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Model/FinetuneGlobal Mean (Cosine) Similarity
Gemma-2b/Gemma-2b-Python-codes0.6691
Mistral-7b/Mistral-7b-MetaMath0.9648
As an ex-Googler, my informed guess would be that Gemma 2B will have been distilled (or perhaps both pruned and distilled) from a larger teacher model, presumably some larger Gemini model — and that Gemma-2b and Gemma-2b-Python-codes may well have been distilled separately, as separate students of two similar-but-not-identical teacher models distilled using different teaching datasets. The fact that the global mean cosine you find here isn't ~0 shows that if so, the separate distillation processes were either warm-started from similar models (presumably a weak 2B model — a sensible way to save some distillation expense), or at least shared the same initial token embeddings/unembeddings.
Regardless of how they were created, these two Gemma models clearly differ pretty significantly, so I'm unsurprised by your subsequent discovery that the SAE basically doesn't transfer between them.
For Mistral 7B, I would be astonished if any distillation was involved, I would expect just a standard combination of fine-tuning followed by either RLHF or something along the lines of DPO. In very high dimensional space, a cosine of 0.96 means "almost identical", so clearly the instruct training here consists of fairly small, targeted changes, and I'm unsurprised that as a result the SAE transfers quite well.
knowing if the intentions of a user are legitimate is very difficult
This sounds more like a security and authentication problem than an AI problem.
Side note: skills vs facts. I framed some of the approaches as teaching false facts / removing some facts - and concrete raw facts is often what is the easiest to evaluate. But I think that the same approach can be used to remove the information that makes LLMs able to use most skills. For example, writing Python code requires the knowledge of the Python syntax and writing recursive functions requires the knowledge of certain patterns (at least for current LLMs, who don’t have the ability to rederive recursive from scratch, especially without a scratchpad), both of which could be unlearned like things that are more clearly “facts”.
If you read e.g. "Fact Finding: Attempting to Reverse-Engineer Factual Recall on the Neuron Level", current thinking in mechanistic interpretability is that simple memorization of otherwise random facts (i.e. ones where there are no helpful "rules of thumb" to get many cases right) uses different kinds of learned neural circuits that learning of skills does. If this were in fact the case, then unlearning of facts and skills might have different characteristics. In particular, for learnt skills, if mechanistic interpretability can locate and interpret the learned circuit implementing a skills, then we can edit them directly (as has been done successfully in a few cases). However, we've so far had no luck at interpreting neural circuitry for large collections of basically-random facts, and there are some theoretical arguments suggesting that such circuitry may be inherently hard to interpret, at least using current techniques.
I think something that might be quite illuminating for this factual recall question (as well has having potential safety uses) is editing the facts. Suppose, for this case, you take just the layer 2-6 MLPs with frozen attention, you warm-start from the existing model, add a loss function term that penalizes changes to the model away from that initialization (perhaps using a combination of L1 and L2 norms), and train that model on a dataset that consists of your full set of athlete names embeddings and their sports (in a frequency ratio matching the original training data, so with more copies of data about more famous athletes), but with one factual edit to it to change the sport of one athlete. Train until it has memorized this slightly edited set of facts reasonably well, and then look at what the pattern of weights and neurons that changed significantly is. Repeat several times for the same athlete, and see how consistent/stochastic the results are. Repeat for many athlete/sport edit combinations. This should give you a lot of information on how widely distributed the representation of the data on a specific athlete is, and ought to give you enough information to distinguish between not only your single step vs hashing hypotheses, but also things like bagging and combinations of different algorithms. Even more interesting would be to do this not just for an athlete's sport, but also some independent fact about them like their number.
Of course, this is computationally somewhat expensive, and you do need to find metaparameters that don't make this too expensive, while encouraging the resulting change to be as localized as possible consistent with getting a good score on the altered fact.
I take your point that the way an Infra-Bayesian system makes decisions isn't the same as a human — it presumably doesn't share our cognitive biases, and the pessimism element 'Murphy' in it seems stronger than for most humans. I normally assume that if there's something I don't understand about the environment that's injecting noise into the outcome of my actions, the noise-related parts of results aren't going to be well-optimized, so they're going to be worse than I could have achieved had I had full understanding, but that even leaving things to chance I may sometimes get some good luck along with the bad — I don't generally assume that everything I can't control will have literally the worst possible outcome. So I guess in Infra-Bayesian terms I'm assuming that Murphy is somewhat constrained by laws that I'm not yet aware of, and may never be aware of.
My take on Murphy is that it's a systematization of the force of entropy trying to revert the environment to a thermodynamic equilibrium state, and of the common fact that the utility of that equilibrium state is usually pretty low. One of the flaws I see in Infra-Bayesianism is that there are sometimes (hard to reach but physically possible) states whose utility to me is even lower than the thermodynamic equilibrium (such as a policy that scores less than 20% on a 5-option multiple choice quiz so does worse than random guessing, or a minefield left over after a war that is actually worse than a blasted wasteland) where increasing entropy would actually help improve things. In a hellworld, randomly throwing money wrenches in the gears is a moderately effective strategy. In those unusual cases Infra-Bayesianism's Murphy no longer aligns with the actual effects of entropy/Knightian uncertainty.
The observation that gains saturate has a fairly simple explanation from evolutionary theory: the increased evolutionary fitness advantage from large material gains saturates (especially in a hunter-gatherer environment). Successfully hunting a rabbit will keep me from starving for a day; but if I successfully hunt a mammoth, I can't keep the meat for long enough for it to feed me for years. The best I can do is feed everyone in the village for a few days, hoping they remember this later when my hunting is less successful, and do a bunch of extra work to make some jerky with the rest. The evolutionary advantage is sub-linear in the kilograms of raw meat. In more recent agricultural societies, rich and powerful men like Ramses II who had O(100) children needed a lot more than 50 times the average resources of men in their society to achieve that outcome (and of course that evolutionary strategy isn't possible for women). Even today, if I'm unlucky enough to get pancreatic cancer it doesn't matter how rich I am: all that money isn't going to save me, even if I'm as rich as Steve Jobs.
Similarly, on the downside, from a personal evolutionary fitness point of view, saturation also makes sense, since there is a limit to how bad things can get: once I, my family, and everyone else in the tribe related to me are all dead, it's game over, and my personal evolutionary fitness doesn't really care whether everyone else in the region also died, or not.
So it seems to me that at least the first diagram above of prospect theory may be an example of humans being aligned with evolution's utility function.
I don't have a good evolutionary explanation for the second diagram, unless it's a mechanism to compensate for some psychological or statistical bias in how hunter-gatherers obtain information about and estimate risks, and/or how that compares to modern mathematical risk measures like probabilities and percentages.
We want our value-learner AI to learn to have the same preference order over outcomes as humans, which requires its goal to be to find (or at least learn to act according to) a utility function as close as possible to some aggregate of ours (if humans actually had utility functions rather than a collection of cognitive biases) up to an arbitrary monotonically-increasing mapping. We also want its preference order over probability distributions of outcomes to match ours, which requires it to find a utility function that matches ours up to an increasing affine (linear, i.e. scale and shift) transformation. So, once it has made good progress on its value learning, its utility function ought to make a lot of sense to us.
The sequence on Infra-Bayesianism motivates the min (a.k.a. Murphy) part of its argmax min by wanting to establish lower bounds on utility — that's a valid viewpoint. My own interest in Infra-Bayesianism comes from a different motivation: Murphy's min encodes directly into Infra-Bayesian decision making the generally true, inter-related facts that 1) for an optimizer, uncertainty on the true world model injects noise into your optimization process which almost always makes the outcome worse 2) the optimizer's curse usually results in you exploring outcomes whose true utility you had overestimated, so your regret is generally higher than you had expected 3) most everyday environments and situations are already highly optimized, so random perturbations of their state almost invariably make things worse. All of which justify pessimism and conservatism.
The problem with this argument, is that it's only true when the utility of the current state is higher than the utility of the maximum-entropy equilibrium state of the environment (the state that increasingly randomizing it tends to move it towards due to the law of big numbers). In everyday situations this is almost always true -- making random changes to a human body or in a city will almost invariable make things worse, for example. In most physical environments, randomizing them sufficiently (e.g. by raining meteorites on them, or whatever) will tend to reduce their utility to that of a blasted wasteland (the surface of the moon, for example, has pretty-much reached equilibrium under randomization-by-meteorites, and has a very low utility). However, it's a general feature of human utility functions that there often can be states worse than the maximum-entropy equilibrium. If your environment is a 5-choice multiple-choice test whose utility is the score, the entropic equilibrium is random guessing which will score 20%, and there are chose-wrong-answer policies that score less than that, all the way down to 0% -- and partially randomizing away from one of those policies will make its utility increase towards 20%. Similarly, consider a field of anti-personnel mines left over from a war -- as an array of death and dismemberment waiting to happen, randomizing it with meteorite impacts will clear some mines and make its utility better -- since it starts off actually worse than a blasted wasteland. Or, if a very smart GAI working on alignment research informed you that it had devised an acausal attack that would convert all permanent hellworlds anywhere in the multiverse into blasted wastelands, your initial assumption would probably be that doing that would be a good thing (modulo questions about whether it was pulling your leg, or whether the inhabitants of the hellworld would consider it a hellworld).
In general, hellworlds (or at least local hell-landscapes) like this are rare — they have a negligible probability of arising by chance, so creating one requires work by an unaligned optimizer. So currently, with humans the strongest optimizers on the planet, they usually only arise in adversarial situations such as wars between groups of humans ("War is Hell", as the saying goes). However, Infra-Bayesianism has exactly the wrong intuitions about any hell-environment whose utility is currently lower than that of the entropic equilibrium. If you have an environment that has been carefully optimized by a powerful very-non-aligned optimizer so as to maximize human suffering, then random sabotage such as throwing monkey wrenches in the works or assassinating the diabolical mastermind is actually very likely to improve things (from a human point of view), at least somewhat. Infra-Bayesianism would predict otherwise. I think having your GAI's decision theory based on a system that gives exactly the wrong intuitions about hellworlds is likely to be extremely dangerous.
The solution to this would be what one might call Meso-Bayesianism -- renormalize your utility scores so that of the utility of the maximal entropy state of the environment is by definition zero, and then assume that Murphy minimizes the absolute value of the utility towards the equilibrium utility of zero, not towards a hellworld. (I'm not enough of a pure mathematician to have any idea what this modification does to the network of proofs, other then making the utility renormalization part of a Meso-Bayesian update more complicated.) So then your decision theory understands that any unaligned optimizer trying to create a hellworld is also fighting Murphy, and when fighting them on their home turf Murphy is your ally, since "it's easier to destroy than create" is also true of hellworlds. [Despite the usual formulation of Murphy's law, I actually think the name 'Murphy' suits this particular metaphysical force better -- Infra-Bayesianism's original 'Murphy' might have been better named 'Satan', since it's is wiling to go to any length to create a hellworld, hobbled only by some initially-unknown physical laws.]
1Having since started learning about Infra-Bayesianism, my initial impression is that it's a formal and well-structures mathematical formalism for doing of exactly the kind of mechanism I sketched above for breaking the Optimizer's Curse, by taking the most pessimistic view of the utility over Knightian uncertainty in your hypotheses set.
However, if we found that the classifier was using a feature for "How smart is the human asking the question?" to decide what answer to give (as opposed to how to then phrase it), that would be a red flag.