Currently a MATS scholar working with Vanessa Kosoy on the learning-theoretic agenda for AI Alignment.
Arjun Pitchanathan
Karma: 37
Interesting turn of events for the US to now disincentivize trade with Japan, wonder what Commodore Perry would think
My impression is that prior discussion focused on discretizing . is already boolean here, so if the hypothesis is true then it’s for a different reason.
On this particular example you can achieve deterministic error with latent , but it seems easy to find other examples with ratio > 5 (including over latents ) in the space of distributions over with a random-restart hill-climb. Anyway, my takeaway is that if you think you can derandomize latents in general you should probably try to derandomize the latent for variables , for distributions over boolean variables .
(edited to fix typo in definition of )
To check my understanding: for random variables , the stochastic error of a latent is the maximum among . The deterministic error is the maximum among . If so, the claim in my original comment holds—I also wrote code (manually) to verify. Here’s the fixed claim:
Let . With probability , set , and otherwise draw . Let . Let and . We will investigate latents for . Let be the stochastic error of latent . Now compute the deterministic errors of each of the latents , , , , , , . Then for , all of these latents have deterministic error greater than .
It should be easy to modify the code to consider other latents. I haven’t thought much about proving that there aren’t any other latents better than these, though.
Yeah, my comment went through a few different versions and that statement doesn’t apply to the final setting. I should’ve checked it better before hitting submit, sorry. I only used LLMs for writing code for numerical calculations, so the error is mine. [1]
I think that I didn’t actually use this claim in the numerical calculations, so I’d hope that the rest of the comment continues to hold. I had hoped to verify that before replying, but given that it’s been two weeks already, I don’t know when I’ll manage to get to it.
- ^
I did try to see if it could write a message explaining the claim, but didn’t use that
- ^
Thanks! (I knew enough about Avatar to know what you wrote in your last paragraph, but the rest is new to me)
got more exposition on what you mean with the different elements in this context?
In the case that we live in a simulation, should our reality be treated as “fictional” or “non-fictional”?
What is the actual difference between a “fictional” and “non-fictional” scenario here? I’m not convinced that it’s a failure of general intelligence to not agree with us on this. (It’s certainly a failure of alignment.)
I have not read the post, but am confused as to why it is at −3 karma. Would some of the downvoters care to explain their reasoning?
Epistemic status: Quick dump of something that might be useful to someone. o3 and Opus 4 independently agree on the numerical calculations for the bolded result below, but I didn’t check the calculations myself in any detail.
When we say “roughly”, e.g. or would be fine; it may be a judgement call on our part if the bound is much larger than that.
Let . With probability , set , and otherwise draw . Let . Let and . We will investigate latents for .
Set , then note that the stochastic error ) because induces perfect conditional independence and symmetry of and . Now compute the deterministic errors of , , , which are equal to respectively.
Then it turns out that with , all of these latents have error greater than , if you believe this claude opus 4 artifact (full chat here, corroboration by o3 here). Conditional on there not being some other kind of latent that gets better deterministic error, and the calculations being correct, I would expect that a bit more fiddling around could produce much better bounds, say or more, since I think I’ve explored very little of the search space.
e.g. one could create more As and Bs by either adding more Ys, or more Xs and Zs. Or one could pick the probabilities out of some discrete set of possibilities instead of having them be fixed.
Yes, thanks!
representation of a variable for variable
Hm, I don’t understand what is supposed to be here.
Isn’t it the case that when you sing a high note, you feel something higher in your mouth/larynx/whatever , and when you sing a low note, you feel something lower? Seems difficult to tell whether I actually do need to do that or I’ve just conditioned myself to, because of the metaphor.
If you’re reading the text in a two-dimensional visual display, you are giving yourself an advantage over the LLM. You should actually be reading it in a one-dimensional format with new-line symbols.
(disclosure, I only skimmed your COT for like a few seconds)
the real odds would be less about the ELO and more on whether he was drunk while playing me
not sure if that would help :)
I don’t think this will work because we are already using subscripts to denote which environment’s list we are referring to
I’m not. I guess this is the part that makes it confusing
for readability we define and to be the accessible and outer action spaces of respectively
Do you have a suggestion for alternate notation? I use this because we often need to refer to the action space corresponding to a state. I think this would be needed even with the language framing.
(I also assigned to make it more readable)
Do you have any predictions about the first year when AI assistance will give a 2x/10x/100x factor “productivity boost” to AI research?
I think it’s a feature of the local dialect. I’ve seen it multiple times around here and never outside.