside of a certain rectangle is a forbidden territory. Then you learn that the world is actually three-dimensional, leaving open the question of the height of which the forbidden territory extends.
4. An AI has previously been reasoning in terms of classical physics and been told that it can't leave a box, which it previously defined in terms of classical physics. Then it learns about quantum physics, which allow for definitions of "location" which are substantially different from the classical ones.

As a hint of the direction where I'll be going, let's first take a look at how humans solve these kinds of dilemmas, and consider examples #1 and #2.

The first example - children realizing that items have a volume that's separate from their height - rarely causes any particular crises. Few children have values that would be seriously undermined or otherwise affected by this discovery. We might say that it's a non-issue because none of the children's values have been defined in terms of the affected conceptual domain.

As for the second example, I don't know the exact cognitive process by which it was decided that you didn't need the landowner's permission to fly over their land. But I'm guessing that it involved reasoning like: if the plane flies at a sufficient height, then that doesn't harm the landowner in any way. Flying would become impossible difficult if you had to get separate permission from every person whose land you were going to fly over. And, especially before the invention of radar, a ban on unauthorized flyovers would be next to impossible to enforce anyway.

We might say that after an option became available which forced us to include a new dimension in our existing concept of landownership, we solved the issue by considering it in terms of our existing values.

Concepts, values, and reinforcement learning

Before we go on, we need to talk a bit about why we have concepts and values in the first place.

From an evolutionary perspective, creatures that are better capable of harvesting resources (such as food and mates) and avoiding dangers (such as other creatures who think you're food or after their mates) tend to survive and have offspring at better rates than otherwise comparable creatures who are worse at those things. If a creature is to be flexible and capable of responding to novel situations, it can't just have a pre-programmed set of responses to different things. Instead, it needs to be able to learn how to harvest resources and avoid danger even when things are different from before.

How did evolution achieve that? Essentially, by creating a brain architecture that can, as a very very rough approximation, be seen as consisting of two different parts. One part, which a machine learning researcher might call the reward function, has the task of figuring out when various criteria - such as being hungry or getting food - are met, and issuing the rest of the system either a positive or negative reward based on those conditions. The other part, the learner, then "only" needs to find out how to best optimize for the maximum reward. (And then there is the third part, which includes any region of the brain that's neither of the above, but we don't care about those regions now.)

The mathematical theory of how to learn to optimize for rewards when your environment and reward function are unknown is reinforcement learning (RL), which recent neuroscience indicates is implemented by the brain. An RL agent learns a mapping from states of the world to rewards, as well as a mapping from actions to world-states, and then uses that information to maximize the amount of lifetime rewards it will get.

There are two major reasons why an RL agent, like a human, should learn high-level concepts:

1. They make learning massively easier. Instead of having to separately learn that "in the world-state where I'm sitting naked in my cave and have berries in my hand, putting them in my mouth enables me to eat them" and that "in the world-state where I'm standing fully-clothed in the rain outside and have fish in my hand, putting it in my mouth enables me to eat it" and so on, the agent can learn to identify the world-states that correspond to the abstract concept of having food available, and then learn the appropriate action to take in all those states.
2. There are useful behaviors that need to be bootstrapped from lower-level concepts to higher-level ones in order to be learned. For example, newborns have an innate preference for looking at roughly face-shaped things (Farroni et al. 2005), which develops into a more consistent preference for looking at faces over the first year of life (Frank, Vul & Johnson 2009). One hypothesis is that this bias towards paying attention to the relatively-easy-to-encode-in-genes concept of "face-like things" helps direct attention towards learning valuable but much more complicated concepts, such as ones involved in a basic theory of mind (Gopnik, Slaughter & Meltzoff 1994) and the social skills involved with it.

Viewed in this light, concepts are cognitive tools that are used for getting rewards. At the most primitive level, we should expect a creature to develop concepts that abstract over situations that are similar with regards to the kind of reward that one can gain from taking a certain action in those states. Suppose that a certain action in state s1 gives you a reward, and that there are also states s2 - s5 in which taking some specific action causes you to end up in s1. Then we should expect the creature to develop a common concept for being in the states s2 - s5, and we should expect that concept to be "more similar" to the concept of being in state s1 than to the concept of being in some state that was many actions away.

"More similar" how?

In reinforcement learning theory, reward and value are two different concepts. The reward of a state is the actual reward that the reward function gives you when you're in that state or perform some action in that state. Meanwhile, the value of the state is the maximum total reward that you can expect to get from moving that state to others (times some discount factor). So a state A with reward 0 might have value 5 if you could move from it to state B, which had a reward of 5.

Below is a figure from DeepMind's recent Nature paper, which presented a deep reinforcement learner that was capable of achieving human-level performance or above on 29 of 49 Atari 2600 games (Mnih et al. 2015). The figure is a visualization of the representations that the learning agent has developed for different game-states in Space Invaders. The representations are color-coded depending on the value of the game-state that the representation corresponds to, with red indicating a higher value and blue a lower one.

As can be seen (and is noted in the caption), representations with similar values are mapped closer to each other in the representation space. Also, some game-states which are visually dissimilar to each other but have a similar value are mapped to nearby representations. Likewise, states that are visually similar but have a differing value are mapped away from each other. We could say that the Atari-playing agent has learned a primitive concept space, where the relationships between the concepts (representing game-states) depend on their value and the ease of moving from one game-state to another.

In most artificial RL agents, reward and value are kept strictly separate. In humans (and mammals in general), this doesn't seem to work quite the same way. Rather, if there are things or behaviors which have once given us rewards, we tend to eventually start valuing them for their own sake. If you teach a child to be generous by praising them when they share their toys with others, you don't have to keep doing it all the way to your grave. Eventually they'll internalize the behavior, and start wanting to do it. One might say that the positive feedback actually modifies their reward function, so that they will start getting some amount of pleasure from generous behavior without needing to get external praise for it. In general, behaviors which are learned strongly enough don't need to be reinforced anymore (Pryor 2006).

Why does the human reward function change as well? Possibly because of the bootstrapping problem: there are things such as social status that are very complicated and hard to directly encode as "rewarding" in an infant mind, but which can be learned by associating them with rewards. One researcher I spoke with commented that he "wouldn't be at all surprised" if it turned out that sexual orientation was learned by men and women having slightly different smells, and sexual interest bootstrapping from an innate reward for being in the presence of the right kind of a smell, which the brain then associated with the features usually co-occurring with it. His point wasn't so much that he expected this to be the particular mechanism, but that he wouldn't find it particularly surprising if a core part of the mechanism was something that simple. Remember that incest avoidance seems to bootstrap from the simple cue of "don't be sexually interested in the people you grew up with".

This is, in essence, how I expect human values and human concepts to develop. We have some innate reward function which gives us various kinds of rewards for different kinds of things. Over time we develop a various concepts for the purpose of letting us maximize our rewards, and lived experiences also modify our reward function. Our values are concepts which abstract over situations in which we have previously obtained rewards, and which have become intrinsically rewarding as a result.

Getting back to conceptual expansion

Having defined these things, let's take another look at the two examples we discussed above. As a reminder, they were:

1. Children learn to represent dimensions such as "height" and "volume", as well as "big" and "bright", separately at around age 5.
2. As an inhabitant of the Earth, you've been used to people being unable to fly and landowners being able to forbid others from using their land. Then someone goes and invents an airplane, leaving open the question of the height to which the landowner's control extends.

I summarized my first attempt at describing the consequences of #1 as "it's a non-issue because none of the children's values have been defined in terms of the affected conceptual domain". We can now reframe it as "it's a non-issue because the [concepts that abstract over the world-states which give the child rewards] mostly do not make use of the dimension that's now been split into 'height' and 'volume'".

Admittedly, this new conceptual distinction might be relevant for estimating the value of a few things. A more accurate estimate of the volume of a glass leads to a more accurate estimate of which glass of juice to prefer, for instance. With children, there probably is some intuitive physics module that figures out how to apply this new dimension for that purpose. Even if there wasn't, and it was unclear whether it was the "tall glass" or "high-volume glass" concept that needed be mapped closer to high-value glasses, this could be easily determined by simple experimentation.

As for the airplane example, I summarized my description of it by saying that "after an option became available which forced us to include a new dimension in our existing concept of landownership, we solved the issue by considering it in terms of our existing values". We can similarly reframe this as "after the feature of 'height' suddenly became relevant for the concept of landownership, when it hadn't been a relevant feature dimension for landownership before, we redefined landownership by considering which kind of redefinition would give us the largest amounts of rewarding things". "Rewarding things", here, shouldn't be understood only in terms of concrete physical rewards like money, but also anything else that people have ended up valuing, including abstract concepts like right to ownership.

Note also that different people, having different experiences, ended up making redefinitions. No doubt some landowners felt that the "being in total control of my land and everything above it" was a more important value than "the convenience of people who get to use airplanes"... unless, perhaps, they got to see first-hand the value of flying, in which case the new information could have repositioned the different concepts in their value-space.

As an aside, this also works as a possible partial explanation for e.g. someone being strongly against gay rights until their child comes out of the closet. Someone they care about suddenly benefiting from the concept of "gay rights", which previously had no positive value for them, may end up changing the value of that concept. In essence, they gain new information about the value of the world-states that the concept of "my nation having strong gay rights" abstracts over. (Of course, things don't always go this well, if their concept of homosexuality is too strongly negative to start with.)

The Flatland case follows a similar principle: the Flatlanders have some values that declared the inside of the rectangle a forbidden space. Maybe the inside of the rectangle contains monsters which tend to eat Flatlanders. Once they learn about 3D space, they can rethink about it in terms of their existing values.

Dealing with the AI in the box

This leaves us with the AI case. We have, via various examples, taught the AI to stay in the box, which was defined in terms of classical physics. In other words, the AI has obtained the concept of a box, and has come to associate staying in the box with some reward, or possibly leaving it with a lack of a reward.

Then the AI learns about quantum mechanics. It learns that in the QM formulation of the universe, "location" is not a fundamental or well-defined concept anymore - and in some theories, even the concept of "space" is no longer fundamental or well-defined. What happens?

Let's look at the human equivalent for this example: a physicist who learns about quantum mechanics. Do they start thinking that since location is no longer well-defined, they can now safely jump out of the window on the sixth floor?

Maybe some do. But I would wager that most don't. Why not?

The physicist cares about QM concepts to the extent that the said concepts are linked to things that the physicist values. Maybe the physicist finds it rewarding to develop a better understanding of QM, to gain social status by making important discoveries, and to pay their rent by understanding the concepts well enough to continue to do research. These are some of the things that the QM concepts are useful for. Likely the brain has some kind of causal model indicating that the QM concepts are relevant tools for achieving those particular rewards. At the same time, the physicist also has various other things they care about, like being healthy and hanging out with their friends. These are values that can be better furthered by modeling the world in terms of classical physics.

In some sense, the physicist knows that if they started thinking "location is ill-defined, so I can safely jump out of the window", then that would be changing the map, not the territory. It wouldn't help them get the rewards of being healthy and getting to hang out with friends - even if a hypothetical physicist who did make that redefinition would think otherwise. It all adds up to normality.

A part of this comes from the fact that the physicist's reward function remains defined over immediate sensory experiences, as well as values which are linked to those. Even if you convince yourself that the location of food is ill-defined and you thus don't need to eat, you will still suffer the negative reward of being hungry. The physicist knows that no matter how they change their definition of the world, that won't affect their actual sensory experience and the rewards they get from that.

So to prevent the AI from leaving the box by suitably redefining reality, we have to somehow find a way for the same reasoning to apply to it. I haven't worked out a rigorous definition for this, but it needs to somehow learn to care about being in the box in classical terms, and realize that no redefinition of "location" or "space" is going to alter what happens in the classical model. Also, its rewards need to be defined over models to a sufficient extent to avoid wireheading (Hibbard 2011), so that it will think that trying to leave the box by redefining things would count as self-delusion, and not accomplish the things it really cared about. This way, the AI's concept for "being in the box" should remain firmly linked to the classical interpretation of physics, not the QM interpretation of physics, because it's acting in terms of the classical model that has always given it the most reward.

It is my hope that this could also be made to extend to cases where the AI learns to think in terms of concepts that are totally dissimilar to ours. If it learns a new conceptual dimension, how should that affect its existing concepts? Well, it can figure out how to reclassify the existing concepts that are affected by that change, based on what kind of a classification ends up producing the most reward... when the reward function is defined over the old model.

Next post in series: World-models as tools.

## Concept Safety: The problem of alien concepts

15 17 April 2015 02:09PM

I'm currently reading through some relevant literature for preparing my FLI grant proposal on the topic of concept learning and AI safety. I figured that I might as well write down the research ideas I get while doing so, so as to get some feedback and clarify my thoughts. I will posting these in a series of "Concept Safety"-titled articles.

In the previous post in this series, I talked about how one might get an AI to have similar concepts as humans. However, one would intuitively assume that a superintelligent AI might eventually develop the capability to entertain far more sophisticated concepts than humans would ever be capable of having. Is that a problem?

Just what are concepts, anyway?

To answer the question, we first need to define what exactly it is that we mean by a "concept", and why exactly more sophisticated concepts would be a problem.

Unfortunately, there isn't really any standard definition of this in the literature, with different theorists having different definitions. Machery even argues that the term "concept" doesn't refer to a natural kind, and that we should just get rid of the whole term. If nothing else, this definition from Kruschke (2008) is at least amusing:

Models of categorization are usually designed to address data from laboratory experiments, so “categorization” might be best defined as the class of behavioral data generated by experiments that ostensibly study categorization.

Because I don't really have the time to survey the whole literature and try to come up with one grand theory of the subject, I will for now limit my scope and only consider two compatible definitions of the term.

Definition 1: Concepts as multimodal neural representations. I touched upon this definition in the last post, where I mentioned studies indicating that the brain seems to have shared neural representations for e.g. the touch and sight of a banana. Current neuroscience seems to indicate the existence of brain areas where representations from several different senses are combined together into higher-level representations, and where the activation of any such higher-level representation will also end up activating the lower sense modalities in turn. As summarized by Man et al. (2013):

Briefly, the Damasio framework proposes an architecture of convergence-divergence zones (CDZ) and a mechanism of time-locked retroactivation. Convergence-divergence zones are arranged in a multi-level hierarchy, with higher-level CDZs being both sensitive to, and capable of reinstating, specific patterns of activity in lower-level CDZs. Successive levels of CDZs are tuned to detect increasingly complex features. Each more-complex feature is defined by the conjunction and configuration of multiple less-complex features detected by the preceding level. CDZs at the highest levels of the hierarchy achieve the highest level of semantic and contextual integration, across all sensory modalities. At the foundations of the hierarchy lie the early sensory cortices, each containing a mapped (i.e., retinotopic, tonotopic, or somatotopic) representation of sensory space. When a CDZ is activated by an input pattern that resembles the template for which it has been tuned, it retro-activates the template pattern of lower-level CDZs. This continues down the hierarchy of CDZs, resulting in an ensemble of well-specified and time-locked activity extending to the early sensory cortices.

On this account, my mental concept for "dog" consists of a neural activation pattern making up the sight, sound, etc. of some dog - either a generic prototypical dog or some more specific dog. Likely the pattern is not just limited to sensory information, either, but may be associated with e.g. motor programs related to dogs. For example, the program for throwing a ball for the dog to fetch. One version of this hypothesis, the Perceptual Symbol Systems account, calls such multimodal representations simulators, and describes them as follows (Niedenthal et al. 2005):

A simulator integrates the modality-specific content of a category across instances and provides the ability to identify items encountered subsequently as instances of the same category. Consider a simulator for the social category, politician. Following exposure to different politicians, visual information about how typical politicians look (i.e., based on their typical age, sex, and role constraints on their dress and their facial expressions) becomes integrated in the simulator, along with auditory information for how they typically sound when they talk (or scream or grovel), motor programs for interacting with them, typical emotional responses induced in interactions or exposures to them, and so forth. The consequence is a system distributed throughout the brain’s feature and association areas that essentially represents knowledge of the social category, politician.

The inclusion of such "extra-sensory" features helps understand how even abstract concepts could fit this framework: for example, one's understanding of the concept of a derivative might be partially linked to the procedural programs one has developed while solving derivatives. For a more detailed hypothesis of how abstract mathematics may emerge from basic sensory and motor programs and concepts, I recommend Lakoff & Nuñez (2001).

Definition 2: Concepts as areas in a psychological space. This definition, while being compatible with the previous one, looks at concepts more "from the inside". Gärdenfors (2000) defines the basic building blocks of a psychological conceptual space to be various quality dimensions, such as temperature, weight, brightness, pitch, and the spatial dimensions of height, width, and depth. These are psychological in the sense of being derived from our phenomenal experience of certain kinds of properties, rather than the way in which they might exist in some objective reality.

For example, one way of modeling the psychological sense of color is via a color space defined by the quality dimensions of hue (represented by the familiar color circle), chromaticness (saturation), and brightness.

The second phenomenal dimension of color is chromaticness (saturation), which ranges from grey (zero color intensity) to increasingly greater intensities. This dimension is isomorphic to an interval of the real line. The third dimension is brightness which varies from white to black and is thus a linear dimension with two end points. The two latter dimensions are not totally independent, since the possible variation of the chromaticness dimension decreases as the values of the brightness dimension approaches the extreme points of black and white, respectively. In other words, for an almost white or almost black color, there can be very little variation in its chromaticness. This is modeled by letting that chromaticness and brightness dimension together generate a triangular representation ... Together these three dimensions, one with circular structure and two with linear, make up the color space. This space is often illustrated by the so called color spindle

This kind of a representation is different from the physical wavelength representation of color, where e.g. the hue is mostly related to the wavelength of the color. The wavelength representation of hue would be linear, but due to the properties of the human visual system, the psychological representation of hue is circular.

Gärdenfors defines two quality dimensions to be integral if a value cannot be given for an object on one dimension without also giving it a value for the other dimension: for example, an object cannot be given a hue value without also giving it a brightness value. Dimensions that are not integral with each other are separable. A conceptual domain is a set of integral dimensions that are separable from all other dimensions: for example, the three color-dimensions form the domain of color.

From these definitions, Gärdenfors develops a theory of concepts where more complicated conceptual spaces can be formed by combining lower-level domains. Concepts, then, are particular regions in these conceptual spaces: for example, the concept of "blue" can be defined as a particular region in the domain of color. Notice that the notion of various combinations of basic perceptual domains making more complicated conceptual spaces possible fits well together with the models discussed in our previous definition. There more complicated concepts were made possible by combining basic neural representations for e.g. different sensory modalities.

The origin of the different quality dimensions could also emerge from the specific properties of the different simulators, as in PSS theory.

Thus definition #1 allows us to talk about what a concept might "look like from the outside", with definition #2 talking about what the same concept might "look like from the inside".

Interestingly, Gärdenfors hypothesizes that much of the work involved with learning new concepts has to do with learning new quality dimensions to fit into one's conceptual space, and that once this is done, all that remains is the comparatively much simpler task of just dividing up the new domain to match seen examples.

For example, consider the (phenomenal) dimension of volume. The experiments on "conservation" performed by Piaget and his followers indicate that small children have no separate representation of volume; they confuse the volume of a liquid with the height of the liquid in its container. It is only at about the age of five years that they learn to represent the two dimensions separately. Similarly, three- and four-year-olds confuse high with tall, big with bright, and so forth (Carey 1978).

The problem of alien concepts

With these definitions for concepts, we can now consider what problems would follow if we started off with a very human-like AI that had the same concepts as we did, but then expanded its conceptual space to allow for entirely new kinds of concepts. This could happen if it self-modified to have new kinds of sensory or thought modalities that it could associate its existing concepts with, thus developing new kinds of quality dimensions.

An analogy helps demonstrate this problem: suppose that you're operating in a two-dimensional space, where a rectangle has been drawn to mark a certain area as "forbidden" or "allowed". Say that you're an inhabitant of Flatland. But then you suddenly become aware that actually, the world is three-dimensional, and has a height dimension as well! That raises the question of, how should the "forbidden" or "allowed" area be understood in this new three-dimensional world? Do the walls of the rectangle extend infinitely in the height dimension, or perhaps just some certain distance in it? If just a certain distance, does the rectangle have a "roof" or "floor", or can you just enter (or leave) the rectangle from the top or the bottom? There doesn't seem to be any clear way to tell.

As a historical curiosity, this dilemma actually kind of really happened when airplanes were invented: could landowners forbid airplanes from flying over their land, or was the ownership of the land limited to some specific height, above which the landowners had no control? Courts and legislation eventually settled on the latter answer. A more AI-relevant example might be if one was trying to limit the AI with rules such as "stay within this box here", and the AI then gained an intuitive understanding of quantum mechanics, which might allow it to escape from the box without violating the rule in terms of its new concept space.

More generally, if previously your concepts had N dimensions and now they have N+1, you might find something that fulfilled all the previous criteria while still being different from what we'd prefer if we knew about the N+1th dimension.

In the next post, I will present some (very preliminary and probably wrong) ideas for solving this problem.

Next post in series: What are concepts for, and how to deal with alien concepts.

## Concept Safety: Producing similar AI-human concept spaces

30 14 April 2015 08:39PM

I'm currently reading through some relevant literature for preparing my FLI grant proposal on the topic of concept learning and AI safety. I figured that I might as well write down the research ideas I get while doing so, so as to get some feedback and clarify my thoughts. I will posting these in a series of "Concept Safety"-titled articles.

A frequently-raised worry about AI is that it may reason in ways which are very different from us, and understand the world in a very alien manner. For example, Armstrong, Sandberg & Bostrom (2012) consider the possibility of restricting an AI via "rule-based motivational control" and programming it to follow restrictions like "stay within this lead box here", but they raise worries about the difficulty of rigorously defining "this lead box here". To address this, they go on to consider the possibility of making an AI internalize human concepts via feedback, with the AI being told whether or not some behavior is good or bad and then constructing a corresponding world-model based on that. The authors are however worried that this may fail, because

Humans seem quite adept at constructing the correct generalisations – most of us have correctly deduced what we should/should not be doing in general situations (whether or not we follow those rules). But humans share a common of genetic design, which the OAI would likely not have. Sharing, for instance, derives partially from genetic predisposition to reciprocal altruism: the OAI may not integrate the same concept as a human child would. Though reinforcement learning has a good track record, it is neither a panacea nor a guarantee that the OAIs generalisations agree with ours.

Addressing this, a possibility that I raised in Sotala (2015) was that possibly the concept-learning mechanisms in the human brain are actually relatively simple, and that we could replicate the human concept learning process by replicating those rules. I'll start this post by discussing a closely related hypothesis: that given a specific learning or reasoning task and a certain kind of data, there is an optimal way to organize the data that will naturally emerge. If this were the case, then AI and human reasoning might naturally tend to learn the same kinds of concepts, even if they were using very different mechanisms. Later on the post, I will discuss how one might try to verify that similar representations had in fact been learned, and how to set up a system to make them even more similar.

Word embedding

A particularly fascinating branch of recent research relates to the learning of word embeddings, which are mappings of words to very high-dimensional vectors. It turns out that if you train a system on one of several kinds of tasks, such as being able to classify sentences as valid or invalid, this builds up a space of word vectors that reflects the relationships between the words. For example, there seems to be a male/female dimension to words, so that there's a "female vector" that we can add to the word "man" to get "woman" - or, equivalently, which we can subtract from "woman" to get "man". And it so happens (Mikolov, Yih & Zweig 2013) that we can also get from the word "king" to the word "queen" by adding the same vector to "king". In general, we can (roughly) get to the male/female version of any word vector by adding or subtracting this one difference vector!

Why would this happen? Well, a learner that needs to classify sentences as valid or invalid needs to classify the sentence "the king sat on his throne" as valid while classifying the sentence "the king sat on her throne" as invalid. So including a gender dimension on the built-up representation makes sense.

But gender isn't the only kind of relationship that gets reflected in the geometry of the word space. Here are a few more:

It turns out (Mikolov et al. 2013) that with the right kind of training mechanism, a lot of relationships that we're intuitively aware of become automatically learned and represented in the concept geometry. And like Olah (2014) comments:

It’s important to appreciate that all of these properties of W are side effects. We didn’t try to have similar words be close together. We didn’t try to have analogies encoded with difference vectors. All we tried to do was perform a simple task, like predicting whether a sentence was valid. These properties more or less popped out of the optimization process.

This seems to be a great strength of neural networks: they learn better ways to represent data, automatically. Representing data well, in turn, seems to be essential to success at many machine learning problems. Word embeddings are just a particularly striking example of learning a representation.

It gets even more interesting, for we can use these for translation. Since Olah has already written an excellent exposition of this, I'll just quote him:

We can learn to embed words from two different languages in a single, shared space. In this case, we learn to embed English and Mandarin Chinese words in the same space.

We train two word embeddings, Wen and Wzh in a manner similar to how we did above. However, we know that certain English words and Chinese words have similar meanings. So, we optimize for an additional property: words that we know are close translations should be close together.

Of course, we observe that the words we knew had similar meanings end up close together. Since we optimized for that, it’s not surprising. More interesting is that words we didn’t know were translations end up close together.

In light of our previous experiences with word embeddings, this may not seem too surprising. Word embeddings pull similar words together, so if an English and Chinese word we know to mean similar things are near each other, their synonyms will also end up near each other. We also know that things like gender differences tend to end up being represented with a constant difference vector. It seems like forcing enough points to line up should force these difference vectors to be the same in both the English and Chinese embeddings. A result of this would be that if we know that two male versions of words translate to each other, we should also get the female words to translate to each other.

Intuitively, it feels a bit like the two languages have a similar ‘shape’ and that by forcing them to line up at different points, they overlap and other points get pulled into the right positions.

After this, it gets even more interesting. Suppose you had this space of word vectors, and then you also had a system which translated images into vectors in the same space. If you have images of dogs, you put them near the word vector for dog. If you have images of Clippy you put them near word vector for "paperclip". And so on.

You do that, and then you take some class of images the image-classifier was never trained on, like images of cats. You ask it to place the cat-image somewhere in the vector space. Where does it end up?

You guessed it: in the rough region of the "cat" words. Olah once more:

This was done by members of the Stanford group with only 8 known classes (and 2 unknown classes). The results are already quite impressive. But with so few known classes, there are very few points to interpolate the relationship between images and semantic space off of.

The Google group did a much larger version – instead of 8 categories, they used 1,000 – around the same time (Frome et al. (2013)) and has followed up with a new variation (Norouzi et al. (2014)). Both are based on a very powerful image classification model (from Krizehvsky et al. (2012)), but embed images into the word embedding space in different ways.

The results are impressive. While they may not get images of unknown classes to the precise vector representing that class, they are able to get to the right neighborhood. So, if you ask it to classify images of unknown classes and the classes are fairly different, it can distinguish between the different classes.

Even though I’ve never seen a Aesculapian snake or an Armadillo before, if you show me a picture of one and a picture of the other, I can tell you which is which because I have a general idea of what sort of animal is associated with each word. These networks can accomplish the same thing.

These algorithms made no attempt of being biologically realistic in any way. They didn't try classifying data the way the brain does it: they just tried classifying data using whatever worked. And it turned out that this was enough to start constructing a multimodal representation space where a lot of the relationships between entities were similar to the way humans understand the world.

How useful is this?

"Well, that's cool", you might now say. "But those word spaces were constructed from human linguistic data, for the purpose of predicting human sentences. Of course they're going to classify the world in the same way as humans do: they're basically learning the human representation of the world. That doesn't mean that an autonomously learning AI, with its own learning faculties and systems, is necessarily going to learn a similar internal representation, or to have similar concepts."

This is a fair criticism. But it is mildly suggestive of the possibility that an AI that was trained to understand the world via feedback from human operators would end up building a similar conceptual space. At least assuming that we chose the right learning algorithms.

When we train a language model to classify sentences by labeling some of them as valid and others as invalid, there's a hidden structure implicit in our answers: the structure of how we understand the world, and of how we think of the meaning of words. The language model extracts that hidden structure and begins to classify previously unseen things in terms of those implicit reasoning patterns. Similarly, if we gave an AI feedback about what kinds of actions counted as "leaving the box" and which ones didn't, there would be a certain way of viewing and conceptualizing the world implied by that feedback, one which the AI could learn.

Comparing representations

"Hmm, maaaaaaaaybe", is your skeptical answer. "But how would you ever know? Like, you can test the AI in your training situation, but how do you know that it's actually acquired a similar-enough representation and not something wildly off? And it's one thing to look at those vector spaces and claim that there are human-like relationships among the different items, but that's still a little hand-wavy. We don't actually know that the human brain does anything remotely similar to represent concepts."

Here we turn, for a moment, to neuroscience.

Multivariate Cross-Classification (MVCC) is a clever neuroscience methodology used for figuring out whether different neural representations of the same thing have something in common. For example, we may be interested in whether the visual and tactile representation of a banana have something in common.

We can test this by having several test subjects look at pictures of objects such as apples and bananas while sitting in a brain scanner. We then feed the scans of their brains into a machine learning classifier and teach it to distinguish between the neural activity of looking at an apple, versus the neural activity of looking at a banana. Next we have our test subjects (still sitting in the brain scanners) touch some bananas and apples, and ask our machine learning classifier to guess whether the resulting neural activity is the result of touching a banana or an apple. If the classifier - which has not been trained on the "touch" representations, only on the "sight" representations - manages to achieve a better-than-chance performance on this latter task, then we can conclude that the neural representation for e.g. "the sight of a banana" has something in common with the neural representation for "the touch of a banana".

A particularly fascinating experiment of this type is that of Shinkareva et al. (2011), who showed their test subjects both the written words for different tools and dwellings, and, separately, line-drawing images of the same tools and dwellings. A machine-learning classifier was both trained on image-evoked activity and made to predict word-evoked activity and vice versa, and achieved a high accuracy on category classification for both tasks. Even more interestingly, the representations seemed to be similar between subjects. Training the classifier on the word representations of all but one participant, and then having it classify the image representation of the left-out participant, also achieved a reliable (p<0.05) category classification for 8 out of 12 participants. This suggests a relatively similar concept space between humans of a similar background.

We can now hypothesize some ways of testing the similarity of the AI's concept space with that of humans. Possibly the most interesting one might be to develop a translation between a human's and an AI's internal representations of concepts. Take a human's neural activation when they're thinking of some concept, and then take the AI's internal activation when it is thinking of the same concept, and plot them in a shared space similar to the English-Mandarin translation. To what extent do the two concept geometries have similar shapes, allowing one to take a human's neural activation of the word "cat" to find the AI's internal representation of the word "cat"? To the extent that this is possible, one could probably establish that the two share highly similar concept systems.

One could also try to more explicitly optimize for such a similarity. For instance, one could train the AI to make predictions of different concepts, with the additional constraint that its internal representation must be such that a machine-learning classifier trained on a human's neural representations will correctly identify concept-clusters within the AI. This might force internal similarities on the representation beyond the ones that would already be formed from similarities in the data.

Next post in series: The problem of alien concepts.

## [link] Thoughts on defining human preferences

6 31 March 2015 10:08AM

Abstract: Discussion of how we might want to define human preferences, particularly in the context of building an AI intended to learn and implement those preferences. Starts with actual arguments about the applicability of the VNM utility theorem, then towards the end gets into hypotheses that are less well defended but possibly more important. At the very end, suggests that current hypothesizing about AI safety might be overemphasizing “discovering our preferences” over “creating our preferences”.

## Status - is it what we think it is?

20 30 March 2015 09:37PM

I was re-reading the chapter on status in Impro (excerpt), and I noticed that Johnstone seemed to be implying that different people are comfortable at different levels of status: some prefer being high status and others prefer being low status. I found this peculiar, because the prevailing notion in the rationalistsphere seems to be that everyone's constantly engaged in status games aiming to achieve higher status. I've even seen arguments to the effect that a true post-scarcity society is impossible, because status is zero-sum and there will always be people at the bottom of the status hierarchy.

But if some people preferred to have low status, this whole dilemma might be avoided, if a mix of statuses could be find that left everyone happy.

First question - is Johnstone's "status" talking about the same thing as our "status"? He famously claimed that "status is something you do, not something that you are", and that

I should really talk about dominance and submission, but I'd create a resistance. Students who will agree readily to raising or lowering their status may object if asked to 'dominate' or 'submit'.

Viewed via this lens, it makes sense that some people would prefer being in a low status role: if you try to take control of the group, you become subject to various status challenges, and may be held responsible for the decisions you make. It's often easier to remain low status and let others make the decisions.

But there's still something odd about saying that one would "prefer to be low status", at least in the sense in which we usually use the term. Intuitively, a person may be happy being low status in the sense of not being dominant, but most people are still likely to desire something that feels kind of like status in order to be happy. Something like respect, and the feeling that others like them. And a lot of the classical "status-seeking behaviors" seem to be about securing the respect of others. In that sense, there seems to be something intuitive true in the "everyone is engaged in status games and wants to be higher-status" claim.

So I think that there are two different things that we call "status" which are related, but worth distinguishing.

1) General respect and liking. This is "something you have", and is not inherently zero-sum. You can achieve it by doing things that are zero-sum, like being the best fan fiction writer in the country, but you can also do it by things like being considered generally friendly and pleasant to be around. One of the lessons that I picked up from The Charisma Myth was that you can be likable by just being interested in the other person and displaying body language that signals your interest in the other person.

Basically, this is "do other people get warm fuzzies from being around you / hearing about you / consuming your work", and is not zero-sum because e.g. two people who both have great social skills and show interest in you can both produce the same amount of warm fuzzies, independent of each other's existence.

But again, specific sources of this can be zero-sum: if you respect someone a lot for their art, but then run across into even better art and realize that the person you previously admired is pretty poor in comparison, that can reduce the respect you feel for them. It's just that there are also other sources of liking which aren't necessarily zero-sum.

2) Dominance and control of the group. It's inherently zero-sum because at most one person can have absolute say on the decisions of the group. This is "something you do": having the respect and liking of the people in the group (see above) makes it easier for you to assert dominance and makes the others more willing to let you do so, but you can also voluntarily abstain from using that power and leave the decisions to others. (Interestingly, in some cases this can even increase the extent to which you are liked, which translates to a further boost in the ability to control the group, if you so desired.)

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Morendil and I previously suggested a definition of status as "the general purpose ability to influence a group", but I think that definition was somewhat off in conflating the two senses above.

I've always had the vague feeling that the "everyone can't always be happy because status is zero-sum" claim felt off in some sense that I was unable to properly articulate, but this seems to resolve the issue. If this model were true, it would also make me happy, because it would imply that we can avoid zero-sum status fights while still making everybody content.

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