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. $2ϵ$ or $3ϵ$ would be fine; it may be a judgement call on our part if the bound is much larger than that. 

Let $Y\sim \text{Ber}\left(p\right)$. With probability $r$, set $Z:=X$, and otherwise draw $Z\sim \text{Ber}\left(p\right)$. Let $Y\sim \text{Ber}\left(1/2\right)$. Let $A=X\oplus Y$ and $B=Y\oplus Z$. We will investigate latents for $(A,B)$. 

Set $\Lambda :=Y$, then note that the stochastic error $ϵ:=I(A;Y|B)$) because $Y$ induces perfect conditional independence and symmetry of $A$ and $B$. Now compute the deterministic errors of $\Lambda :=Y$, $\Lambda :=0$, $\Lambda :=A$, which are equal to $H(Y\mid A),I(A;B),H\left(A|B\right)$ respectively. 

Then it turns out that with $p:=0.9,r:=0.44$, all of these latents have error greater than $5ϵ$, 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 $10ϵ$ 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 $p,r$ out of some discrete set of possibilities instead of having them be fixed.

Yes, thanks!

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 :) 

Do you have any predictions about the first year when AI assistance will give a 2x/10x/100x factor "productivity boost" to AI research?