This is an early pre-review preprint of a paper published in Physica Scripta Vol. 92, No. 11 (Focus Issue on 21st Century Frontiers); it does not reflect the changes made during review. For the most recent preprint, see the version on the author's website.
First written: Sep. 2016
What kinds of fundamental limits are there in how capable artificial intelligence (AI) systems might become? Two questions in particular are of interest: 1) How much more capable could AI become relative to humans, and 2) how easily could superhuman capability be acquired? To answer these questions, I will consider the literature on human expertise and intelligence, discuss its relevance for AI, and consider how AI could improve on humans in two major aspects of thought and expertise, namely mental simulation and pattern recognition. I find that although there are very real limits to prediction, it seems like AI could still substantially improve on human intelligence, possibly even mastering domains which are currently too hard for humans. In practice, the limits of prediction do not seem to pose much of a meaningful upper bound on AI’s capabilities, nor do we have any nontrivial lower bounds on how much time it might take to achieve a superhuman level of capability. Scenarios with AI systems becoming major or even dominant actors within timescales on the order of mere days or weeks seem to remain within the range of plausibility.
- The development of human expertise
- Implications for AI
Since Turing (1950), the dream of artificial intelligence (AI) research has been the creation of a “machine that could think”. While current expert consensus believes the creation of such a system to still take several decades if not more (Müller & Bostrom 2016), recent progress in AI has still raised worries about the challenges involved with increasingly capable AI systems (Future of Life Institute 2015, Amodei et al. 2016).
In addition to the risks posed by near-term developments, there is the possibility of AI systems eventually reaching superhuman levels of intelligence, eventually breaking out of human control (Bostrom 2014). Various research agendas and lists of research priorities have been suggested for managing the challenges that this level of capability would pose to society (Soares & Fallenstein 2014, Russell et al. 2015, Amodei et al. 2016, Taylor et al. 2016).
For managing the challenges presented by increasingly capable AI systems, one needs to know how capable those systems might ultimately become, and how quickly. If AI systems can rapidly achieve strong capabilities, becoming powerful enough to take control of the world before any human can react, then that implies a very different approach than one where AI capabilities develop gradually over many decades, never getting substantially past the human level (Sotala & Yampolskiy, 2015). We might phrase these questions as:
- How much more capable can AIs become relative to humans?
- How easily (in terms of needed time and resources) could superhuman capability be acquired?
Views on these questions vary. Authors such as Bostrom 2014 and Yudkowsky (2008) argue for the possibility of a fast leap in intelligence, with both offering hypothetical example scenarios where an AI rapidly acquires a dominant position over humanity. On the other hand, Anderson (2010) and Lawrence (2016) appeal to fundamental limits on predictability – and thus intelligence – posed by the complexity of the environment. Lawrence writes:
‘Practitioners who have performed sensitivity analysis on time series prediction will know how quickly uncertainty accumulates as you try to look forward in time. There is normally a time frame ahead of which things become too misty to compute any more. Further computational power doesn’t help you in this instance, because uncertainty dominates. Reducing model uncertainty requires exponentially greater computation. We might try to handle this uncertainty by quantifying it, but even this can prove intractable.
So just like the elusive concept of infinite precision in mechanical machining, there is likely a limit on the degree to which an entity can be intelligent. We cannot predict with infinite precision and this will render our predictions useless on some particular time horizon.
The limit on predictive precision is imposed by the exponential growth in complexity of exact simulation, coupled with the accumulation of error associated with the necessary abstraction of our predictive models. As we predict forward these uncertainties can saturate dominating our predictions. As a result we often only have a very vague notion of what is to come. This limit on our predictive ability places a fundamental limit on our ability to make intelligent decisions.’
We might summarize this as saying that, past a certain point, increased intelligence is only of limited benefit, for the unpredictability of the environment means that you would have to spend exponentially more resources to evaluate a vastly increasing amount of possibilities.
Noise also accumulates over time, reducing the reliability of your models. For many kinds of predictions, increasing the prediction window would require an exponential increase in the amount of measurements (Martela 2016). For instance, weather models become increasingly uncertain when projected farther out in time. Forecasters can only access a limited amount of observations relative to the weather system’s degrees of freedom, and any initial imprecisions will magnify over time and cause the accuracy to deteriorate (Buizza, 2002). The accuracy of any long-term weather prediction will thus always be bounded by the number of available data points. Similar considerations could also apply to attempts to predict things such as the behavior of human societies.
When models being plagued both by the exponentially increasing amount of complexity and also the exponentially increasing amount of noise, the advantage that even a superhuman intelligence might have over humans may be limited.
On the other hand, it is not obvious whether this point of view really is in conflict with the assumption of AI being able to quickly grow to become powerful. There being limits to prediction does not imply that humans would be particularly close to the limits, nor that it would necessarily take a great amount of time to move from sub-human to superhuman capability.
This article attempts to consider these questions by considering what we know about expertise and intelligence. After reviewing the relevant research on human expertise, I will discuss its relevance for AI, and consider how AI could improve on humans in two major aspects of thought and expertise, namely mental simulation and pattern recognition. My current conclusion is that although the limits to prediction are real, it seems like AI could still substantially improve on human intelligence, possibly even mastering domains which are currently too hard for humans. The possibility of AI developing significant real-world capabilities in a relatively brief time seems like one that cannot be ruled out.
The development of human expertise
Ideally, we might turn to theoretical AI research for a precise theory about acquiring cognitive capabilities. Unfortunately AI research is not at this point yet. Instead we will consider the research on human expertise and decision-making.
Expertise as mental representations
There exists a preliminary understanding, if not of the details of human decision-making, then at least the general outline. A picture that emerges from this research is that expertise is about developing the correct mental representations (Klein 1999; Ericsson & Pool, 2016).
A mental representation is a very general concept. In the words of expertise researcher Anders Ericsson (Ericsson & Pool, 2016):
‘A mental representation is a mental structure that corresponds to an object, an idea, a collection of information, or anything else, concrete or abstract, that the brain is thinking about. A simple example is a visual image. Mention the Mona Lisa, for instance, and many people will immediately ‘see’ an image of the painting in their minds; that image is their mental representation of the Mona Lisa. Some people’s representations are more detailed and accurate than others, and they can report, for example, details about the background, about where Mona Lisa is sitting, and about her hairstyle and her eyebrows.‘
Domain-specific mental representations are important because they allow experts to know what something means; know what to expect; know what good performance should feel like; know how to achieve the good performance; know the right goals for a given situation; know the steps necessary for achieving those goals; mentally simulate how something might happen; learn more detailed mental representations for improving their skills (Klein, 1999; Ericsson & Pool, 2016).
Although good decision-making is often thought of as a careful deliberation of all the possible options, such a type of thinking tends to be typical of novices (Klein, 1999). A novice will have to try to carefully reason their way through to an answer, and will often do poorly regardless, because they do not know what things are relevant to take into account and which ones are not. An expert doesn’t need to – they are experienced enough to instantly know what to do.
A specific model of expertise is the Recognition-Primed Decision-Making (RPD) model (Klein, 1999). First, a decision-maker sees some situation, such as a fire for a firefighter or a design problem for an architect. The situation may then be recognized as familiar, such as a typical garage fire. Recognizing a familiar situation means understanding what goals make sense and what should be focused on, which cues to pay attention to, what to expect next and when a violation of expectations shows that something is amiss, and knowing what the typical ways of responding are. Ideally, the expert will instantly know what to do.
If the situation is unfamiliar, then the expert may need to construct a mental simulation of what is going on, how things might have developed to this point, and what effect different actions would have. For example, a firefighter thinking about how to rescue someone from a difficult spot might mentally simulate where different rescue harnesses might be attached on the person, and whether that would exert dangerous amounts of force on them.
Mental representations are necessary for a good simulation, as they let the expert know what things to take into account, what things could plausibly be tried, and what effects they would have. In the example, the firefighter’s knowledge allows him to predict that specific ways of attaching the rescue harness would have dangerous consequences, while others are safe.
Developing mental representations
Mental representations are developed through practice. A novice will try out something and see what happens as a result. This gives them a rough mental representation and a prediction of what might happen if they try the same thing again, leading them to try out the same thing again or do something else instead.
Just practice isn’t enough, however – there also needs to be feedback. Someone may do a practice drill over and over again and think that they are practicing and thus improving – but without some sign of how well that is going, they may just keep repeating the same mistakes over and over (Ericsson & Pool, 2016).
The importance of quality feedback is worth emphasizing. Skills do not develop unless there is feedback that is conducive to developing better mental representations. In fact, there are entire fields in which experienced practitioners are not much better than novices, because the field does not provide them with enough feedback. Shanteau (1992) provides the following breakdown of professions for which there is agreement on the nature of their performance:
|Good performance||Bad performance|
|Weather Forecasters||Clinical Psychologists|
|Test Pilots||Student Admissions|
|Soil Judges||Court Judges|
|Chess Masters||Behavioral Researchers|
|Grain Inspectors||Polygraph (Lie Detector) Judges|
|Photo Interpreters||Intelligence Analysts|
|Insurance Analysts||Stock Brokers|
In analyzing why some domains enable the development of genuine expertise and others don’t, Shanteau identified a number of considerations that relate to the nature of feedback. In an occupation like weather forecasting, the criteria you use for forecasting are always the same; you will always be facing the same task and can practice it over and over; you get quick and feedback on whether your prediction was correct; you can use formal tools to analyze what you predicted would happen and why that prediction did or didn’t happen; and things can be analyzed in objective terms. This allows weather forecasters to develop powerful mental representations that get better and better at making the correct prediction.
Contrast this with someone like an intelligence analyst. The analyst may be called upon to analyze very different clues and situations; each of the tasks may be unique, making it harder to know which lessons from previous tasks apply; for many of the analyses, one might never know whether they were right or not; and questions about socio-cultural matters tend to be much more subjective than questions about weather, making objective analysis impossible. In short, for much of the work that the analyst does, there is simply no feedback available to tell whether the analyst has made the right judgment or not. And without feedback, there is no way to improve one’s mental representations, and thus expertise.
A slightly different look on expertise is the heuristics & biases literature, which frequently portrays even experts as being easily mistaken. In contrast, the expertise literature that we have reviewed so far has viewed experts as being typically capable and as having trustworthy intuition. Kahneman & Klein (2009) make an attempt to reconcile the two fields, and come to agree that:
- Expert intuition may be trustworthy, if the intuition relates to a ‘high-validity’ domain and the expert has had a chance to learn the regularities in that domain.
- A domain is ‘high-validity’ if ‘there are stable relationships between objectively identifiable cues and subsequent events or between cues and the outcomes of possible actions’.
- Medicine and firefighting have fairly high validity, whereas predictions of the future value of individual stocks and long-term1 forecasts of political events are domains with practically zero validity.
- ‘Some [domains] are both highly valid and substantially uncertain. Poker and warfare are examples. The best moves in such situations reliably increase the potential for success.’
- ‘[A domain] of high validity is a necessary condition for the development of skilled intuitions. Other necessary conditions include adequate opportunities for learning the [domain] (prolonged practice and feedback that is both rapid and unequivocal). If [a domain] provides valid cues and good feedback, skill and expert intuition will eventually develop in individuals of sufficient talent. ‘
This consensus is in line with what we have covered so far, though it also includes the consideration of validity. One cannot learn mental representations that would predict a domain or dictate the right actions for different situations in a domain, if that domain is simply too complicated or chaotic to be predicted. Kahneman & Klein provide the following illustrative example of a domain simply being impossible to predict:
‘When Tetlock […] embarked on his ambitious study of long-term forecasts of strategic and economic events by experts, the outcome of his research was not obvious. Fifteen years later it was quite clear that the highly educated and experienced experts that he studied were not superior to untrained readers of newspapers in their ability to make accurate long-term forecasts of political events. The depressing consistency of the experts’ failure to outdo the novices in this task suggests that the problem is in the environment: Long-term forecasting must fail because large-scale historical developments are too complex to be forecast. The task is simply impossible. A thought experiment can help. Consider what the history of the 20th century might have been if the three fertilized eggs that became Hitler, Stalin, and Mao had been female. The century would surely have been very different, but can one know how?’
Meanwhile, practice does help in more predictable domains. A recent meta-analysis (Macnamara, Hambrick, & Oswald, 2014) on the effects of practice on skill found that the more predictable an activity was, the more practice contributed to performance in that activity.
Implications for AI
Having reviewed some necessary background, we will now finally get back to the topic of superintelligence capabilities.
Relevance for AI
Similarly to humans, AI systems cannot reach intelligent conclusions by a mere brute force calculation of every possibility. Rather, an intelligence needs to learn to exploit predictable regularities in the world in order to develop further. All machine learning based systems are based on this principle: they can be said to learn a ‘mental’ representation of the world, analogous to the way humans do.
A strong reason to expect that AI systems will also end up developing roughly human-like mental representations for carrying out different tasks is that the representations of human experts are in a sense an optimal solution to the problems at hand. A human expert will have learned to identify the smallest set of cues that will let them know how to act in a certain situation; their mental representations encode information about how to choose the correct actions using the least amount of thought (Klein 1999).
Machine learning also tries to focus its analysis on exactly the right number of cues that will provide the right predictions, ignoring any irrelevant information. Traditional machine learning approaches have relied extensively on feature engineering, a labor-intensive process where humans determine which cues in the data are worth paying attention to.
A major reason behind the recent success of deep learning models is their capability for feature learning or representation learning: being able to independently discover high-level features in the data which are worth paying attention to, without (as much) external guidance (Bengio, Courville, & Vincent, 2012). Being able to identify and extract the most important features of the data allows the system to make its decisions based on the smallest amount of cues that allows it to reach the right judgment – just as human experts learn to identify the most relevant cues in the situations that they encounter.
Finally, the aspect of increasingly detailed mental representations giving an expert a yardstick to compare their performance against (Ericsson & Pool 2016) has an analogue in reinforcement learning methods. In deep reinforcement learning, a deep learning model learns to estimate how valuable a specific state of the world is, after which the system takes actions to move the world towards that state (Mnih et al., 2015). Similarly, a human expert comes to learn that specific states (e.g. a certain feeling in the body when diving) are valuable, and can then increasingly orient their behavior so as to achieve this state.
In summary, both human experts and current state-of-the-art AI systems use mental representations as the building blocks of their expertise. As there have been no serious alternative accounts presented of how expertise might work, I will assume that the capabilities of hypothetical superintelligences will depend on them developing the correct mental representations.
This paper set out to consider two main questions:
- How much more capable can AIs become relative to humans?
- How easily (in terms of needed time and resources) could superhuman capability be acquired?
Let us now return to these.
The argument for an AI’s predictive capabilities being limited was that there are limits to prediction, and that predicting events an ever-increasing amount forward in time requires exponential reasoning power as well as measurement points, quickly becoming intractable. How capable could an AI become despite these two points?
The components of human expertise might be roughly divided into two: building up a battery of accurate mental representations, and being able to use them for mental simulations. Similarly, approaches to artificial intelligence can roughly be divided into pattern recognition and model-building (Lake, Ullman, Tenenbaum, & Gershman, 2016), depending on whether patterns in data or models of the world are treated as the primary unit of thought.
As this kind of a distinction seems to emerge both from psychology and AI research, I will assume that an AI’s expertise will also involve acquiring mental representations (or equivalently, doing pattern recognition) as well as accurately using them in mental simulations. We will consider these two separately.
An interesting look at the potential benefits offered by improved mental simulation ability come from looking at Philip Tetlock’s Good Judgement Project (GJP), popularized in the book Superforecasting (Tetlock & Gardner, 2015).2 Participating in a contest to forecast the probability of various events, the best GJP participants – the so-called ‘superforecasters’ – managed to make predictions whose accuracy outperformed those of professional intelligence analysts working with access to classified data.3 This is particularly interesting as the superforecasters had no particular domain expertise in answering most of the questions, with sample questions including ones such as
- Will North Korea launch a new multistage missile before May 10, 2014?
- Will Russian armed forces enter Kharkiv, Ukraine, by May 10, 2014?
- Will there be a significant attack on Israeli territory before May 10, 2014?
- Will Robert Mugabe cease to be President of Zimbabwe by September 30, 2011?
- Will Greece remain a member of the EU through June 1, 2012?
Tetlock & Gardner report the superforecasters’ accuracy in terms of Brier score, which is a scale between 0 and 2, with 0.5 indicating random guessing.4 On this scale, superforecasters had a score of 0.25 at the end of GJP’s first year, compared to 0.37 of the other forecasters participating in the project. By the end of the second year, superforecasters had improved their Brier score to 0.07 (Mellers et al., 2014). Superforecasters could also project further out in time: their accuracy at making predictions 300 days out was better as the other forecasters’ accuracy at making predictions 100 days out. In terms of being on the right side of 50/50, GJP’s best wisdom-of-the-crowd algorithms (deriving an overall prediction from the different forecasters’ predictions) delivered a correct prediction on 86% of all daily forecasts (Tetlock, Mellers, & Rohrbaugh, 2014).
The superforecasters’ success relied on a number of techniques, but a central one was the ability to consider and judge the relevance of a number of factors that might cause a prediction to become true or false. Tetlock & Gardner illustrate this technique by discussing how a superforecaster, Bill Flack, approached the question of whether an investigation of Yasser Arafat’s remains would reveal traces of polonium, suggestive of Arafat having been poisoned by Israel:
‘Bill unpacked the question by asking himself ‘What would it take for the answer to be yes? What would it take for it to be no?’ He realized that the first step of his analysis had nothing to do with politics. Polonium decays quickly. For the answer to be yes, scientists would have to be able to detect polonium on the remains of a man dead for years. Could they? A teammate had posted a link to the Swiss team’s report on the testing of Arafat’s possessions, so Bill read it, familiarized himself with the science of polonium testing, and was satisfied that they could do it. Only then did he move on to the next stage of the analysis.
Again, Bill asked himself how Arafat’s remains could have been contaminated with enough polonium to trigger a positive result. Obviously, ‘Israel poisoned Arafat’ was one way. But because Bill carefully broke the question down, he realized there were others. Arafat had many Palestinian enemies. They could have poisoned him. It was also possible that there had been ‘intentional postmortem contamination by some Palestinian faction looking to give the appearance that Israel had done a Litvinenko on Arafat,’ Bill told me later. These alternatives mattered because each additional way Arafat’s body could have been contaminated with polonium increased the probability that it was. Bill also noted that only one of the two European teams had to get a positive result for the correct answer to the question to be yes, another factor that nudged the needle in that direction. […]
… there were several pathways to a ‘yes’ answer: Israel could have poisoned Arafat; Arafat’s Palestinian enemies could have poisoned him; or Arafat’s remains could have been contaminated after his death to make it look like a poisoning. Hypotheses like these are the ideal framework for investigating the inside view.
Start with the first hypothesis: Israel poisoned Yasser Arafat with polonium. What would it take for that to be true?
- Israel had, or could obtain, polonium.
- Israel wanted Arafat dead badly enough to take a big risk.
- Israel had the ability to poison Arafat with polonium.
Each of these elements could then be researched—looking for evidence pro and con—to get a sense of how likely they are to be true, and therefore how likely the hypothesis is to be true. Then it’s on to the next hypothesis. And the next. ‘
Tetlock does not go into detail about the prerequisites for being able to carry out such analysis – other than noting that it’s slow and effortful – but there are some considerations that seem like plausible prerequisites. First, a person needs to have enough general knowledge to generate different possibilities for how an event could have come true. Next, they need the ability to analyze and investigate those possibilities further, either personally acquiring the relevant domain knowledge for evaluating their plausibility, or finding a relevant subject matter expert. In this example, Bill familiarized himself with the science of polonium testing until he was satisfied that it would be possible to detect polonium traces from a long time ago.
This suggests a general procedure which an AI could also follow in order to predict the possibility of something in which it does not yet have expertise. An AI that was trying to predict the outcome of some specific question could work tap into its existing general knowledge in an attempt to identify relevant causal factors; if it failed to generate them, it could look into existing disciplines which seemed relevant for the question. For each identified possibility, it could branch off a new subprocess to do research into that particular direction, sharing information as necessary with a main process whose purpose was to integrate the insights derived from all the relevant searches.
Such a capability for several parallel streams of attention could provide a major advantage. A human researcher or forecaster who branches off to do research on a subquestion will need to make sure that they don’t lose track of the big picture, and needs to have an idea of whether they are making meaningful progress on that subquestion and whether it would be better to devote attention to something else instead. To the extent that there can be several parallel streams of attention, these issues can be alleviated, with a main stream focusing on the overall question and substreams on specific subpossibilities.
How much could this improve on human forecasters? Forecasters performed better when they were placed on teams where they shared information between each other, which similarly allowed an extent of parallelism in prediction-making, in that different forecasters could pursue their own angles and directions in exploring the problem. The differences between individual forecasters and teams of forecasters with comparable levels of training ranged between 0.05 and 0.10 Brier points at the end of the first year, and between 0.02 and 0.08 Brier points at the end of the second year (Mellers et al., 2014). In humans however, it seems likely that the extent of parallelism was constrained by the fact that each forecaster had to independently familiarize themselves with much of the same material, and that their ability to share knowledge between each other was limited by the speed of writing and reading. This suggests a possibility for further improvement.
|Example: parallel streams of attention with a LIDA-like architecture
How could different streams of attention within an AI share information between each other? Recall that we have defined the development of expertise as the ability to accumulate mental patterns which are used to identify relevant cues and to indicate what predictions should be derived out of those. A computational model for attention and consciousness is Global Workspace Theory (Baars, 2002; 2005), of which a particular AI implementation is the LIDA model (Franklin & Patterson, 2006; Franklin, Madl, D’Mello, & Snaider, 2014; Madl, Franklin, Chen, Montaldi, & Trappl, 2016). LIDA is a model of the mind that is inspired by psychological and neuroscientific research and attempts to capture its main mechanisms. We can use LIDA to get a rough example of what having several ‘streams of attention’ would mean, and how information could be exchanged between them.
LIDA works by means of an understand-attend-act cycle. In each cycle, low-level sensory information is initially interpreted so as to associate it with higher-level concepts to form a ‘percept’, which is then sent to a workspace. In the workspace, the percept activates further associations in other memory systems, which are combined with the percept to create a Current Situational Model, an understanding of what is going on at this moment.
The entirety of the Current Situational Model is likely to be too complex for the agent to process, so it needs to select a part of it to elevate to the level of conscious attention to be acted upon. This is carried out using ‘attention codelets’, small pieces of code that attempt to train attention on some particular piece of information, each with their own set of concerns of what is important. Attention codelets with matching concerns form coalitions of what to attend, competing against other coalitions. Whichever coalition ends up winning the competition will have its chosen part of the Current Situational Model ‘become conscious’, broadcast to the rest of the system, and particularly Procedural Memory.
The Procedural Memory holds schemes, or templates of different actions that can be taken in different contexts. Schemes which include a context or an action that matches the contents of the conscious broadcast become available as candidates for possible actions. They are copied to the Action Selection mechanism, which chooses a single action to perform. The selected action is further sent to Sensory-Motor Memory, which contains information of how exactly to perform the action. The outcome of taking this action manifests itself as new sensory information, beginning the cognitive cycle anew.
Here is a description of how this process – or something like it – might be applied in the case of an AI seeking to predict the outcome of a specific question, such as the ‘will Saudi Arabia agree to oil production cuts’ question discussed below. The decision to consider this question has been made in an earlier cognitive cycle, and information relevant to it is now available in the inner environment and the Current Situational Model. The concepts of Saudi Arabia and oil production trigger several associations in the AI’s memory systems, such as the fact that oil prices will affect Saudi Arabia’s financial situation, and that oil prices are also influenced by other factors such as global demand. Two coalitions of attention codelets might form, one focusing on the current financial situation and another on influences on oil prices.
In LIDA, these codelets would normally compete, and one of them would win and trigger a specific action, such as a deeper investigation of Saudi Arabia’s financial situation. In our hypothetical AI however, it might be enough that both coalitions manage to exceed some threshold level of success, indicating them both to be potentially relevant. In that case, new instances of the Procedural Memory, Action Selection and Sensory-Motor Memory mechanisms might be initialized, with one coalition sending its contents to the first set of instances and the other to another. These streams could then independently carry out searches of the information that was deemed relevant, also having their own local Situational Models and Workspaces focusing on content relevant for this search. As they worked, these streams would update the various memory subsystems with the results of their learning, making new associations and attention codelets available to all attentional streams. Their functioning could be supervised by a general high-level attention stream, whose task was to evaluate the performance of the various lower-level streams and allocate resources between them accordingly.
In general, accurate forecasting requires an ability to carry out sophisticated causal modeling about a variety of interacting factors. Tetlock & Gardner write:
‘The commentary that superforecasters post on GJP forums is rife with ‘on the one hand/ on the other’ dialectical banter. And superforecasters have more than two hands. ‘On the one hand, Saudi Arabia runs few risks in letting oil prices remain low because it has large financial reserves,’ wrote a superforecaster trying to decide if the Saudis would agree to OPEC production cuts in November 2014. ‘On the other hand, Saudi Arabia needs higher prices to support higher social spending to buy obedience to the monarchy. Yet on the third hand, the Saudis may believe they can’t control the drivers of the price dive, like the drilling frenzy in North America and falling global demand. So they may see production cuts as futile. Net answer: Feels no-ish, 80%.’ (As it turned out, the Saudis did not support production cuts— much to the shock of many experts.) […] Superforecasters pursue point-counterpoint discussions routinely, and they keep at them long past the point where most people would succumb to migraines.’
This suggests that an AI with sufficient hardware capability could achieve considerable prediction ability by its capability to explore many different perspectives and causal factors at once. The mental simulations of humans tend to be limited to around three causal factors and six transition states (Klein, 1999). The discussion of the superforecasters clearly brought up many more possibilities, and their accuracy suggests moderate ability to integrate all those factors together. Yet comments such as ‘feels no-ish’ suggests that they still couldn’t construct a full-blown mental simulation in which the various causal factors would have influenced each other based on principled rules which could be inspected, evaluated, and revised based on feedback and accuracy. This seems especially plausible given that Klein speculates the limits in the size of human mental simulations to come from working memory limitations.
AI systems with larger working memory capacities might be able to construct much more detailed simulations. Contemporary computer models can involve simulations with thousands or tens of thousands variables, though flexibly incorporating diverse mental representations into a single simulation will probably take considerably more memory and computing power than what is used in today’s models.
These simulations do not necessarily need to incorporate an exponentially increasing number of variables in order to achieve better prediction accuracy. As previously noted, superforecasters were more accurate at making predictions 300 days out than the rest of the forecasters in GJP were at making predictions 100 days out. Given that at least some of the superforecasters only used a few hours a day on making their predictions, and that they had many predictions to rate, they probably did not consider a vastly larger amount of factors than the rest of the forecasters.
Klein (1999) offers an example of a professor who used three causal factors (the rate of inflation, the rate of unemployment, and the rate of foreign exchange) and a few transitions to relatively accurately simulate how the Polish economy would develop in response to the decision to convert from socialism to a market economy. In contrast, less sophisticated experts could only name two variables (inflation and unemployment) and not develop any simulations at all, basing their predictions mostly on their ideological leanings.
Having large explicit models also allows for the models to be adjusted in response to feedback. The excerpt below describes how the professor expected unemployment to develop, and how it actually developed:
‘If the government had the courage to drop unproductive industries, many people would lose their jobs. This would start in about six months as the government sorted things out. The unemployment would be small by U.S. standards, rising from less than 1 percent to maybe 10 percent. For Poland, this increase would be shocking. Politically, it might be more than the government could tolerate and might force it to end the experiment with capitalism. When we reviewed his estimates, we found that unemployment had not risen as quickly as he expected, probably, Andrzej believed, because the government was not as ruthless as it said it would be in closing unproductive plants. Even worse, if a plant was productive in areas A, B, and C and was terrible in D and E, then as long as they made a profit, they continued their operations without shutting down areas D and E. So the system faced a built-in resistance to increased unemployment (Klein, 1999).’
In this example, the model failed to predict the government’s caution, which could then be added as an additional variable to consider for the next model. The addition of this variable alone might then considerably increase the accuracy of the simulation.
Tetlock & Gardner report that the superforecasters used highly granular probability estimates – carefully thinking about whether the probability of an event was 3% as opposed to 4%, for instance – and that the granularity actually contributed to accuracy, with the predictions getting less accurate if they were rounded to the closest 5%. Given that such granularity was achieved by integrating various possibilities and considerations, it seems like an ability to consider and integrate an even larger amount of possibilities might provide even increased granularity, and thus a prediction edge.
In summary, an AI could be able to run vastly larger mental simulations than humans could, with this possibility being subject to computing power limitations; given this, its simulations could also be explicit, allowing it to adjust and correct them in response to feedback to provide improved prediction accuracy; and it could have several streams of attention running concurrently and sharing information between each other. Existing evidence from human experts suggests that large increases to prediction capability might not necessarily need a large increase in the number of variables considered, and that even small increases can provide considerable additional gains.
Rate of capability growth
How fast could an AI develop the ability to run comprehensive and large mental simulations?5 Creating larger mental simulations than humans have access to seems to require extensive computational resources, either from hardware or optimized software. As an additional consideration, we have previously mentioned limited working memory restricting the capabilities of humans, but human working memory is not the same thing as RAM in computer systems. If one were running a simulation of the human brain in a computer, one could not increase the brain’s available working memory simply by increasing the amount of RAM the simulation had access to. Rather, it has been hypothesized that working memory differences between individuals may reflect things such as the ability to discriminate between relevant and irrelevant information (Unsworth & Engle, 2007), which could be related to things like brain network structure and thus be more of a software than a hardware issue.6 Yudkowsky (2013) notes that if increased intelligence would be a simple matter of scaling up the brain, the road from chimpanzees to humans would likely have been much shorter, as simple factors such as brain size can respond rapidly to evolutionary selection pressure.
Thus, advances in mental simulation size depend on i) hardware progress ii) advances in software engineering. Hardware progress in hard to predict, but advances in software engineering capabilities might be doable using mostly theoretical and mathematical research. This would require the development of expertise in mathematics, programming, and theoretical computer science.
Much of mathematical problem-solving is about having a library of procedures, reformulations, and heuristics that one can try (Polya, 1990), as well as developing a familiarity and understanding of many kinds of mathematical results, which one may then later on recognize as relevant. This seems like the kind of task that relies strongly on pattern-matching abilities, and might in principle be in reach by an advanced deep reinforcement learning system that was fed a sufficiently large library of heuristics and worked proofs to let it develop superhuman mathematical intuition.7 Modern-day theorem provers often know what kinds of steps are valid, but not which steps are worth taking; merging them with the ‘artificial intuition’ of deep reinforcement learning systems might eventually produce systems with superhuman mathematical ability.
Progress in this field could allow AI systems to achieve superhuman abilities in math research, considerably increasing their ability to develop more optimized software to take full advantage of the available hardware. To the extent that relatively small increases in the number of variables considered in a high-level simulation would allow for dramatically increased prediction ability (as is suggested by e.g. the superforecasters being better predictors with thrice the prediction horizon of less accurate forecasters), moderate increases in the size of the AI’s simulations could translate to drastic increases in terms of real-world capability.
Yudkowsky (2013) notes that although the evolutionary record strongly suggests that algorithmic improvements were needed for taking us from chimpanzees to humans, the record rules out exponentially increasing hardware always being needed for linear cognitive gains: the size of the human brain is only four times that of the chimpanzee brain. This further suggests that relatively limited improvements could allow for drastic increases in intelligence.
The capability to run large simulations isn’t enough by itself. The AI also needs to acquire a sufficiently large number of patterns to be included in the simulations, to predict how different pieces in the simulation behave.
When it comes to well-defined tasks, current AI systems excel at pattern recognition, being able to analyze vast amounts of data and build them into an overall model, finding regularities that human experts never would have. For instance, human experts would likely have been unable to anticipate that men who ‘like’ the Facebook page ‘Being Confused After Waking Up From Naps’ are more likely to be heterosexual (Kosinski, Stillwell, & Graepel, 2013). Similarly, the Go-playing AI AlphaGo, whose good performance against the expert player Lee Sedol could to a large extent be attributed to its built-up understanding of the kinds of board patterns that predict victory, managed to make moves that Go professionals watching the game considered creative and novel.
The ability to find subtle patterns in data suggests that AI systems might be able to make predictions in domains which humans currently consider impossible to predict. We previously discussed the issue of the (predictive) validity of a domain, with domains being said to have higher validity if ‘there are stable relationships between objectively identifiable cues and subsequent events or between cues and the outcomes of possible actions’ (Kahneman & Klein, 2009). A field could also be valid despite being substantially uncertain, with warfare and poker being listed as examples of fields that were valid (letting a skilled actor improve their average performance) despite also being highly uncertain (with good performance not being guaranteed even for a skilled actor).
We already know that the validity of a field also depends on an actor’s cognitive and technological abilities. For example, weather forecasting used to be a field in which almost no objectively identifiable cues were available, relying mostly on guesswork and intuition, but the development of modern meteorological theory made it a much more valid field (Shanteau, 1992). Thus, even fields which have low validity to humans with modern-day capabilities, could become more valid for more advanced actors.
A possible example of a domain that is currently relatively low-validity, but which could become substantially more valid, is that of predicting the behavior of individual humans. Machine learning tools can already generate personality profiles harvested from people’s Facebook ‘likes’ that are slightly more accurate than the profiles made by people’s human friends (Youyou et al. 2015), and can be used to predict private traits such as sexual orientation (Kosinski et al. 2013). This has been achieved using a relatively limited amount of data and not much intelligence; a more sophisticated modeling process could probably make even better predictions from the same data.
Taleb (2007) has argued for history being strongly driven by ‘black swan’ events, events with such a low probability that they are unanticipated and unprepared for, but which have an enormous impact on the world. To the extent that this is accurate, it suggests limits on the validity of prediction. However, Tetlock & Gardner (2015) argue that while the black swans themselves may be unanticipated, once the event has happened its consequences may be much easier to predict. Commenting on the notion of the 9/11 terrorist attacks as a black swan event, they write:
‘We may have no evidence that superforecasters can foresee events like those of September 11, 2001, but we do have a warehouse of evidence that they can forecast questions like: Will the United States threaten military action if the Taliban don’t hand over Osama bin Laden? Will the Taliban comply? Will bin Laden flee Afghanistan prior to the invasion? To the extent that such forecasts can anticipate the consequences of events like 9/ 11, and these consequences make a black swan what it is, we can forecast black swans.’
Thus, even though an AI might be unable to predict some very rare events, once those events have happened, it could utilize its built-up knowledge of how people typically react to different events in order to predict the consequences better than anyone else.
Rates of capability growth
How quickly could an AI acquire more knowledge and mental representations? Here again opinions differ. Hibbard (2016) argues, based on Mahoney’s (2008) argument for intelligence being a function of both resources and knowledge, that explosive growth is unlikely. Benthall (2017) makes a similar argument. On the other hand, authors such as Bostrom (2014) and Yudkowsky (2008) suggesting the possibility for fast increases.
How to improve learning speed?
We know that among humans, there are considerable differences in the extent to which people learn. Human cognitive differences have a strong neural and genetic basis (Deary, Penke, & Johnson, 2010), and strongly predict academic performance (Deary et al., 2007), socio-economic outcomes (Strenze, 2007), and job performance and the effectiveness of on-the-job learning and experience (Gottfredson, 1997). There also exist child prodigies who before adolescence achieve a level of performance comparable to an adult professional, without having been able to spend comparable amounts of time training (Ruthsatz, Ruthsatz, & Stephens, 2013). In general, some people are able to learn faster from the same experiences, notice relevant patterns faster, and continue learning from experience even past the point where others cease to achieve additional gains.8
While there is so far no clear consensus on why some people learn faster than others, there are some clear clues. Individual differences in cognitive abilities may be a result of differences in a combination of factors, such as working memory capacity, attention control, and long-term memory (Unsworth et al., 2014). Ruthsatz et al. (2013), in turn, note that ‘child prodigies’ skills are highly dependent on a few features of their cognitive profiles, including elevated general IQs, exceptional working memories, and elevated attention to detail‘.
Many tasks require paying attention to many things at once, with a risk of overloading the learner’s working memory before some of the performance has been automated. For an example, McPherson & Renwick (2001) consider children who are learning to play instruments, and note that children who had previously learned to play another instrument were faster learners. They suggest this to be in part because the act of reading musical notation had become automated for these children, saving them from the need to process notation in working memory and allowing them to focus entirely on learning the actual instrument.
This general phenomenon has been recognized in education research. Complex activities that require multiple subskills can be hard to master even if the students have moderate competence in each individual subskill, as using several of them at the same time can produce an overwhelming cognitive load (Ambrose et al. 2010, chap. 4). Recommended strategies for dealing with this include reducing the scope of the problem at first and then building up to increasingly complex scopes. For instance, ‘a piano teacher might ask students to practice only the right hand part of a piece, and then only the left hand part, before combining them‘ (ibid).
An increased working memory capacity, which is empirically associated with faster learning capabilities, could theoretically assist in learning in allowing more things to be comprehended simultaneously without them overwhelming the learner. Thus, an AI with a large working memory could learn and master at once much more complicated wholes than humans.
Additionally, we have seen that a key part of efficient learning is the ability to monitor one’s own performance and to notice errors which need correcting; this seems in line with cognitive abilities correlating with attentional control and elevated attention to detail. McPherson & Renwick (2001) also remark on the ability of some students to play through a piece with considerably fewer errors on their second run-through than the first one, suggesting that this indicates ‘an outstanding ability to retain a mental representation of […] performance between run-throughs, and to use this as a basis for learning from […] errors‘. In contrast, children who learned more slowly seemed to either not notice their mistakes, or alternatively to not remember them when they played the piece again.
Whatever the AI analogues of working and long-term memory, attentional control, and attention to detail are, it seems at least plausible that these could be improved upon by drawing exclusively on relatively theoretical research and in-house experiments. This might enable an AI to both absorb vast datasets, as current-day deep learning systems do, and also learn from superhumanly small amounts of data.
Limits of learning speed
How much can the human learning speed be improved upon? This remains an open question. There are likely to be sharply diminishing returns at some point, but we do not know whether they are near the human level. Human intelligence seems constrained by a number of biological and physical factors that are unrelated to gains from intelligence. Plausible constraints include the size of the birth canal limiting the volume of human brains, the brain’s extensive energy requirements limiting the overall amount of cells, limits to the speed of signaling in neurons, an increasing proportion of the brain’s volume being spent on wiring and connections (rather than actual computation) as the number of neurons grows, and inherent unreliabilities in the operation of ion channels (Fox, 2011). There doesn’t seem to be any obvious reason for why the threshold for diminishing gains from intelligence to learning speed would just happen to coincide with the level of intelligence allowed by our current biology. Alternatively, there could have been diminishing returns all along, but ones which still made it worthwhile for evolution to keep investing in additional intelligence.
The available evidence also seems to suggest that within the human range at least, increased intelligence continues to contribute to additional gains. The Study of Mathematically Precocious Youth (SMPY) is a 50-year longitudinal study involving over 5,000 exceptionally talented individuals identified between 1972 and 1997. Despite its name, many its participants are more verbally than mathematically talented. The study has led to several publications; among others, Wai et al. (2005) and Lubinski & Benbow (2006) examine the question of whether ability differences within the top 1% of the human population make a difference in life.
Comparing the top (Q4) and bottom (Q1) quartiles of two cohorts within this study shows both to significantly differ from the ordinary population, as well as from each other. Out of the general population, about 1% will obtain a doctoral degree, whereas 20% of Q1 and 32% of Q4 did. 0.4% of Q1 achieved tenure at a top-50 US university, as did 3% of Q4. Looking at a 1 to 10,000 cohort, 19% had earned patents, as compared to 7.5% of the Q4 group, 3.8% of the Q1 group, or 1% of the general population.
It is important to emphasize that the evidence we’ve reviewed so far does not merely mean that an AI could potentially learn faster in terms of time: it also suggests that the AI could potentially learn faster in terms of training data. The smaller datasets an AI needs in order to develop accurate mental representations, the faster it can adapt to new situations.
However, learning faster in terms of time is also important. Various versions of AlphaGo were trained for maybe a year in total, whereas Lee Sedol had been playing professionally since 1995, with professional qualification requiring a considerable amount of intense training by itself. A twenty-fold advantage in learning speed could already provide for a major advantage, particularly when dealing with novel situations that humans have little previous experience of.
Besides the considerations we have already discussed, there seems to be potential for accelerated learning through more detailed analysis of experiences. For example, chess players improve most effectively by studying the games of grandmasters, and trying to predict what moves the grandmasters would have made in any situation. When the grandmaster play deviates from the move that the student would have made, the student goes back to try to see what they missed (Ericsson & Pool, 2016). This kind of detailed study is effortful however, and can only be sustained for limited amounts at a time. With enough computational resources, the AI could routinely run this kind of analysis on all sense data it received, constantly attempting to build increasingly detailed models and mental representations that would correctly predict the data.
How much interaction is needed?
Some commentators, such as Hibbard (2016) argue that knowledge requires interaction with the world, so the AI would be forced to learn over an extended period of time as the interaction takes time.
From our previous review, we know that feedback is needed for the development of expertise. However, one may also get feedback from studying static materials. As we noted before, chess players spend more time studying published matches and trying to predict the grandmaster moves – and then getting feedback when they look up the next move and have their prediction confirmed or falsified – than they do actually playing matches against live opponents (Ericsson & Pool, 2016). The Go-playing AlphaGo system did not achieve its skill by spending large amounts of time playing human opponents, but rather studying the games of humans and playing games against itself (Silver et al. 2016). And while any individual human can only study a single game at a time, AI systems could study a vast number of games in parallel and learn from all of them.9
An important difference is that domains such as chess and Go are formally specified domains, which an AI can perfectly simulate. For a domain such as social interaction, the AI’s ability to accurately simulate the behavior of humans is limited by its current competence in the domain. While it can run a simulation based on its existing model of human behavior, predicting how humans would behave based on that model, it needs external data in order to find out how accurate its prediction was.
This is not necessarily a problem however, given the vast (and ever-increasing) amount of recorded social interaction happening online. YouTube, e-mail lists, forums, blogs, and social media services all provide rich records of various kinds of social interaction, for an AI to test its predictive models against without needing to engage in interaction of its own. Scientific papers – increasingly available on an open access basis – on topics such as psychology and sociology offer additional information for the AI to supplement its understanding with, as do various guides to social skills. All of this information could be acquired simply by downloading it, with the main constraints being the time needed to find, download, and process the data, rather than time needed for social interactions.
As noted earlier, relatively crude statistical methods can already extract relatively accurate psychological profiles out of data such as people’s Facebook ‘likes’ (Kosinski et al., 2013, Youyou et al., 2015), giving reason to suspect that a general AI could develop very accurate predictive abilities given the kind of a process described above.
Several other domains, such as software security and mathematics seem similarly amenable to being mastered largely without needing to interact with the world outside the AI, other than searching for relevant materials. Some domains such as physics would probably need novel experiments, but an AI focusing on the domains that were the easiest and fastest for it to master might find sufficient sources of capability from those alone.
Given the above considerations, it does not seem to me like an AI’s speed of learning would necessarily be strongly interaction-constrained.
We set out to consider the fundamental practical limits of intelligence, and the limits to how quickly an AI system could acquire very high levels of capability.
Fictional representations of high intelligence often depict a picture of geniuses as masterminds who have an almost godlike prediction ability, laying out intricate multi-step plans where every contingency is planned for in advance (TVTropes 2017a). When discussing “superintelligent” AI systems, one might easily think that the discussion was postulating something along the lines of those fictional examples, and rightly reject it as unrealistic.
Given what we know about the limits of prediction, for AI to make a single plan which takes into account every possibility is surely impossible. However, having reviewed the science of human expertise, we have found that experts who are good at their domains tend to develop powerful mental representations which let them react to various situations as they arise, and to simulate different plans and outcomes in their heads.
Looking from humans to AIs, we have found that AI might be able to run much more sophisticated mental simulations than humans could. Given human intelligence differences and empirical and theoretical considerations about working memory being a major constraint for intelligence, the empirical finding that increased intelligence continues to benefit people throughout the whole human range, and the observation that it would be unlikely for the theoretical limits of intelligence to coincide with the biological and physical constraints that human intelligence currently faces, it seems like AIs could come to learn considerably faster from data than humans do. It also seems like in many domains, this could be achieved by using existing materials as a source of feedback for predictions, without necessarily being constrained by time taken for interacting with the external world.
Thus, it looks that even though an AI system couldn’t make a single superplan for world conquest right from the beginning, it could still have a superhuman ability to adapt and learn from changing and novel situations, and react to those faster than its human adversaries. As an analogy, experts playing most games can’t precompute a winning strategy right from the first move either, but they can still react and adapt to the game’s evolving situation better than a novice can, enabling them to win.10
Many of the hypothetical advantages – such as a larger working memory, the ability to consider more possibilities at once, and the ability to practice on many training instances in parallel – that AI might have seem to depend on available computing power. Thus the amount of hardware the AI had at its disposal could limit its capabilities, but there exists the possibility of developing better-optimized algorithms by initially specializing in fields such as programming and theoretical computer science, which the AI might become very good at.
One consideration which we have not yet properly addressed is the technology landscape at the time when the AI arrives (Tomasik 2014/2016, sec. 7). If a general AI can be developed, then various forms of sophisticated narrow AI will also be in existence. Some of them could be used to detect and react to a general AI, and tools such as sophisticated personal profiling for purposes of social manipulation will likely already be in existence. Considering how these influence the considerations discussed here is an important question, but one which is outside the scope of this article.
In summary, in practice the limits of prediction do not seem to pose much of a meaningful upper bound on AI’s capabilities. Even if AI could not create a complete master plan from scratch, it could still outperform humans in crucial domains, developing and using superior expertise than what humans were capable of. Aside for trivial limits derived from physical constraints, such as ‘the AI couldn’t become superhumanly capable literally instantly’, we also haven’t seen a way to establish a practical lower bound on how much time it would take for AI to achieve superhuman capability. Takeover scenarios with timescales on the order of mere days or weeks seem to remain within the range of plausibility.
Thank you to David Althaus, Stuart Armstrong, Bill Hibbard, David Krueger, Josh Marlow, Carl Shulman, and Brian Tomasik on helpful comments on this paper.
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Xanatos Gambit. (2017). TV Tropes. Retrieved March 20, 2017, from http://tvtropes.org/pmwiki/pmwiki.php/Main/XanatosGambit
Xanatos Speed Chess. (2017). TV Tropes. Retrieved March 20, 2017, from http://tvtropes.org/pmwiki/pmwiki.php/Main/XanatosSpeedChess
- Kahneman & Klein do not define what they mean by ‘long-term’, but geopolitical events up to a year or so away can be predicted with reasonable accuracy, with the accuracy falling towards chance for events 3 to 5 years away. (Tetlock & Gardner 2015, p. 5). (back)
- Except for when citations to other content are explicitly included, all the discussion about superforecasters and the Good Judgment Project uses Superforecasting as its source. (back)
- Though this claim needs to be treated with some caution, as no official information about the intelligence analysts’ performance has been published. The claim is based on Washington Post editor David Ignatius writing that ‘a participant in the project’ had told him that superforecasters had ‘performed about 30 percent better than the average for intelligence community analysts who could read intercepts and other secret data’ (Ignatius, 2013). The intelligence community has neither confirmed nor denied this statement, and Philip Tetlock has stated that he believes it to be true. (back)
- A version of the scale which ranges between 0 and 1 is also commonly used. (back)
- This section does not consider how fast the AI could develop the necessary mental representations to be used in the simulations. That question will be discussed in the next section. (back)
- Though it is worth noting that g does correlate to some extent with brain size, with a mean correlation of 0.4 in measurements that are obtained using brain imaging as opposed to external measurements of brain size (Rushton & Ankney, 2009). This would seem to suggest that the raw number of neurons and thus ‘general hardware capacity’ would also be relevant. (back)
- See Whalen (2016) for preliminary work in this direction. (back)
- Readers who are familiar with the ‘deliberate practice’ literature may wonder if that literature might not contradict these claims about the impact of intelligence. After all, the deliberate practice research suggests that talent is irrelevant, and that deliberate, well-supervised training is the only thing that matters. However, as noted by the field’s inventor, deliberate practice is a concept that is applicable to some very specific – one might even say artificial – domains:
‘[Deliberate practice] requires a field that is already reasonably well developed— that is, a field in which the best performers have attained a level of performance that clearly sets them apart from people who are just entering the field. We’re referring to activities like musical performance (obviously), ballet and other sorts of dance, chess, and many individual and team sports, particularly the sports in which athletes are scored for their individual performance, such as gymnastics, figure skating, or diving. What areas don’t qualify? Pretty much anything in which there is little or no direct competition, such as gardening and other hobbies, for instance, and many of the jobs in today’s workplace— business manager, teacher, electrician, engineer, consultant, and so on. These are not areas where you’re likely to find accumulated knowledge about deliberate practice, simply because there are no objective criteria for superior performance.’
(Ericsson & Pool, 2016)
Fields that have well-defined, objective criteria for good performance are ones which are the easiest to master using even current-day AI methods – in fact, they’re basically the only ones that can be truly mastered using current-day AI methods.
A somewhat cheeky way to summarize these results would be by saying that, in the kinds of fields that could be mastered without general intelligence, general intelligence isn’t the most important thing. This even seems to be Ericsson’s own theoretical stance: that in these fields, general intelligence eventually ceases to matter because the expert will have developed specialized mental representations that they can just rely on in every situation. So these results are not very interesting to us, who are interested in domains that do require general intelligence. (back)
- See Mnih et al. (2015) for a discussion of how incorporating parallel learning improves upon on modern deep learning systems. (back)
- This is to say, while we concluded that the fictional trope of a “Xanatos Gambit” (TVTropes 2017a) is unrealistic, the one of “Xanatos Speed Chess” (TVTropes 2017b) might be a much more accurate description of how a superintelligent AI actually acted. (back)