An eccentric dreamer in search of truth and happiness for all. Formerly posted on Felicifia back in the day under the same name. Been a member of Less Wrong and involved in Effective Altruism since roughly 2013.
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So, my main idea is that the principle of maximum entropy aka the principle of indifference suggests a prior of 1/n where n is the number of possibilities or classes. P x 2 − 1 leads to p = 0.5 for c = 0. What I want is for c = 0 to lead to p = 1/n rather than 0.5, so that it works in the multiclass cases where n is greater than 2.
Correlation space is between −1 and 1, with 1 being the same (definitely true), −1 being the opposite (definitely false), and 0 being orthogonal (very uncertain). I had the idea that you could assume maximum uncertainty to be 0 in correlation space, and 1/n (the uniform distribution) in probability space.
I tried asking ChatGPT, Gemini, and Claude to come up with a formula that converts between correlation space to probability space while preserving the relationship 0 = 1/n. I came up with such a formula a while back, so I figure it shouldn’t be hard. They all offered formulas, all of which were shown to be very much wrong when I actually graphed them to check.
I was not aware of these. Thanks!
Thanks for the clarifications. My naive estimate is obviously just a simplistic ballpark figure using some rough approximations, so I appreciate adding some precision.
Also, even if we can train and run a model the size of the human brain, it would still be many orders of magnitude less energy efficient than an actual brain. Human brains use barely 20 watts. This hypothetical GPU brain would require enormous data centres of power, and each H100 GPU uses 700 watts alone.
I’ve been looking at the numbers with regards to how many GPUs it would take to train a model with as many parameters as the human brain has synapses. The human brain has 100 trillion synapses, and they are sparse and very efficiently connected. A regular AI model fully connects every neuron in a given layer to every neuron in the previous layer, so that would be less efficient.
The average H100 has 80 GB of VRAM, so assuming that each parameter is 32 bits, then you have about 20 billion per GPU. So, you’d need 10,000 GPUs to fit a single instance of a human brain in RAM, maybe. If you assume inefficiencies and need to have data in memory as well you could ballpark another order of magnitude so 100,000 might be needed.
For comparison, it’s widely believed that OpenAI trained GPT4 on about 10,000 A100s that Microsoft let them use from their Azure supercomputer, most likely the one listed as third most powerful in the world by the Top500 list.
Recently though, Microsoft and Meta have both moved to acquire more GPUs that put them in the 100,000 range, and Elon Musk’s X.ai recently managed to get a 100,000 H100 GPU supercomputer online in Memphis.
So, in theory at least, we are nearly at the point where they can train a human brain sized model in terms of memory. However, keep in mind that training such a model would take a ton of compute time. I haven’t done to calculations yet for FLOPS so I don’t know if it’s feasible yet.
Just some quick back of the envelope analysis.
I ran out of the usage limit for GPT-4o (seems to just be 10 prompts every 5 hours) and it switched to GPT-4o-mini. I tried asking it the Alpha Omega question and it made some math nonsense up, so it seems like the model matters for this for some reason.
So, a while back I came up with an obscure idea I called the Alpha Omega Theorem and posted it on the Less Wrong forums. Given how there’s only one post about it, it shouldn’t be something that LLMs would know about. So in the past, I’d ask them “What is the Alpha Omega Theorem?”, and they’d always make up some nonsense about a mathematical theory that doesn’t actually exist. More recently, Google Gemini and Microsoft Bing Chat would use search to find my post and use that as the basis for their explanation. However, I only have the free version of ChatGPT and Claude, so they don’t have access to the Internet and would make stuff up.
A couple days ago I tried the question on ChatGPT again, and GPT-4o managed to correctly say that there isn’t a widely known concept of that name in math or science, and basically said it didn’t know. Claude still makes up a nonsensical math theory. I also today tried telling Google Gemini not to use search, and it also said it did not know rather than making stuff up.
I’m actually pretty surprised by this. Looks like OpenAI and Google figured out how to reduce hallucinations somehow.
I’m wondering what people’s opinions are on how urgent alignment work is. I’m a former ML scientist who previously worked at Maluuba and Huawei Canada, but switched industries into game development, at least in part to avoid contributing to AI capabilities research. I tried earlier to interview with FAR and Generally Intelligent, but didn’t get in. I’ve also done some cursory independent AI safety research in interpretability and game theoretic ideas my spare time, though nothing interesting enough to publish yet.
My wife also recently had a baby, and caring for him is a substantial time sink, especially for the next year until daycare starts. Is it worth considering things like hiring a nanny, if it’ll free me up to actually do more AI safety research? I’m uncertain if I can realistically contribute to the field, but I also feel like AGI could potentially be coming very soon, and maybe I should make the effort just in case it makes some meaningful difference.
Thanks for the reply!
So, the main issue I’m finding with putting them all into one proposal is that there’s a 1000 character limit on the main summary section where you describe the project, and I cannot figure out how to cram multiple ideas into that 1000 characters without seriously compromising the quality of my explanations for each.
I’m not sure if exceeding that character limit will get my proposal thrown out without being looked at though, so I hesitate to try that. Any thoughts?
I already tried discussing a very similar concept I call Superrational Signalling in this post. It got almost no attention, and I have doubts that Less Wrong is receptive to such ideas.
I also tried actually programming a Game Theoretic simulation to try to test the idea, which you can find here, along with code and explanation. Haven’t gotten around to making a full post about it though (just a shortform).
So, I have three very distinct ideas for projects that I’m thinking about applying to the Long Term Future Fund for. Does anyone happen to know if it’s better to try to fit them all into one application, or split them into three separate applications?
Recently I tried out an experiment using the code from the Geometry of Truth paper to try to see if using simple label words like “true” and “false” could substitute for the datasets used to create truth probes. I also tried out a truth probe algorithm based on classifying with the higher cosine similarity to the mean vectors.
Initial results seemed to suggest that the label word vectors were sorta acceptable, albeit not nearly as good (around 70% accurate rather than 95%+ like with the datasets). However, testing on harder test sets showed much worse accuracy (sometimes below chance, somehow). So I can probably conclude that the label word vectors alone aren’t sufficient for a good truth probe.
Interestingly, the cosine similarity approach worked almost identically well as the mass mean (aka difference in means) approach used in the paper. Unlike the mass mean approach though, the cosine similarity approach can be extended to a multi-class situation. Though, logistic regression can also be extended similarly, so it may not be particularly useful either, and I’m not sure there’s even a use case for a multi-class probe.
Anyways, I just thought I’d write up the results here in the unlikely event someone finds this kind of negative result as useful information.
Update: I made an interactive webpage where you can run the simulation and experiment with a different payoff matrix and changes to various other parameters.
So, I adjusted the aggressor system to work like alliances or defensive pacts instead of a universal memory tag. Basically, now players make allies when they both cooperate and aren’t already enemies, and make enemies when defected against first, which sets all their allies to also consider the defector an enemy. This, doesn’t change the result much. The alliance of nice strategies still wins the vast majority of the time.
I also tried out false flag scenarios where 50% of the time the victim of a defect first against non-enemy will actually be mistaken for the attacker. This has a small effect. There is a slight increase in the probability of an Opportunist strategy winning, but most of the time the alliance of nice strategies still wins, albeit with slightly fewer survivors on average.
My guess for why this happens is that nasty strategies rarely stay in alliances very long because they usually attack a fellow member at some point, and eventually, after sufficient rounds one of their false flag attempts will fail and they will inevitably be kicked from the alliance and be retaliated against.
The real world implications of this remain that it appears that your best bet of surviving in the long run as a person or civilization is to play a nice strategy, because if you play a nasty strategy, you are much less likely to survive in the long run.
In the limit, if the nasty strategies win, there will only be one survivor, dog eat dog highlander style, and your odds of being that winner are 1/N, where N is the number of players. On the other hand, if you play a nice strategy, you increase the strength of the nice alliance, and when the nice alliance wins as it usually does, you’re much more likely to be a survivor and have flourished together.
My simulation currently by default has 150 players, 60 of which are nice. On average about 15 of these survive to round 200, which is a 25% survival rate. This seems bad, but the survival rate of nasty strategies is less than 1%. If I switch the model to use 50 Avengers and 50 Opportunists, on average 25 Avengers survive to zero Opportunists, a 50% survival rate for the Avengers.
Thus, increasing the proportion of starting nice players increases the odds of nice players surviving, so there is an incentive to play nice.
Admittedly this is a fairly simple set up without things like uncertainty and mistakes, so yes, it may not really apply to the real world. I just find it interesting that it implies that strong coordinated retribution can, at least in this toy set up, be useful for shaping the environment into one where cooperation thrives, even after accounting for power differentials and the ability to kill opponents outright, which otherwise change the game enough that straight Tit-For-Tat doesn’t automatically dominate.
It’s possible there are some situations where this may resemble the real world. Like, if you ignore mere accusations and focus on just actual clear cut cases where you know the aggression has occurred, such as with countries and wars, it seems to resemble how alliances form and retaliation occurs when anybody in the alliance is attacked?
I personally also see it as relevant for something like hypothetical powerful alien AGIs that can see everything that happens from space, and so there could be some kind of advanced game theoretic coordination at a distance with this. Though that admittedly is highly speculative.
It would be nice though if there was a reason to be cooperative even to weaker entities as that would imply that AGI could possibly have game theoretic reasons not to destroy us.
Okay, so I decided to do an experiment in Python code where I modify the Iterated Prisoner’s Dilemma to include Death, Asymmetric Power, and Aggressor Reputation, and run simulations to test how different strategies do. Basically, each player can now die if their points falls to zero or below, and the payoff matrix uses their points as a variable such that there is a power difference that affects what happens. Also, if a player defects first in any round of any match against a non-aggressor, they get the aggressor label, which matters for some strategies that target aggressors.
Long story short, there’s a particular strategy I call Avenger, which is Grim Trigger but also retaliates against aggressors (even if the aggression was against a different player) that ensures that the cooperative strategies (ones that never defect first against a non-aggressor) win if the game goes enough rounds. Without Avenger though, there’s a chance that a single Opportunist strategy player wins instead. Opportunist will Defect when stronger and play Tit-For-Tat otherwise.
I feel like this has interesting real world implications.Interestingly, Enforcer, which is Tit-For-Tat but also opens with Defect against aggressors, is not enough to ensure the cooperative strategies always win. For some reason you need Avenger in the mix.
Edit: In case anyone wants the code, it’s here.
I was recently trying to figure out a way to calculate my P(Doom) using math. I initially tried just making a back of the envelope calculation by making a list of For and Against arguments and then dividing the number of For arguments by the total number of arguments. This led to a P(Doom) of 55%, which later got revised to 40% when I added more Against arguments. I also looked into using Bayes Theorem and actual probability calculations, but determining P(E | H) and P(E) to input into P(H | E) = P(E | H) * P(H) / P(E) is surprisingly hard and confusing.
p = (n^c * (c + 1)) / (2^c * n)
As far as I know, this is unpublished in the literature. It’s a pretty obscure use case, so that’s not surprising. I have doubts I’ll ever get around to publishing the paper I wanted to write that uses this in an activation function to replace softmax in neural nets, so it probably doesn’t matter much if I show it here.