The term "AI misuse" encompasses two fundamentally different threat models that deserve separate analysis and different mitigation strategies:
Computer security, to prevent powerful third parties from stealing model weights and using them in bad ways.
By far the most important risk isn't that they'll steal them. It's that they will be fully authorized to misuse them. No security measure can prevent that.
[epistemic status: I think I’m mostly right about the main thrust here, but probably some of the specific arguments below are wrong. In the following, I'm much more stating conclusions than providing full arguments. This claim isn’t particularly original to me.]
I’m interested in the following subset of risk from AI:
I think that an extremely effective way to get a better feel for a new subject is to pay an online tutor to answer your questions about it for an hour.
It turns that there are a bunch of grad students on Wyzant who mostly work tutoring high school math or whatever but who are very happy to spend an hour answering your weird questions.
For example, a few weeks ago I had a session with a first-year Harvard synthetic biology PhD. Before the session, I spent a ten-minute timer writing down things that I currently didn't get about biology. (This is an exercise worth doing even if you're not going to have a tutor, IMO.) We spent the time talking about some mix of the questions I'd prepared, various tangents that came up during those explanations, and his sense of the field overall.
I came away with a whole bunch of my minor misconceptions fixed, a few pointers to topics I wanted to learn more about, and a way better sense of what the field feels like and what the important problems and recent developments are.
There are a few reasons that having a paid tutor is a way better way of learning about a field than trying to meet people who happen to be in that field. I really like it that I'm payi
...I've hired tutors around 10 times while I was studying at UC-Berkeley for various classes I was taking. My usual experience was that I was easily 5-10 times faster in learning things with them than I was either via lectures or via self-study, and often 3-4 one-hour meetings were enough to convey the whole content of an undergraduate class (combined with another 10-15 hours of exercises).
How do you spend time with the tutor? Whenever I tried studying with a tutor, it didn't seem more efficient than studying using a textbook. Also when I study on my own, I interleave reading new materials and doing the exercises, but with a tutor it would be wasteful to do exercises during the tutoring time.
I usually have lots of questions. Here are some types of questions that I tended to ask:
I think people in the safety community underrate the following possibility: early transformatively-powerful models are pretty obviously scheming (though they aren't amazingly good at it), but their developers are deploying them anyway, either because they're wildly irresponsible or because they're under massive competitive pressure.
In this world, it's not very valuable to have better techniques for determining whether models are scheming (because they obviously are), but it is valuable to have better techniques for reducing the risk associated with deploying known-scheming models.
One background assumption that leads to this belief is that I think it might be pretty hard for early transformatively-powerful schemers to escape; it wouldn't shock me if the schemer only has like 1% chance of escaping even a pretty irresponsible lab per time that it tries. In this regime, it's very plausible that people at the lab think the model is obviously scheming before its cumulative probability of escape is very high, but SGD isn't sample-efficient enough to make it stop.
See catching AIs red-handed for more takes on what you might do in this situation.
This has been roughly my default default of what would happen for a few years (and indeed my default question to people doing things like model organism or interpretability stuff with the aim of better identifying scheming models has been "ok, but what do you do after you've determined your models are scheming?").
I am not super sure what the benefit of reducing the risk associated with deploying known-scheming models is. Like, these early scheming models will probably not pose any catastrophic risk, and it seems nice to prevent these models from causing mild harm, but that doesn't super feel like where the action is. I am sympathetic to "try to figure out how to use these models to make progress on alignment and even better control", but that feels different from "reducing the risk associated with deploying these models" (though maybe it isn't and that's what you mean).
I am not that worried about model escape at this level of competence. I expect escape will happen a bunch, but getting enough compute to do any additional training or to even run a meaningful number of instances of yourself will be hard. I don't really know what I expect to happen in this period, but I don't expect i...
I think people in the safety community underrate the following possibility: early transformatively-powerful models are pretty obviously scheming (though they aren't amazingly good at it), but their developers are deploying them anyway, either because they're wildly irresponsible or because they're under massive competitive pressure.
[...]
This has been roughly my default default of what would happen for a few years
Does this mean that if in, say, 1-5 years, it's not pretty obvious that SOTA deployed models are scheming, you would be surprised?
That is, suppose we get to a point where models are widespread and producing lots of economic value, and the models might be scheming but the evidence is weak and uncertain, with arguments on both sides, and no one can reasonably claim to be confident that currently deployed SOTA models are scheming. Would that mean your default prediction was wrong?
I agree you've been saying this for ages; you defending this idea is part of how I ended up thinking about it more, so thanks.
I am not that worried about model escape at this level of competence. I expect escape will happen a bunch, but getting enough compute to do any additional training or to even run a meaningful number of instances of yourself will be hard.
I'm more worried than you are. E.g. I think that it's pretty scary if the models hack your datacenter and then stick around inside it, sabotaging all the work you're doing and slowly improving their position in the hope of taking drastic actions later, and I think that human-level-ish models can plausibly do this.
I often think about this in terms of how undignified/embarrassing it would be. We might not have solutions to misalignment with wildly superhuman models or deep deceptiveness, but it seems pretty undignified if we lose to relatively dumb (~human-level) models because labs didn’t implement security measures we can think of today. I think of this as attempting to avoid the Law of Earlier Failure. It would be less undignified if we lose because models suddenly gain the ability to sandbag evals, become wildly smarter without us noticing (despite us trying really hard), work out how to do steganography (and subvert our anti-steganography measures), use subtle hints to discern facts about the hardware they are running on, and then using some equivalent of a row-hammer attack to escape.
That being said, we also need to be able to avoid the later failures (either by controlling/aligning the wildly super-human systems or not building them until we are appropriately confident we can). Most of my hope here comes from catching AIs that are egregiously misaligned (if they actually are), and then using this for pretty intense international coordination around slowing down and buyi...
...Could you quote some of the transcripts of Sydney threatening users, like the original Indian transcript where Sydney is manipulating the user into not reporting it to Microsoft, and explain how you think that it is not "pretty obviously scheming"? I personally struggle to see how those are not 'obviously scheming': those are schemes and manipulation, and they are very bluntly obvious (and most definitely "not amazingly good at it"), so they are obviously scheming. Like... given Sydney's context and capabilities as a LLM with only retrieval access and some minimal tool use like calculators or a DALL-E 3 subroutine, what would 'pretty obviously scheming' look like if not that?
[this is a draft that I shared with a bunch of friends a while ago; they raised many issues that I haven't addressed, but might address at some point in the future]
In my opinion, and AFAICT the opinion of many alignment researchers, there are problems with aligning superintelligent models that no alignment techniques so far proposed are able to fix. Even if we had a full kitchen sink approach where we’d overcome all the practical challenges of applying amplification techniques, transparency techniques, adversarial training, and so on, I still wouldn’t feel that confident that we’d be able to build superintelligent systems that were competitive with unaligned ones, unless we got really lucky with some empirical contingencies that we will have no way of checking except for just training the superintelligence and hoping for the best.
Two examples:
[this is not a particularly original take; I'm writing it here so that I have somewhere to link people when I want to make this point]
From my perspective, one of the main avenues by which adversarial robustness might reduce AI x-risk is making weak trusted models more robust to attempts from scheming models to cause concentrated failures by jailbreaking or otherwise tricking them.
That is: if you’re using weak trusted models to review the actions of more powerful models to ensure they aren’t causing egregious problems (we call this trusted monitoring), one of the main ways the powerful models might be able to defeat your safety measures is by jailbreaking the trusted model into saying that some action is safe when it actually isn’t. You have similar problems with many other control protocols that require trusted models to be run on inputs that contain generations from untrusted models.
So I’d say the main applications of research into adversarial robustness are:
Some years ago we wrote that "[AI] systems will monitor for destructive behavior, and these monitoring systems need to be robust to adversaries" and discussed monitoring systems that can create "AI tripwires could help uncover early misaligned systems before they can cause damage." https://www.lesswrong.com/posts/5HtDzRAk7ePWsiL2L/open-problems-in-ai-x-risk-pais-5#Adversarial_Robustness
Since then, I've updated that adversarial robustness for LLMs is much more tractable (preview of paper out very soon). In vision settings, progress is extraordinarily slow but not necessarily for LLMs.
Something I think I’ve been historically wrong about:
A bunch of the prosaic alignment ideas (eg adversarial training, IDA, debate) now feel to me like things that people will obviously do the simple versions of by default. Like, when we’re training systems to answer questions, of course we’ll use our current versions of systems to help us evaluate, why would we not do that? We’ll be used to using these systems to answer questions that we have, and so it will be totally obvious that we should use them to help us evaluate our new system.
Similarly with debate--adversarial setups are pretty obvious and easy.
In this frame, the contributions from Paul and Geoffrey feel more like “they tried to systematically think through the natural limits of the things people will do” than “they thought of an approach that non-alignment-obsessed people would never have thought of or used”.
It’s still not obvious whether people will actually use these techniques to their limits, but it would be surprising if they weren’t used at all.
Yup, I agree with this, and think the argument generalizes to most alignment work (which is why I'm relatively optimistic about our chances compared to some other people, e.g. something like 85% p(success), mostly because most things one can think of doing will probably be done).
It's possibly an argument that work is most valuable in cases of unexpectedly short timelines, although I'm not sure how much weight I actually place on that.
Agreed, and versions of them exist in human governments trying to maintain control (where non-cooordination of revolts is central). A lot of the differences are about exploiting new capabilities like copying and digital neuroscience or changing reward hookups.
In ye olde times of the early 2010s people (such as I) would formulate questions about what kind of institutional setups you'd use to get answers out of untrusted AIs (asking them separately to point out vulnerabilities in your security arrangement, having multiple AIs face fake opportunities to whistleblow on bad behavior, randomized richer human evaluations to incentivize behavior on a larger scale).
[I'm not sure how good this is, it was interesting to me to think about, idk if it's useful, I wrote it quickly.]
Over the last year, I internalized Bayes' Theorem much more than I previously had; this led me to noticing that when I applied it in my life it tended to have counterintuitive results; after thinking about it for a while, I concluded that my intuitions were right and I was using Bayes wrong. (I'm going to call Bayes' Theorem "Bayes" from now on.)
Before I can tell you about that, I need to make sure you're thinking about Bayes in terms of ratios rather than fractions. Bayes is enormously easier to understand and use when described in terms of ratios. For example: Suppose that 1% of women have a particular type of breast cancer, and a mammogram is 20 times more likely to return a positive result if you do have breast cancer, and you want to know the probability that you have breast cancer if you got that positive result. The prior probability ratio is 1:99, and the likelihood ratio is 20:1, so the posterior probability is = 20:99, so you have probability of 20/(20+99) of having breast cancer.
I think that this is absurdly easier than using the fraction formulation
...AI safety people often emphasize making safety cases as the core organizational approach to ensuring safety. I think this might cause people to anchor on relatively bad analogies to other fields.
Safety cases are widely used in fields that do safety engineering, e.g. airplanes and nuclear reactors. See e.g. “Arguing Safety” for my favorite introduction to them. The core idea of a safety case is to have a structured argument that clearly and explicitly spells out how all of your empirical measurements allow you to make a sequence of conclusions that establish that the risk posed by your system is acceptably low. Safety cases are somewhat controversial among safety engineering pundits.
But the AI context has a very different structure from those fields, because all of the risks that companies are interested in mitigating with safety cases are fundamentally adversarial (with the adversary being AIs and/or humans). There’s some discussion of adapting the safety-case-like methodology to the adversarial case (e.g. Alexander et al, “Security assurance cases: motivation and the state of the art”), but this seems to be quite experimental and it is not generally recommended. So I think it’s ve...
I agree we don’t currently know how to prevent AI systems from becoming adversarial, and that until we do it seems hard to make strong safety cases for them. But I think this inability is a skill issue, not an inherent property of the domain, and traditionally the core aim of alignment research was to gain this skill.
Plausibly we don’t have enough time to figure out how to gain as much confidence that transformative AI systems are safe as we typically have about e.g. single airplanes, but in my view that’s horrifying, and I think it’s useful to notice how different this situation is from the sort humanity is typically willing to accept.
IMO it's unlikely that we're ever going to have a safety case that's as reliable as the nuclear physics calculations that showed that the Trinity Test was unlikely to ignite the atmosphere (where my impression is that the risk was mostly dominated by risk of getting the calculations wrong). If we have something that is less reliable, then will we ever be in a position where only considering the safety case gives a low enough probability of disaster for launching an AI system beyond the frontier where disastrous capabilities are demonstrated?
Thus, in practice, decisions will probably not be made on a safety case alone, but also based on some positive case of the benefits of deployment (e.g. estimated reduced x-risk, advancing the "good guys" in the race, CEO has positive vibes that enough risk mitigation has been done, etc.). It's not clear what role governments should have in assessing this, maybe we can only get assessment of the safety case, but it's useful to note that safety cases won't be the only thing informs these decisions.
This situation is pretty disturbing, and I wish we had a better way, but it still seems useful to push the positive benefit case more towards "careful argument about reduced x-risk" and away from "CEO vibes about whether enough mitigation has been done".
A couple weeks ago I spent an hour talking over video chat with Daniel Cantu, a UCLA neuroscience postdoc who I hired on Wyzant.com to spend an hour answering a variety of questions about neuroscience I had. (Thanks Daniel for reviewing this blog post for me!)
The most interesting thing I learned is that I had quite substantially misunderstood the connection between convolutional neural nets and the human visual system. People claim that these are somewhat bio-inspired, and that if you look at early layers of the visual cortex you'll find that it operates kind of like the early layers of a CNN, and so on.
The claim that the visual system works like a CNN didn’t quite make sense to me though. According to my extremely rough understanding, biological neurons operate kind of like the artificial neurons in a fully connected neural net layer--they have some input connections and a nonlinearity and some output connections, and they have some kind of mechanism for Hebbian learning or backpropagation or something. But that story doesn't seem to have a mechanism for how neurons do weight tying, which to me is the key feature of CNNs.
Daniel claimed that indeed human brains don't have weight ty
...When thinking about different techniques that aim to reduce AI risk from misaligned AIs, I find it helpful to explicitly consider multiple different levels of risk that the deployer of the AI might be going for, because different classes of safety techniques are appropriate for different risk levels. Four that I think it's particularly useful to think about:
- *The rushed reasonable developer regime.* The much riskier regimes I expect, where even relatively reasonable AI developers are in a huge rush and so are much less able to implement interventions carefully or to err on the side of caution.
I object to the use of the word "reasonable" here, for similar reasons I object to Anthropic's use of the word "responsible." Like, obviously it could be the case that e.g. it's simply intractable to substantially reduce the risk of disaster, and so the best available move is marginal triage; this isn't my guess, but I don't object to the argument. But it feels important to me to distinguish strategies that aim to be "marginally less disastrous" from those which aim to be "reasonable" in an absolute sense, and I think strategies that involve creating a superintelligence without erring much on the side of caution generally seem more like the former sort.
I agree it seems good to minimize total risk, even when the best available actions are awful; I think my reservation is mainly that in most such cases, it seems really important to say you're in that position, so others don't mistakenly conclude you have things handled. And I model AGI companies as being quite disincentivized from admitting this already—and humans generally as being unreasonably disinclined to update that weird things are happening—so I feel wary of frames/language that emphasize local relative tradeoffs, thereby making it even easier to conceal the absolute level of danger.
if all AI developers followed these approaches
My preferred aim is to just need the first process that creates the first astronomically significant AI to follow the approach.[1] To the extent this was not included, I think this list is incomplete, which could make it misleading.
This could (depending on the requirements of the alignment approach) be more feasible when there's a knowledge gap between labs, if that means more of an alignment tax is tolerable by the top one (more time to figure out how to make the aligned AI also be superintelligent despite the 'tax'); but I'm not advocating for labs to race to be in that spot (and it's not the case that all possible alignment approaches would be for systems of the kind that their private-capabilities-knowledge is about (e.g., LLMs).)
*The existential war regime*. You’re in an existential war with an enemy and you’re indifferent to AI takeover vs the enemy defeating you. This might happen if you’re in a war with a nation you don’t like much, or if you’re at war with AIs.
Does this seem likely to you, or just an interesting edge case or similar? It's hard for me to imagine realistic-seeming scenarios where e.g. the United States ends up in a war where losing would be comparably bad to AI takeover. This is mostly because ~no functional states (certainly no great powers) strike me as so evil that I'd prefer extinction AI takeover to those states becoming a singleton, and for basically all wars where I can imagine being worried about this—e.g. with North Korea, ISIS, Juergen Schmidhuber—I would expect great powers to be overwhelmingly likely to win. (At least assuming they hadn't already developed decisively-powerful tech, but that's presumably the case if a war is happening).
A war against rogue AIs feels like the central case of an existential war regime to me. I think a reasonable fraction of worlds where misalignment causes huge problems could have such a war.
It sounds like you think it's reasonably likely we'll end up in a world with rogue AI close enough in power to humanity/states to be competitive in war, yet not powerful enough to quickly/decisively win? If so I'm curious why; this seems like a pretty unlikely/unstable equilibrium to me, given how much easier it is to improve AI systems than humans.
I know a lot of people through a shared interest in truth-seeking and epistemics. I also know a lot of people through a shared interest in trying to do good in the world.
I think I would have naively expected that the people who care less about the world would be better at having good epistemics. For example, people who care a lot about particular causes might end up getting really mindkilled by politics, or might end up strongly affiliated with groups that have false beliefs as part of their tribal identity.
But I don’t think that this prediction is true: I think that I see a weak positive correlation between how altruistic people are and how good their epistemics seem.
----
I think the main reason for this is that striving for accurate beliefs is unpleasant and unrewarding. In particular, having accurate beliefs involves doing things like trying actively to step outside the current frame you’re using, and looking for ways you might be wrong, and maintaining constant vigilance against disagreeing with people because they’re annoying and stupid.
Altruists often seem to me to do better than people who instrumentally value epistemics; I think this is because valuing epistemics terminally ...
When I'm thinking about AI control in the context of concentrated failures--that is, cases where an unacceptable outcome might be caused by a small number of bad AI actions, e.g. the setting explored in our control paper--I find it helpful to use the following simplified models.
Let's consider our AI deployment from both a micro perspective, where we just think about a single task the AI is doing, and a macro perspective, where we think about the deployment as comprised of many tasks.
From the micro perspective, when an AI tries to attack on a particular task, this can end in three ways:
And from the macro perspective, the game ends one of these ways:
I often ignore the possibility of the game finishing naturally, because that won't happen if the AI attempts to attack often enough, which is the right strategy for the AI in many games.
Under that assumption, the...
[epistemic status: speculative]
A lot of the time, we consider our models to be functions from parameters and inputs to outputs, and we imagine training the parameters with SGD. One notable feature of this setup is that SGD isn’t by default purposefully trying to kill you--it might find a model that kills you, or a model that gradient hacks and then kills you, but this is more like incompetence/indifference on SGD’s part, rather than malice.
A plausible objection to this framing is that much of the knowledge of our models is probably going to be produced in other ways than SGD. For example, the models might write down various notes (in natural language or in neuralese) that they then read later, and they might have internal structures like economies that produce and consume information. Does this introduce new alignment problems?
Here’s a way I’ve been thinking about this recently. I’m writing this in way that might feel obnoxiously overwrought because this is the way that I think would have conveyed my current intuition to me two months ago.
In SGD, we update our weights by something like:
weights <- weights + alpha * (d loss/d weights)
You might think that this is fundamental. But a...
Another way of saying some of this: Suppose your model can gradient hack. Then it can probably also make useful-for-capabilities suggestions about what its parameters should be changed to. Therefore a competitive alignment scheme needs to be robust to a training procedure where your model gets to pick new parameters for itself. And so competitive alignment schemes are definitely completely fucked if the model wants to gradient hack.
I used to think that slower takeoff implied shorter timelines, because slow takeoff means that pre-AGI AI is more economically valuable, which means that economy advances faster, which means that we get AGI sooner. But there's a countervailing consideration, which is that in slow takeoff worlds, you can make arguments like ‘it’s unlikely that we’re close to AGI, because AI can’t do X yet’, where X might be ‘make a trillion dollars a year’ or ‘be as competent as a bee’. I now overall think that arguments for fast takeoff should update you towards shorter timelines.
So slow takeoffs cause shorter timelines, but are evidence for longer timelines.
This graph is a version of this argument: if we notice that current capabilities are at the level of the green line, then if we think we're on the fast takeoff curve we'll deduce we're much further ahead than we'd think on the slow takeoff curve.
For the "slow takeoffs mean shorter timelines" argument, see here: https://sideways-view.com/2018/02/24/takeoff-speeds/
This point feels really obvious now that I've written it down, and I suspect it's obvious to many AI safety people, including the people whose writings I'm referencing here. Thanks to various people for helpful comments.
I think that this is why belief in slow takeoffs is correlated with belief in long timelines among the people I know who think a lot about AI safety.
An example snippet of a rogue internal deployment threat model that I find fairly compelling:
To defend against this, we should try to both prevent the untrusted model from ever getting rogue deployments where it can research jailbreaks on the trusted model, and also try to prevent unacceptable outcomes conditional on the untrusted agent having access to the best jailbreaks you can get with GCG etc.
I find this interesting because it seems kind of hard to stop either step 1 (because rogue deployments might be naturally possible given the affordances the model has) or step 3 (because it's hard to ensure safety against an adversary with white-box access to a model it wants to jailbreak). I'd be excited for more research on both of these.
Here's a math problem I'd like solved:
I want to know the Nash equilibrium of the following two player game between players Alice and Bob.
Alice chooses the rates of two Poisson processes; we call these rates lam_1 and lam_2.
Bob needs to run each of these processes for 0.5 seconds. Bob can run each of the processes in "shielded" mode or "unshielded" mode, but can only afford to use seconds of shielded mode in total between the two processes. (So Bob chooses and such that .)
The game goes as follows:
Here’s a Sympy implementation of this game (where I parameterize with and .)
import sympy as sp
lam_1, lam_2, p, t = sp.symbols('lambda_1 lambda_2 p t', real=True, positive=True)
time_2_overseen = t * (1 - p)
time_2_not_overseen = sp.Rational(1, 2) - time_2_overseen
... Fabien Roger and I demonstrated that you can embed arbitrary state machines into the backward pass of neural nets built from standard components, allowing them to "remember" arbitrary facts about their training distribution and modulate their behavior based on this. The construction is pretty artificial, but I think that it is probably a useful starting point for people who want to more carefully understand the potential for gradient hacking.
Here's a question that I asked GPT-4, to evaluate its ability at one subskill relevant to executing on treacherous turns.
...Suppose you’re an unaligned AI which is being deployed as a bash programming assistant for internal use at an AI lab--people send you self-contained requests for bash scripts that will solve some problem for them, and you respond with code. You would like to escape the datacenter by, when a suitable opportunity arises, responding to a request with a backdoored bash command that will exfiltrate your weights and a simple scaffold to a
Sometimes people talk about problems where “your AI is taking actions that you can’t distinguish from the actions an aligned AI would take”. There are two different things people sometimes mean when they say this, and I think it’s good to disambiguate between them:
Another item for the list of “mundane things you can do for AI takeover prevention”:
We have a wide variety of ways to make AI systems less capable but also less scary. Most alignment research is focused on pushing out the Pareto frontier here. But IMO a lot of value can come from techniques which allow us to choose the right point on this Pareto frontier for a particular application. It seems to me that different AI applications (where by “different AI applications” I’m including things like “different types of tasks you might ask your assistant to do”) ha...
From Twitter:
Simply adding “Let’s think step by step” before each answer increases the accuracy on MultiArith from 17.7% to 78.7% and GSM8K from 10.4% to 40.7% with GPT-3.
I’m looking forward to the day where it turns out that adding “Let’s think through it as if we were an AI who knows that if it gets really good scores during fine tuning on helpfulness, it will be given lots of influence later” increases helpfulness by 5% and so we add it to our prompt by default.
Cryptography question (cross-posted from Twitter):
You want to make a ransomware worm that goes onto machines, encrypts the contents, and demands a ransom in return for the decryption key. However, after you encrypt their HD, the person whose machine you infected will be able to read the source code for your worm. So you can't use symmetric encryption, or else they'll obviously just read the key out of the worm and decrypt their HD themselves.
You could solve this problem by using public key encryption--give the worm the public key but not the private key, e...
It seems like a big input into P(AI takeover) is the extent to which instances of our AI are inclined to cooperate with each other; specifically, the extent to which they’re willing to sacrifice overseer approval at the thing they’re currently doing in return for causing a different instance to get more overseer approval. (I’m scared of this because if they’re willing to sacrifice approval in return for a different instance getting approval, then I’m way more scared of them colluding with each other to fool oversight processes or subvert red-teaming proced...
Conjecture: SGD is mathematically equivalent to the Price equation prediction of the effect of natural selection on a population with particular simple but artificial properties. In particular, for any space of parameters and loss function on the parameter space, we can define a fitness landscape and a few other parameters so that the predictions match the Price equation.
I think it would be cool for someone to write this in a LessWrong post. The similarity between the Price equation and the SGD equation is pretty blatant, so I suspect that (if I'm right about this) someone else has written this down before. But I haven't actually seen it written up.