MIRI’s new, 93-page technical report by Eliezer Yudkowsky, “Intelligence Explosion Microeconomics,” has now been released. The report explains one of the open problems of our research program. Here’s the abstract:

I. J. Good’s thesis of the ‘intelligence explosion’ is that a sufficiently advanced machine intelligence could build a smarter version of itself, which could in turn build an even smarter version of itself, and that this process could continue enough to vastly exceed human intelligence. As Sandberg (2010) correctly notes, there are several attempts to lay down return-on-investment formulas intended to represent sharp speedups in economic or technological growth, but very little attempt has been made to deal formally with I. J. Good’s intelligence explosion thesis as such.

I identify the key issue as returns on cognitive reinvestment – the ability to invest more computing power, faster computers, or improved cognitive algorithms to yield cognitive labor which produces larger brains, faster brains, or better mind designs. There are many phenomena in the world which have been argued as evidentially relevant to this question, from the observed course of hominid evolution, to Moore’s Law, to the competence over time of machine chess-playing systems, and many more. I go into some depth on the sort of debates which then arise on how to interpret such evidence. I propose that the next step forward in analyzing positions on the intelligence explosion would be to formalize return-on-investment curves, so that each stance can say formally which possible microfoundations they hold to be falsified by historical observations already made. More generally, I pose multiple open questions of ‘returns on cognitive reinvestment’ or ‘intelligence explosion microeconomics’. Although such questions have received little attention thus far, they seem highly relevant to policy choices affecting the outcomes for Earth-originating intelligent life.

The preferred place for public discussion of this research is here. There is also a private mailing list for technical discussants, which you can apply to join here.

Singularity Hypotheses: A Scientific and Philosophical Assessment has now been published by Springer, in hardcover and ebook forms.

The book contains 20 chapters about the prospect of machine superintelligence, including 4 chapters by MIRI researchers and research associates.

“Intelligence Explosion: Evidence and Import” (pdf) by Luke Muehlhauser and (previous MIRI researcher) Anna Salamon reviews

the evidence for and against three claims: that (1) there is a substantial chance we will create human-level AI before 2100, that (2) if human-level AI is created, there is a good chance vastly superhuman AI will follow via an “intelligence explosion,” and that (3) an uncontrolled intelligence explosion could destroy everything we value, but a controlled intelligence explosion would benefit humanity enormously if we can achieve it. We conclude with recommendations for increasing the odds of a controlled intelligence explosion relative to an uncontrolled intelligence explosion.

“Intelligence Explosion and Machine Ethics” (pdf) by Luke Muehlhauser and Louie Helm discusses the challenges of formal value systems for use in AI:

Many researchers have argued that a self-improving artificial intelligence (AI) could become so vastly more powerful than humans that we would not be able to stop it from achieving its goals. If so, and if the AI’s goals differ from ours, then this could be disastrous for humans. One proposed solution is to program the AI’s goal system to want what we want before the AI self-improves beyond our capacity to control it. Unfortunately, it is difficult to specify what we want. After clarifying what we mean by “intelligence,” we offer a series of “intuition pumps” from the field of moral philosophy for our conclusion that human values are complex and difficult to specify. We then survey the evidence from the psychology of motivation, moral psychology, and neuroeconomics that supports our position. We conclude by recommending ideal preference theories of value as a promising approach for developing a machine ethics suitable for navigating an intelligence explosion or “technological singularity.”

“Friendly Artificial Intelligence” by Eliezer Yudkowsky is a shortened version of Yudkowsky (2008).

Finally, “Artificial General Intelligence and the Human Mental Model” (pdf) by Roman Yampolskiy and (MIRI research associate) Joshua Fox  reviews the dangers of anthropomorphizing machine intelligences:

When the first artificial general intelligences are built, they may improve themselves to far-above-human levels. Speculations about such future entities are already affected by anthropomorphic bias, which leads to erroneous analogies with human minds. In this chapter, we apply a goal-oriented understanding of intelligence to show that humanity occupies only a tiny portion of the design space of possible minds. This space is much larger than what we are familiar with from the human example; and the mental architectures and goals of future superintelligences need not have most of the properties of human minds. A new approach to cognitive science and philosophy of mind, one not centered on the human example, is needed to help us understand the challenges which we will face when a power greater than us emerges.

The book also includes brief, critical responses to most chapters, including responses written by Eliezer Yudkowsky and (previous MIRI staffer) Michael Anissimov.

During his time as a research fellow for MIRI, Alex Altair wrote a paper on Timeless Decision Theory (TDT) that has now been published:  “A Comparison of Decision Algorithms on Newcomblike Problems.”

Altair’s paper is both more succinct and also more precise in its formulation of TDT than Yudkowsky’s earlier paper “Timeless Decision Theory.” Thus, Altair’s paper should serve as a handy introduction to TDT for philosophers, computer scientists, and mathematicians, while Yudkowsky’s paper remains required reading for anyone interested to develop TDT further, for it covers more ground than Altair’s paper.

Altair’s abstract reads:

When formulated using Bayesian networks, two standard decision algorithms (Evidential Decision Theory and Causal Decision Theory) can be shown to fail systematically when faced with aspects of the prisoner’s dilemma and so-called “Newcomblike” problems. We describe a new form of decision algorithm, called Timeless Decision Theory, which consistently wins on these problems.

We may submit to a journal later, but we’ve published the current version to our website so that readers won’t need to wait two years (from submission to acceptance to publication) to read it.

For a gentle introduction to the entire field of normative decision theory (including TDT), see Muehlhauser and Williamson’s Decision Theory FAQ.

Update: See Reflection in Probabilistic Logic for more details on how this result relates to MIRI’s research mission.

In a recent blog post we described one of the results of our 1st MIRI Workshop on Logic, Probability, and Reflection:

The participants worked on the foundations of probabilistic reflective reasoning. In particular, they showed that a careful formalization of probabilistic logic can circumvent many classical paradoxes of self-reference. Applied to metamathematics, this framework provides (what seems to be) the first definition of truth which is expressive enough for use in reflective reasoning.

In short, the result described is a “loophole” in Tarski’s undefinability theorem (1936).

An early draft of the paper describing this result is now available: download it here. Its authors are Paul Christiano (UC Berkeley), Eliezer Yudkowsky (MIRI), Marcello Herreshoff (Google), and Mihály Bárász (Google). An excerpt from the paper is included below:

Unfortunately, it is impossible for any expressive language to contain its own truth predicate True…

There are a few standard responses to this challenge.

The first and most popular is to work with meta-languages…

A second approach is to accept that some sentences, such as the liar sentence G, are neither true nor false…

Although this construction successfully dodges the “undefinability of truth” it is somewhat unsatisfying. There is no predicate in these languages to test if a sentence… is undefined, and there is no bound on the number of sentences which remain undefined. In fact, if we are specifically concerned with self-reference, then a great number of properties of interest (and not just pathological counterexamples) become undefined.

In this paper we show that it is possible to perform a similar construction over probabilistic logic. Though a language cannot contain its own truth predicate True, it can nevertheless contain its own “subjective probability” function P. The assigned probabilities can be reflectively consistent in the sense of an appropriate analog of the reflection property 1. In practice, most meaningful assertions must already be treated probabilistically, and very little is lost by allowing some sentences to have probabilities intermediate between 0 and 1.

Another paper showing an application of this result to set theory is forthcoming.