#proof complexity

[pv1isalsoimportant]

anime girl proof complexity! ANIME GIRL PROOF COMPLEXITY!

Logic seminar at IM CAS; Metamathematics of Resolution Lower Bounds: A TFNP Perspective, Hanlin Ren, Oxford Univ.

[qonphuceingey]

I’ve been thinking a bit about AI and its cognition for the past few days.

When an AI thinks about an problem and figured out the idea to solve it, there are a couple cases for the solution.

Case 1) It already knows the solution. It just presents the solution near instantly.

Case 2) If it synthesises n different ideas together linearly, like a chain of logical deduction with n axioms in use along the way, it can arrive at the solution. The n ideas needed are probably whatever the question is about. The AI already knows each of these n ideas in the way mentioned in the previous case. This is somewhat like applying a known theorem to a problem.

Case 3) If it needs to chain asymptotically more than n ideas to get the solution (like n^{2} ideas or e^{n}). Once all of these sub problems are solved, this reverts back to a Case 2 problem. While there are different algorithms, like nlogn or n!, that I could use to describe the problems that fit into this case, and I’m sure I could extend these categories infinitely by picking bigger and bigger algorithms, I don’t think it really matters how much further over n it is, since it all depends on what the AI already knows. The point is that problems in this category require solving sub problems.

Currently I feel like AI and LLMs are stuck at the level of category 2, and probably only for low values of n. I’m thinking of this as something like halfway up the category.

I think once they get into the level of category 3, where they’re not just applying information we already know but sort of synthesising it themselves, that’s when we get a runaway AGI effect, since they can perform research on themselves.

It’s also interesting to think about the recursive nature of discovery and invention and research. You should really be able to solve any problem by applying the method in category 2 to it, and attempting to guess what ideas you’d need to prove for each stage and checking their validity via the exact same method.

I think AIs current limitations on this are probably things like the context window (so they forget stage 1 once they hit stage 17) and perhaps the ability to recursively apply this idea. I don’t know enough about how they’re training the models to say if they’ve been trying to implement this recursion or not, although I assume they have, as this is a pretty obvious idea to try.

What I do think the AIs are pretty good at right now is guessing what ideas might be useful to try and prove. I’m sure they could be better, but it’s impressive they’ve risen to essentially my level at this task. To be fair though, the AI typically goes for the most surface level answer possible, and doesn’t try to get deeper into a topic unless prompted. This lack of curiosity might be a downside too. They certainly know enough and can think clearly enough to come to these conclusions, but they can’t be bothered to since a standard answer is just as well received generally.

Very interesting. I’m excited to see where it goes.

[uncanny-tranny]

Basically, my philosophy around disability fakers is: I would rather a thousand people fake a disability than have one disabled person suffer without care, aids, compassion, or any help.

[crustyfloor]

With Till's bond with Ivan, I interpret it as very "proximity breeds intimacy." With the way Till eventually forms a close bond with Ivan, even if their relationship is not quite as smooth sailing, it's very interpretative of how Till sees people, what he says vs what he does, and whatnot.

Till finds his very first love in Mizi, as it is, it's more puppy love-ish, but seriously, he thinks the world of Mizi. I think the major difference in Ivan and Till is that Till holds no such ideals or expresses that kind of affection for Ivan outwardly- they bicker and fight, but ultimately, they just naturally gravitate towards each other, and they form an inseparable attachment. Although sympathetic, it's not because Till sees Ivan as pitiable or anything of the sort. He genuinely cares because he just does.

Even in the meteor shower scene, it wasn't any hard feelings towards Ivan that made Till turn away, even though in Cure all that Ivan sees if Till's back, that minute's hesitation that we see says Till didn't want to do this with intent to hurt Ivan without a second thought or that he didn't care about it at all

Till is honest with his feelings with no restrictions, he gets pissed with Ivan but Ivan's attachment and want to be close to Till, therefore causing them to spend time together, passively made him grow used to Ivan. To care for him because he inevitably became one of the closest people to Till in his life, and I think it's in the subtlety that we can see Till doesn't really push Ivan away anyway, probably even allows himself to be comfortable with Ivan and seek him out sometimes cause that's just how friends are

Even in that silly intimacy rating chart, Ivan came second to Mizi, with a significant 70%, even though the whole comment section was Till complaining about how much of a nuisance he is, well, that's just the truth... Ivan does things that he can't figure out or that irritate him, like in these instances

And Till is honest about that, but even so, it seems like Till also grew more lenient to Ivan's quirks and got used to his presence over time, the more their relationship was established, Till's relationship with Ivan is like a crash course in trying to find the line of toleration, so I don't want to say sometimes when Ivan comes off intentionally provoking Till isn't just trying to ignore him, but as aforementioned, proximity breeds intimacy, also familiarity. I think, despite all this (especially the Cafeteria scene in Cure, what a story, Ivan intentionally nags Till, and Till, having been so used to it, simply shrugs him off), Till sees Ivan with familiarity, and that's why he doesn't hate him for the things he does, accepts him because even for how guarded his heart is, in io's prayers he would always chase after love and connection. His affection is genuine and unconditional when he cares about someone or something, it took nothing for him to devote his soul to Mizi and to care about Ivan because of the memories they have together

Because Till always loved Ivan, and "love" isn't just restricted to romantic love either, but when Till identifies the ones he cares about and sees as friends, it's always those three... I think one of the hardest things about this dynamic is that Ivan thinks of himself as a mere character in Till's life that he doesn't care about because there's no way a person like Till could care about a person like Ivan to such a degree, it's just unfathomable. But Till always considered Ivan close, what they have may not be as simple as friendship or the like, but it's something close and personal

puh

[poorly-drawn-mdzs]

He was just being a silly little guy!

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[artuurle]

"I'm picking at my sweater Aware that some day I will die Just praying and hoping That I can leave something behind"

Alt without most the shading under the cut

this guy sucks lets kill him with hammers

[the-commonplace-book]

Trump wants to enforce gender assignment at conception based on biological sex. AFAB and AMAB are out. Absolutely every single American will now be AFAC (assigned female at conception). Congrats on the gender.

[nabesthetics]

hey

[windcarvedlyre]

The more I try to analyse Komaeda the more apparent it becomes that he's a hypocrite about everything. Ever. All the time. Cognitive dissonance all the way down.

[wysecollection]

I have no proof for this but maybe the reason a lot of systems have introjects from more recent/popular media is because when the disorder was getting brutally misunderstood on Tiktok and other social medias was around 2020-2021 which was also when kin culture was becoming more "normal" or mainstream (I'm aware it existed in full force before, just that a lot of new people were getting into it), and was also during a time that people were spending a lot of time indoors and engaging in media during a globally isolating and stressful time and pwDID found it easier (not by choice but by their brain's function) to take traits from fictional characters that made them feel less alone.

[pv1isalsoimportant]

Studying for a logic in computer science exam and going insane. Here are some of my favourite bits.

[sieglinde-freud]

one thing i never realized bc i always either pair chrom with olivia or make him gay is that not every sibling calls lucina “luce” and its making me crazy. inigo and brady call her “luce” for short. cynthia calls her “lucy” (MY FAV), and kjelle and morgan just call her “lucina.” why did they make this change across supports. “to add personality” you say and to that i say YES obviously but also. potential of telling us more about how close lucina was with each potential sibling? maybe. what im getting at here is chrom!kjelle and lucina maybe suffering the most in terms of feelings of inadequacy and having that slight strain that keeps them from being close. this does not apply to morgan bc i chalk his up to memory loss BUT. you could also say that lucina never let him get close because she’s wary of him. hows that. and if you read closely what im actually saying is that i need an au where all six of them are siblings and not all of them have the brand of the exalt

[wellijustfinnihedoneofthebooks]

"Batman has a contingency plan for everyone in the justice league" false, one angry look from wonder woman and that sub'll fall in line

[vampire-nyx]

Honestly really disappointing and upsetting that just after I found the pills that make you green comics the creator turned out to very much extremely hate people like me

[mathematical-cheese]

Just realised there's a convoluted proof for showing that any smooth vector bundle is homotopy equivalent to its base space

[starlight-lesbians]

idk i think greaseball is dumb not because she misspelled one word, but just because of like Every Single Choice she makes up until she apologizes to Dinah

like taking her girlfriend for granted? dumb. trying to sabotage rusty instead of relying on her own ability? stupidddd! generally acting like an bully? dumb dumb

and like i’ve written about her numerous complexes multiple times, i get it, however she’s still dumb for that (/mostly affectionate)

i love her and can make fun of her a little bit i think. greaseball was kind of always written as kind of a meathead jock but i think in later versions they’ve done a good job giving him/her some more depth.

they made gb more sympathetic over time too which is nice, if you wanna redeem a character you kinda have to make them likable to an extent

idk yall she’s my favorite girlfailure at the end of the day.