redlizard

I would say that some formal proofs are actually impossible

Plausible. In the aftermath of spectre and meltdown I spent a fair amount of time thinking on how you could formally prove a piece of software to be free of information-leaking side channels, even *assuming* that the same thing holds for all dependent components such as underlying processors and operating systems and the like, and got mostly nowhere.

In fact, I think survival timelines might even require anyone who might be working on classes of software reliability that don't relate to alignment to actually switch their focus to alignment at this point.

Does that include those working on software correctness and reliability in general, without a security focus? I would expect better tools for making software that is free of bugs, such as programs that include correctness proofs as well as some of the lesser formal methods, to be on the critical path to survival -- for the simple reason that any number of mundane programming mistakes in a supposedly-aligned AI could easily kill us all. I was under the impression that you agree with this ["Assurance Requires Formal Proofs"]. I expect formal proofs of *security* in particular to be largely a corollary of this -- a C program that is proven to correctly accomplish any particular goal will necessarily not have any buffer overflows in it, for this would invoke undefined behavior which would make your proof not go through. This does not necessarily apply to all security properties, but I would expect it to apply to most of them.

Yes, I agree with this.

I cannot judge to what degree I agree with your strategic assessment of this technique, though. I interpreted your top-level post as judging that assurances based on formal proofs are realistically out of reach as a practical approach; whereas my own assessment is that making proven-correct [and therefore proven-secure] software a practical reality is a considerably less impossible problem than many other aspects of AI alignment, and indeed one I anticipate to actually happen in a timeline in which aligned AI materializes.

Assurance Requires Formal Proofs, Which Are Provably Impossible

The Halting Problem puts a certain standard of formalism outside our reach

This is really not true. The halting problem only makes it impossible to write a program that can analyze a piece of code and then reliably say "this is secure" or "this is insecure". It is completely possible to write an analyzer that can say "this is secure" for some inputs, "this is definitely insecure for reason X" for some other inputs, and "I am uncertain about your input so please go improve it" for everything in between. In particular, it is completely possible to have a machine-checkable proof system going along with executable code that can express proofs of extremely strong security properties for almost every program you might wish to run in practice, which can then judge "I can confirm this is secure" or "I can not confirm that this is secure which may or may not indicate an actual problem so go fix it".

Pulling this off in practice is still fiendishly difficult, of course, and progress in this field has been frustratingly slow. But there is no theoretical reason to suspect that this is fundamentally out of reach. (Or at least, not in the halting problem; Löb's theorem does provide some real limitations here that are particularly relevant for AI correctness proofs. But that is fairly niche relative to the broader notion of software correctness and security proofs.)

We see this a lot on major events, as I’ve noted before, like the Super Bowl or the World Cup. If you are on the ball, you’ll bet somewhat more on a big event, but you won’t bet that much more on it than on other things that have similarly crazy prices. So the amount of smart money does not scale up that much. Whereas the dumb money, especially the partisans and gamblers, come out of the woodwork and massively scale up.

This sounds like it should generalize to "in big events, especially those on which there are vast numbers of partisans on both sides, the prediction markets will reliably be insane and therefore close to useless for prediction purposes". Is that something one sees in practice for things like the World Cup?

One way the World Cup and Super Bowl differ from the election is that in a championship match, only a modest fraction of the people interested in the tournament as a whole will be partisans for the two contestants participating in the championship match; whereas in the election, I would expect the partisan coefficient to be much higher than that. Would that affect the degree to which the dumb money will overwhelm the smart money? I would expect so.

I do not think you are selling a strawman, but the notion that a utility function should be computable seems to me to be completely absurd. It seems like a confusion born from not understanding what computability means in practice.

Say I have a computer that will simulate an arbitrary Turing machine T, and will award me one utilon when that machine halts, and do nothing for me until that happens. With some clever cryptocurrency scheme, this is a scenario I could actually build today. My utility function ought plausibly to have a term in it that assigns a positive value to the computer simulating a halting Turing machine, and zero to the computer simulating a non-halting Turing machine. Yet the assumption of utility function computability would rule out this very sensible desire structure.

If I live in a Conway's Game of Life universe, there may be some chunk of universe somewhere that will eventually end up destroying all life (in the biological sense, not the Game of Life sense) in my universe. I assign lower utility to universes where this is the case, than to those were it is not. Is that computable? No.

More prosaically, as far as I currently understand, the universe we actually live in seems to be continuous in nature, and its state may not be describable even in principle with a finite number of bits. And even if it is, I do not actually know this, which means my utility function is also over potential universes (which, as far as I know, might be the one I live in) that require an infinite amount of state bits. Why in the world would one expect a utility function over an uncountable domain to be computable?

As far as I can see, the motivation for requiring a utility function to be computable is that this would make optimization for said utility function to be a great deal easier. Certainly this is true; there are powerful optimization techniques that apply only to computable utility functions, that an optimizer with an uncomputable utility function does not have access to in their full form. But the utility function is not up for grabs; the fact that life will be easier for me if I want a certain thing, should not be taken as an indication that that is want I want! This seems to me like the cart-before-horse error of trying to interpret the problem as one that is easier to solve, rather than the problem one actually wants solved.

One argument is that U() should be computable because the agent has to be able to use it in computations. If you can't evaluate U(), how are you supposed to use it? If U() exists as an actual module somewhere in the brain, how is it supposed to be implemented?

This line of thought here illustrates very well the (I claim) grossly mistaken intuition for assuming computability. If you can't evaluate U() perfectly, then perhaps what your brain is doing is only an approximation of what you really want, and perhaps the same constraint will hold for any greater mind that you can devise. But that does not mean that what your brain is optimizing for is necessarily what it actually wants! There is no requirement at all that your brain is a perfect judge of the desirability of the world it's looking at, after all (and we know for a fact that it does a far from perfect job at this).

This second claim sounds to me as being a bit trivial. Perhaps it is my reverse engineering background, but I have always taken it for granted that approximately any mechanism is understandable by a clever human given enough effort.

This book [and your review] explains a number of particular pieces of understanding of biological systems in detail, which is super interesting; but the mere point that these things can be understood with sufficient study almost feels axiomatic. Ignorance is in the map, not the territory; there are no confusing phenomena, only minds confused by phenomena; etc. Even when I knew nothing about this biological machinery, I never imagined for a second that no understanding was attainable in principle. I only saw *systems that are not optimized for ease of understanding*, and therefore presumably more challenging to understand than systems designed by human engineers which *are* optimized for ease of understanding.

But I get the impression that the real point you are shooting for (and possibly, the point the book is shooting for) is a stronger point than this. Not so much "there is understanding to be had here, if you look deeply enough", but rather a claim about what *particular type of structure* we are likely to find, and how this may or may not conform to the type of structure that humans are trained to look for.

Is this true? If it is, could you expand on this distinction?

If you are going to include formal proofs with your AI showing that the code does what it's supposed to, in the style of Coq and friends, then the characteristics of traditionally unsafe languages are not a deal-breaker. You can totally write provably correct and safe code in C, and you don't need to restrict yourself to a sharply limited version of the language either. You just need to prove that you are doing something sensible each time you perform a potentially unsafe action, such as accessing memory through a pointer.

This slows things down and adds to your burdens of proof, but not really by that much. It's a few more invariants you need to carry around with you throughout your proofs. Where in a safer language you may have to prove that your Foo list is still sorted after a certain operation, in C you will additionally have to prove that your pointer topology is still what you want after a certain operation. No big deal. In particular, a mature toolkit for proving properties about C programs will presumably have tools for automating away the 99% of trivial proof obligations involving pointer topology, leaving something for you to prove only when you are doing something clever.

For any such property that you can screw up, a language that will not allow you to screw it up in the first place will make your life easier and your proofs simpler, which is why OCaml is more popular as a vehicle for proven correct code than C. But if you are proving the correctness of every aspect of your program anyway, this is a pretty minor gain; the amount of stuff there is to prove about your object-level algorithms will be vastly greater than the requirements added by the lack of safety of your programming language. If only because there will be specialized tools for rapidly dealing with the latter, but not the former.

Not all those specialized tools exist just yet. Currently, the program correctness proof systems are pretty good at proving properties about functions [in the mathematical sense] operating on data structured in a way that mathematicians like to work with, and a bit rubbish at everything else people use software to do; it is no coincidence that Coq, Agda, Idris, Isabelle, and friends all work primarily with purely functional languages using some form of constructed types as a data model. But techniques for dealing with computing applications in a broader sense will have to be on the proof-technology roadmap sooner or later, if correctness proofs are ever going to fulfill their promise outside selected examples. And when they do, there will not be a big difference between programming in C and programming in OCaml as far as proving correctness is concerned.

tl;dr: I don't think language safety is going to be more than a rounding error if you want to prove the correctness of a large piece of software down to the last bit, once all the techniques for doing that sort of thing at all are in place. The amount of program-specific logic in need of manual analysis is vastly greater than the amount of boilerplate a safe language can avoid.

The point is: if people understood how their bicycle worked,they’d be able to draw one even without having to literally have one in front of them as they drew it!

I don't think this is actually true. Turning a conceptual understanding into an accurate drawing is a nontrivial skill. It requires substantial spatial visualization ability, as well as quite a bit of drawing skill -- one who is not very skilled in drawing, like myself, might poorly draw one part of a bike, want to add two components to it, and then realize that there is no way to add a third component to the poor drawing without turning it into an illegible mess of ink. There is a reason technical drawing is an explicit course in engineering education.

I built a nontrivial construction yesterday, that I understand in great detail and personally designed in OpenSCAD beforehand, that I could not put on paper by hand in a way that is vaguely mechanically accurate, without a visual reference (be it the actual construction or the CAD model). At least, not in one try -- I might manage if it I threw away the first three sketches.

Even if such a person decides to do this, they will eventually get fed up and leave.

Will they, necessarily? The structure of the problem you describe sounds a lot like any sort of teaching, which involves a lot of finding out what a student misunderstands about a particular topic and then fixing that, even if you clear up that same misunderstanding for a different student every week. There are lots of people who do not get fed up with that. What makes this so different?

This was my experience studying in the Netherlands as well. University officials were indeed on board with this, with the general assumption being that lectures and instructions and labs and such are a learning resource that you can use or not use at your discretion.