Research Lead at CORAL. Director of AI research at ALTER. PhD student in Shay Moran’s group in the Technion (my PhD research and my CORAL/ALTER research are one and the same). See also Google Scholar and LinkedIn.
E-mail: {first name}@alter.org.il
Vanessa Kosoy
Karma: 9,621
Maybe we want a multi-level categorization scheme instead? Something like:
Level 0: Author completely abstains from LLM use in all contexts (not just this post)
Level 1: Author uses LLMs but this particular post was made with no use of LLM whatsoever
Level 2: LLM was used (e.g. to look up information), but no text/images in the post came out of LLM
Level 3: LLM was used for light editing and/or image generation
Level 4: LLM was used for writing substantial parts
Level 5: Mostly LLM-generated with high-level human guidance/control/oversight
Lectures on statistical learning theory for alignment researchers
It occurred to me that one major success story of banning a technology (whether justifiably or not), is the laws against genetic engineering and cloning in humans. It makes me wonder what can we learn from that, which is applicable to promoting a global moratorium on ASI.
10 years ago I argued that approval-based AI might lead to the creation of a memetic supervirus. Relevant quote:
Optimizing human approval is prone to marketing worlds. It seems less dangerous than physicalist AI in the sense that it doesn’t create incentives to take over the world, but it might produce some kind of a hyper-efficient memetic virus.
I don’t think that what we see here is literally that, but the scenario does seem a tad less far-fetched now.
Fixed!
I found LLMs to be very useful for literature research. They can find relevant prior work that you can’t find with a search engine because you don’t know the right keywords. This can be a significant force multiplier.
They also seem potentially useful for quickly producing code for numerical tests of conjectures, but I only started experimenting with that.
Other use cases where I found LLMs beneficial:
Taking a photo of a menu in French (or providing a link to it) and asking it which dishes are vegan.
Recommending movies (I am a little wary of some kind of meme poisoning, but I don’t watch movies very often, so seems ok).
That said, I do agree that early adopters seem like they’re overeager and maybe even harming themselves in some way.
I did link the relevant section of my agenda post:
This work is my first rigorous foray into compositional learning theory.
A brief and simplified summary:
In order to have powerful learning algorithms with safety guarantees, we first need learning algorithms with powerful generalization guarantees that we know how to rigorously formulate (otherwise how do you know the algorithm will correctly infer the intended goal/behavior from the training data?).
Additionally, in order to formally specify “aligned to human values”, we need to formally specify “human values”, and it seems likely that the specification of “X’s values” should be something akin to “the utility function w.r.t. which X has [specific type of powerful performance guarantees]”. These powerful performance guarantees are probably a form/extension of powerful generalization guarantees.
Both reasons require us to understand the kind of natural powerful generalization guarantees that efficient learning algorithms can satisfy. Moreover, such understanding would likely be applicable to deep learning as well, as it seems likely deep learning algorithms satisfy such guarantees, but we currently don’t know how to formulate them.
I conjecture that a key missing ingredient in deriving efficient learning algorithms with powerful guarantees (more powerful than anything we already understand in computational learning theory), is understanding the role of compositionality in learning. This is because compositionality is a ubiquitous feature of our thinking about the world and, intuitively, particular forms of compositionality are strong candidates for properties that are both very general and strong enough to enable efficient learning. This line of thinking led me to some success in the context of control theory, which is a necessary ingredient of the kind of guarantees we will ultimately need.
I identified sequence prediction / online learning in the deterministic realizable case as a relatively easy (but already highly non-trivial) starting point for investigating compositional learning.
For the reasons stated in the OP, this led me to ambiguous online learning.
I’m open to chatting on Discord.
New Paper: Ambiguous Online Learning
I never did quite that thing successfully. I did have one time when I dropped progressively unsubtle hints on a guy, who remained stubbornly oblivious for a long time until he finally got the message and reciprocated.
Btw, what are some ways we can incorporate heuristics into our algorithm while staying on level 1-2?
We don’t know how the prove to required desiderata about the heuristic, but we can still reasonably conjecture them and support the conjectures with empirical tests.
We can’t prove or even conjecture anything useful-in-itself about the heuristic, but the way the heuristic is incorporated into the overall algorithm makes it safe. For example, maybe the heuristic produces suggestions together with formal certificates of their validity. More generally, we can imagine an oracle-machine (where the heuristic is slotted into the oracle) about which we cannot necessarily prove something like a regret bound w.r.t. the optimal policy, but we can prove (or at least conjecture) a regret bound w.r.t. some fixed simple reference policy. That is, the safety guarantee shows that no matter what the oracle does, the overall system is not worse than “doing nothing”. Maybe, modulo weak provable assumptions about the oracle, e.g. that it satisfies a particular computational complexity bound.
[Epistemic status: very fresh idea, quite speculative but intriguing.] We can’t find even a guarantee like a above for a worst-case computationally bounded oracle. However, we can prove (or at least conjecture) some kind of an “average-case” guarantee. For example, maybe we have high probability of safety for a random oracle. However, assuming a uniformly random oracle is quite weak. More optimistically, maybe we can prove safety even for any oracle that is pseudorandom against some complexity class (where we want to be as small as possible). Even better, maybe we can prove safety for any oracle in some complexity class (where we want to be as large as possible) that has access to another oracle which is pseudorandom against . If our heuristic is not actually in this category (in particular, is smaller than and our heuristic doesn’t lie in ), this doesn’t formally guarantee anything, but it does provide some evidence for the “robustness” of our high-level scheme.
Hold my beer ;)
I see modeling vs. implementation as a spectrum more than a dichotomy. Something like:
On the “implementation” extreme you prove theorems about the exact algorithm you implement in your AI, s.t. you can even use formal verification to prove these theorems about the actual code you wrote.
Marginally closer to “modeling”, you prove (or at least conjecture) theorems about some algorithm which is vaguely feasible in theory. Some civilization might have used that exact algorithm to build AI, but in our world it’s impractical, e.g. because it’s uncompetitive with other AI designs. However, your actual code is conceptually very close to the idealized algorithm, and you have good arguments why the differences don’t invalidate the safety properties of the idealized model.
Further along the spectrum, your actual algorithm is about as similar to the idealized algorithm as DQN is similar to vanilla Q-learning. Which is to say, it was “inspired” by the idealized algorithm but there’s a lot of heavy lifting done by heuristics. Nevertheless, there is some reason to hope the heuristic aspects don’t change the safety properties.
On the “modeling” extreme, your idealized model is something like AIXI: completely infeasible and bears little direct resemblance to the actual algorithm in your AI. However, there is still some reason to believe real AIs will have similar properties to the idealized model.
More precisely, rather than a 1-dimensional spectrum, there are at least two parameters involved:
How close is the object you make formal statements about to the actual code of your AI, where “closeness” is measured by the strength of the arguments you have for the analogy, on a scale from “they are literally the same” to solid theoretical and/or empirical evidence to pure hand-waving/intuition
How much evidence you have for the formal statements, on a scale from “I proved it within some widely accepted mathematical foundation (e.g. PA)” to “I proved vaguely related things, tried very hard but failed to disprove the thing and/or accumulated some empirical evidence”.
[EDIT: And a 3rd parameter is, how justified/testable the assumptions of your model is. Ideally, you want these assumptions to be grounded in science. Some will likely be philosophical assumptions which cannot be tested empirically, but at least they should fit into a coherent holistic philosophical view. At the very least, you want to make sure you’re not assuming away the core parts of the problem.]
For the purposes of safety, you want to be as close to the implementation end of the spectrum as you can get. However, the model side of the spectrum is still useful as:
A backup plan which is better than nothing, more so if there is some combination of theoretical and empirical justification for the analogizing
A way to demonstrate threat models, as the OP suggests
An intermediate product that helps checking that your theory is heading in the right direction, comparing different research agendas, and maybe even making empirical tests.
Sorry, I was wrong. By Lob’s theorem, all versions of are provably equivalent, so they will trust each other.
IIUC, fixed point equations like that typically have infinitely many solution. So, you defined not one predicate, but an infinite family of them. Therefore, your agent will trust a copy of itself, but usually won’t trust variants of itself with other choices of fixed point. In this sense, this proposal is similar to proposals based on quining (as quining has many fixed points as well).
I don’t know what’s so bad about the “human male” bio. I might have swiped right on that one. (Especially if the profile had additional info that makes him sound interesting.)
TLDR: A new proposal for a prescriptive theory of multi-agent rationality, based on generalizing superrationality using local symmetries.
Hofstadter’s “superrationality” postulates that a rational agent should behave as if other rational agents are similar to itself. In a symmetric game, this implies the selection of a Pareto efficient outcome. However, it’s not clear how to apply this principle to asymmetric games. I propose to solve this by suggesting a notion of “local” symmetry that is much more ubiquitous than global (ordinary) symmetry.
We will focus here entirely on finite deterministic (pure strategy) games. Generalizing this to mixed strategies and infinite games more generally is an important question left for the future.
Quotient Games
Consider a game with a set of players, for each player a non-empty set or pure strategies and a utility function , where . What does it mean for the game to be “symmetric”? We propose a “soft” notion of symmetry that is only sensitive to the ordinal ordering between payoffs. While the cardinal value of the payoff will be important in the stochastic context, we plan to treat the latter by explicitly expanding the strategy space.
Given two games , , a premorphism from to is defined to consist of
A mapping
For each , a mapping
Notice that these mappings induce a mapping via
A premorphism is said to be a homomorpism if and are s.t. that for any and , if then . Homomorphisms makes games into a category in a natural way.
An automorphism of is a homomorphism from to that has an inverse homomorphism. An automorphism of is said to be flat when for any , if then is the identity mapping[1]. A flat symmetry of is a group together with a group homomorphism s.t. is flat for all .
Given a flat symmetry , we can apply the superrationality principle to reduce to the “smaller” quotient game . The players are i.e. orbits in the original player set. Given , we define the set of strategies for player in the game to be
This is non-empty thanks to flatness.
Observe that there is a natural mapping given by
Finally, the utility function of is defined by
It is easy to see that the construction of is functorial w.r.t. the category structure on games that we defined.
We can generalize this further by replacing game homomorphisms with game quasimorphisms: premorphisms satisfying the following relaxed condition on and :
For any and , if then .
This is no longer closed under composition, so no longer defines a category structure[2]. However, we can still define flat quasisymmetries and the associated quotient games, and this construction is still functorial w.r.t. the original (not “quasi”) category structure. Moreover, there is a canonical homomorphism (not just a quasimorphism) from to , even when is a mere quasisymmetry.
The significance of quasisymmetries can be understood as follows.
The set of all games on a fixed set of players with fixed strategy sets naturally forms a topological space[3] . Given a group acting on the game via invertible premorphisms, the subset of where is a symmetry is not closed, in general. However, the subset of where is a quasisymmetry is closed. I believe this will be important when generalizing the formalism to infinite games.
Coarse Graining
What if a game doesn’t have even quasisymmetries? Then, we can look for a coarse graining of the game which does have them.
Consider a game . For each , let be some set and a surjection. Denote . Given any , we have the game in which:
The set of players is .
For any , their set of strategies is . In particular, it implies that the set of outcomes satisfies .
For any , their utility function is .
If for any we choose some this allows us to define the coarse-grained game in which:
The set of players is .
For any , the set of strategies is .
For any and , the utility function is .
Essentially, we rephrased as an extensive form game in which first the game is played and then, if the outcome was , the game is played. This, assuming the expected outcome of game is .
It is also possible to generalize this construction by allowing multivalued .
Local Symmetry Solutions
Given a game , a local symmetry presolution (LSP) is recursively defined to be one of the following:
Assume there is s.t. for any , . Then, any is an LSP of . [Effectively single player game]
Let be a coarse-graining of and for any , let be an LSP of . Let be an LSP of . Define by . Then, is an LSP of .
Let be a quasisymmetry of and let be an LSP of . Then, is an LSP of .
It’s easy to see that an LSP always exists, because for any game we can choose a sequence of coarse-grainings whose effect is making the players choose their strategies one by one (with full knowledge of choices by previous players). However, not all LSP are “born equal”. It seems appealing to prefer LSP which use “more” symmetry. This can be formalized as follows.
The way an LSP is constructed defines the set of coherent outcomes , which is the set of outcomes compatible with the local symmetries[4]. We define it recursively as follows:
For the LSP of an effectively single-player game, we set .
For a coarse-graining LSP, for any , let be the set of coherent outcomes of and let be the set of coherent outcomes of . We then define . Here, is defined by .
For a quasisymmetry LSP, let be the set of coherent outcomes of . We then define .
We define a local symmetry solution (LSS) to be an LSP whose set of coherent outcomes is minimal w.r.t. set inclusion.
Examples
In the Prisoner’s Dilemma, the only LSS is Cooperate-Cooperate.
In Stag Hunt, the only LSS is Stag-Stag.
In Chicken, the only LSS is Swerve-Swerve. If we add a finite number of randomized strategies, it opens more possibilities.
In Battle of the Sexes, assuming a small payoff from going to your preferred place alone, the only LSS is: each player goes to their own preferred place. If we give each player a “coinflip” strategy, then I think the only LSS is both players using the coinflip.
Consider a pure cooperation game where both players have strategies and the payoff is 1 if they choose the same strategy and 0 if they choose different strategies. Then, any outcome is an LSS. I think that, if we add a “fair coinflip” strategy, any LSS has payoff at least . I believe the LSS payoff will approach optimum if we (i) allow randomization (ii) make the game repeated with time long horizon and (iii) add some constraints on the symmetries, but I’ll leave this for a future post.
Consider a pure cooperation game where both players have strategies , the payoff is 2 if both choose , 1 if both choose and 0 if they choose different strategies. Then, the only LSS is .
In any game, an LSS guarantees each player at least their deterministic-maximin payoff. In particular, in a two-player zero-sum game in which a pure Nash equilibrium exists, any LSS is a Nash equilibrium.
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Note that flatness is in general not preserved under composition.
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I believe this can be interpreted as a category enriched over the category of sets and partial functions, with the monoidal structure given by Cartesian product of sets.
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An affine space, even.
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Maybe we can interpret the set of coherent outcomes as a sharp infradistirbution corresponding to the players’ joint belief about the outcome of the game.
Master post for multi-agency. See also.
In (non-monotonic) infra-Bayesian physicalism, there is a vaguely similar asymmetry even though it’s formalized via a loss function. Roughly speaking, the loss function expresses preferences over “which computations are running”. This means that you can have a “positive” preference for a particular computation to run or a “negative” preference for a particular computation not to run[1].
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There are also more complicated possibilities, such as “if P runs then I want Q to run but if P doesn’t run then I rather that Q also doesn’t run” or even preferences that are only expressible in terms of entanglement between computations.
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It’s roughly on the right track, but here are some inaccuracies in your description that stood out to me:
There is no requirement that the “hidden state space” is finite. It is perfectly fine to consider a credal set which is not a polytope (i.e. not a convex hull of a finite set of distributions).
The point of how market prices are computed, missing from your description, is that they prevent any bettor from making unbounded earnings (essentially, by making them bet against each other). This is the same principle as Garrabrant induction. In particular, this implies that if any of our models is true then the market predictions will converge to lying inside the corresponding credal set.
The market predictions do not somehow assume that “the parts of the universe we don’t observe are out to get us”. Thanks to the pessimistic better, they do satisfy the “not too optimistic condition”, but that’s “not too optimistic” relatively to the true environment.
Your entire description only talks about the “estimation” part, not about the “decision” part.
Thanks for the heads up. Can you share which AI models were involved?