Obligatory shill/reminder for any teacher reading this that if they want a never-before-seen educational data science challenge which can’t be solo’d by current-gen AI (and is incidentally super easy to mark) they can just DM me; I might want some kind of compensation if it needs to be extensively customized and/or never released to the public, but just sharing scenarios a few months before I post them on LW is something I’d absolutely do for the love of the game. (and if they want any other kind of challenge then uh good luck with that)
abstractapplic
Karma: 2,933
D&D.Sci: The Choosing Ones
I’m not sure exactly what quantity you are calculating when you refer to the singularity date. Is this the extrapolated date for 50% success at 1 month (167hr) tasks?
. . . not quite: I’d forgotten that your threshold was a man-month, instead of a month of clock time. I’ll redo things with the task length being a month of work for people who do need to eat/sleep/etc: luckily this doesn’t change results much, since 730 hours and 167 hours are right next door on a log(t) scale.
SWAA fits most naturally into the ‘fully_private’ category in the HCAST parlance
Your diagnosis was on the money. Filtering for the union of fully_private HCAST tasks and SWAA tasks (while keeping the three models which caused crashes without SWAAs) does still make forecasts more optimistic, but only nets half an extra year for the every-model model, and two extra years for the since-4o model.
I’ll edit the OP appropriately; thank you for your help. (In retrospect, I probably should have run the numbery stuff past METR before posting, instead of just my qualitative concerns; I figured that if I was successfully reproducing the headline results I would be getting everything else right, but it would still have made sense to get a second opinion.)
Potential biases:
The aforementioned fact that privacy levels are upper bounds on how private things might be: afaik, METR has no airtight way to know what fully_private tasks were leaked or plagiarized or had extremely similar doppelganger tasks coincidentally created by unrelated third parties, or which public_problems had solutions posted somewhere they couldn’t see but which nevertheless made it into the training data, or whether some public_solutions had really good summaries written down somewhere online.
The way later models’ training sets can only ever have more benchmark tasks present in them than earlier ones. (I reiterate that at least some of these tasks were first created around the apparent gradient discontinuity starting with GPT-4o.)
The fact they’re using non-fully_private challenges at all, and therefore testing (in part) the ability of LLMs to solve problems present in (some of their) training datasets. (I get that this isn’t necessarily reassuring as some problems we’d find it scary for AI to solve might also have specific solutions (or hints, or analogies) in the training data.)
The fact they’re using preternaturally clean code-y tasks to measure competence. (I get that this isn’t necessarily reassuring as AI development is arguably a preternaturally clean code-y task.)
The way Baselined tasks tend to be easier and Baselining seems (definitely slightly) biased towards making them look easier still, while Estimated tasks tend to be harder and Estimation seems (potentially greatly) biased towards making them look harder still: the combined effect would be to make progress gradients look artificially steep in analyses where Baselined and Estimated tasks both matter. (To my surprise, Estimated tasks didn’t make much difference to (my reconstruction of) the analysis due (possibly/plausibly/partially) to current task horizons currently being under an hour; but if someone used HCAST to evaluate more capable future models without doing another round of Baselining . . .)
Possibly some other stuff I forgot, idk. (All I can tell you is I don’t remember thinking “this seems like it’s potentially biased against reaching scary conclusions” at any point when reading the papers.)
Notes on the Long Tasks METR paper, from a HCAST task contributor
Looked into it more and you’re right: conventional symbolic regression libraries don’t seem to have the “calculate a quantity then use that as a new variable going forward” behavior I’d have needed to get Total Value and then decide&apply a tax rate based on that. I . . . probably should have coded up a proof-of-concept before impugning everyone including myself.
Reflections on my performance:
There’s an interesting sense in which we all failed this one. Most other players used AI to help them accomplish tasks they’d personally picked out; I eschewed AI altogether and constructed my model with brute force and elbow grease; after reaching a perfect solution, I finally went back and used AIcorrectly, by describing the problem on a high level (manually/meatbrainedly distilled from my initial observations) and asking the machine demiurge what approach would make most sense[1]. From this I learned about the fascinating concept ofSymbolic Regressionand some associated python libraries, which I eagerly anticipate using to (attempt to) steamroll similarly-shaped problems.(There’s a more mundane sense in which I specifically failed this one, since even after building a perfect input-output relation and recognizing the two best archetypes as rebatemaxxing and corpsemaxxing, I still somehow fell at the last hurdle and failed to get a (locally-)optimal corpsemaxxing solution; if the system had followed the original plan, I’d be down a silver coin and up a silver medal. Fortunately for my character’s fortunes and fortune, Fortune chose to smile.)
Reflections on the challenge:
A straightforward scenario, but timed and executed flawlessly. In particular, I found the figuring-things-out gradient (admittedly decoupled from the actually-getting-a-good-answer gradient) blessedly smooth, starting with picking up on the zero-randomness premise[2] and ending with the fun twist that the optimal solution doesn’t involve anything being taxed at the lowest rate[3].
I personally got a lot out of this one: for an evening’s exacting but enjoyable efforts, I learned about an entire new form of model-building, about the utility and limits of modern AI, and about Banker’s Rounding. I vote four-out-of-five for both Quality and Complexity . . . though I recognize that such puzzle-y low-variance games are liable to have higher variance in how they’re received, and I might be towards the upper end of a bell curve here.
- ^
For a lark, I also tried turning on all ChatGPT’s free capabilities and telling it to solve the problem from scratch. It thought for ~30 seconds and then spat out a perfect solution; I spent ~30 further seconds with paperclips dancing before my eyes; I then discovered it hadn’t even managed to download the dataset, and was instead applying the not-unreasonable heuristic “if abstractapplic and simon agree on an answer it’s probably true”.
- ^
There’s something fun about how “magic”, “games”, “bureaucracy”, and “magical game bureaucracy” are equally good justifications for a “wait, what paradigm am I even in here?” layer of difficulty.
- ^
I know that part wasn’t intentional, but I think rebatemaxxing>corpsemaxxing is nontrivially more compelling than the other way round.
- ^
Meta musing:
It looks like the optimal allocation is borderline fraudulent. When I think of in-universe reasons for the TAE to set up Cockatrice Eye rebates the way they did, my best guess is “there’s a bounty on these monsters in particular, and the taxmen figure someone showing up with n Cockatrice Eyes will have killed ceil(n/2) of them”. This makes splitting our four eyes (presumably collected from two monsters) four ways deceptive; my only consolation is that the apparently-standard divide-the-loot-as-evenly-as-possible thing most other adventuring teams seem to be doing also frequently ends up taking advantage of this incentive structure.
framing contradictory evidence as biased or manipulated
Most contradictory evidence is, to some extent (regardless of what it’s contradicting).
dismissing critics as [...] deluded, or self-interested
Most critics are, to some extent (regardless of what they’re criticizing).
Assuming I didn’t make any mistakes in my deductions or decisions, optimal plan goes like this:
Give everyone a Cockatrice Eye (to get the most out of the associated rebate) and a Dragon Head (to dodge the taxing-you-twice-on-every-Head-after-the-first thing).
Give the mage and the rogue a Unicorn Horn and a Zombie Hand each, and give the cleric four Zombie hands; this should get them all as close to the 30sp threshold as possible without wrecking anything else.
Give literally everything else to the fighter, allowing them to bear the entire 212sp cost; if they get mad about it, analogize it to being a meatshield in the financial world as well as the physical.
Thanks for your reply, and (re-)welcome to LW!
My conclusion is that I’m pretty sure you’re wrong in ways that are fun and useful to discuss!
I hope so! Let’s discuss.
(Jsyk you can spoiler possible spoilers on Desktop using “>!” at the start of paragraphs, in case you want to make sure no LWers are spoiled on the contents of a most-of-a-century-old play.)
Regarding the witnesses:
I agree—emphatically! - that eyewitness testimony is a lot less reliable than most people believe. I mostly only brought the witnesses up in my discussion because I thought the jury dismissed them for bad reasons, instead of a general policy of “eyewitnesses are unreliable”. (In retrospect, I could have been a lot clearer on this point.)
Regarding the knife:
I agree that the knife being unique would have made things a lot more clear-cut, but disagree about the implications.
If no-one is deliberately trying to frame the accused, the odds of the real killer happening to use the same brand of knife as the one he favors are very low. (What fraction of knives* available to potential suspects are of that exact type? One in a hundred, maybe? If we assume no frame-up or suicide and start with your prior probability of 10% then a naive Bayesian update and a factor of 100 moves that to >90% even without other evidence**.)
If he is actively being framed . . . that’s not overwhelmingly implausible, since it’s not a secret what kind of knife he uses, and the real killer would be highly motivated to shift blame. However, the idea that he’d have lost his knife, by coincidence, at the same time that someone was using an exact duplicate to frame him (and then couldn’t find it afterwards, even though it would be decisive for his defense) . . . strains credulity. I’m less sure about how to quantify the possibility a real killer took his knife without him knowing, got into the victim’s apartment, and performed the kill all while the accused was out at the movies; but I feel pretty confident the accused’s knife was the murder weapon.
*I’m ignoring the effects of the murder weapon being a knife at all because they’re surprisingly weak. The accused owns a knife and favors using it, but so would many alternative suspects; and the accused cohabiting with the victim implies he also has easy access to many alternative methods—poison, arranging an accident—that Hypothetical Killer X wouldn’t.
**Full disclosure, I didn’t actually perform the calculation until I started writing this post; I admit to being surprised by how little a factor of ~100 changes a ~10% prior probability, though I still feel it’s a stronger effect than you’re accounting for, and for that matter think your base rates are too low to start with (the fight wasn’t just a fight, it was the culmination of years of persistent abuse).
Regarding my conspiracy theories:
I agree that the protagonist having ideological or personal reasons to make the case turn out this way is much more likely than him having been successfully bribed or threatened; aside from anything else, the accused doesn’t seem terribly wealthy or well-connected.
I also agree with your analysis of the racist juror’s emotional state as presented, though I continue to think it’s slightly suspicious that things happened to break that conveniently (the Doylist explanation is of course that the director wanted the bigot to come off as weak and/or needed things to wrap up satisfyingly inside a two-hour runtime, but I’m an incorrigible Watsonian.)
One last, even more speculative thought:
Literally everything the racist juror does in the back half of the movie is weird and suspicious. It’s strange that he expects people to be convinced by his bigoted tirade; it’s also strangely convenient that he’s willing to vote not guilty by the end even though he A) hasn’t changed his mind and B) knows a hung jury would probably eventually lead to the death of the accused, which he wants.
I don’t think it’s likely, but I’d put maybe a ~1% probability on . . .
. . . him being in league with the protagonist, and them running a two-man con on the other ten jurors to get the unanimous verdict they want.
I recently watched (the 1997 movie version of) Twelve Angry Men, and found it fascinating from a Bayesian / confusion-noticing perspective.
My (spoilery) notes (cw death, suspicion, violence etc):
The existence of other knives of the same kind as the murder weapon is almost perfectly useless as evidence. The fact that the knife used was identical to the one the accused owned, and was used to kill so close to when the defendant’s knife (supposedly) went missing, is still too much of a coincidence to ignore. The only way it would realistically be a different knife is if someone was actively trying to frame the defendant, and arranged for his knife to be lost at the same time; and if they could do both of those things, it makes more sense for Hypothetical Secret Mastermind X to just stab the victim with the accused’s actual knife. (This means Juror 8′s illegal purchase of an identical knife in the name of justice was epistemically pointless, and only served to muddy the waters; I’m oddly enamored by the probably-accidental pro-Lawful-Good thematic implications.)
The old man’s testimony is suspect for more reasons than the jurors notice. The lack of fingerprints on the murder weapon suggests the culprit wiped it off first, but the old man claims the culprit ran off immediately after the body hit the floor. However, this aligns with the other reason to consider him unreliable, which is him (allegedly) managing to move quickly enough to see the accused leave the scene; it seems pretty plausible that he got the timing wrong but everything else right.
The paramedic juror’s claim that the knife was used incorrectly—that it’s the kind of knife made to stab up through the gut instead of down through the ribs—doesn’t exonerate the defendant, and might actually incriminate him. It’s a fact about the knife, not the user; if anything, a young man might be more likely than the average assailant to wield his weapon wrong.
The other witness turning out to (probably) habitually wear glasses doesn’t necessarily make her testimony invalid. She could be farsighted, could need reading glasses, or could just habitually wear them to seem intelligent or as a fashion statement. All of these explanations seem more likely than a—by all accounts, scarily competent—prosecutor putting her on the stand without checking she could actually see the murder. (None of the jurors consider requesting additional testimony on this topic, even though it’s both easy to check and the point which ends up deciding the final verdict.)
From all the above, I conclude:
The accused is very likely to have committed the murder.
and
The protagonist probably has some kind of agenda: either he takes issue with capital punishment, knows the defendant personally, strongly dislikes the carceral justice system, is being bribed, or is trying to arrange acquittal for a guilty party just to see if he can.
However
I still think a case can be made for the existence of reasonable doubt.
if and only if
You consider the possibility it was a suicide.
(trigger warning for detailed discussion of that thing I just mentioned)
If I knew for a fact the defendant was innocent, most of my probability mass would be on some variation of the following sequence of events.
The ‘victim’ has his (injury-free) altercation with the accused. This rattles the accused to the point that he forgets to take his knife with him when he leaves for the movies; he falsely assumes that it “fell out of his pocket”.
The ‘victim’ is also rattled, and decides to commit suicide. (Possible motivations: realizing that he can no longer reliably win a fight against the target of his abuse and wanting to quit while he’s ahead, feeling regret about his treatment of the accused, being angry at the accused and wanting to die in such a way that the accused ends up accused.)
The ‘victim’ stabs himself in the chest, and not through the gut, in an attempt to end his life as quickly, painlessly, and dramatically as possible. Possibly he shouts “I’m going to kill you!” as he does this, either out of genuine self-loathing or an attempt to implicate the accused; possibly he makes a point of staggering around near an open window with a knife sticking out of his chest before collapsing; alternatively, the witness testimonies may just be mistaken and/or falsified for reasons discussed in the film.
The accused returns home to find a dead body and two policemen. Between the lingering effects of earlier events, the presence of the victim’s corpse, his current predicament and (quite plausibly) some mind-altering substances he chooses not to admit to using in the subsequent trial . . . the accused finds himself unable to provide satisfactory answers when the police ask for the titles and lead actors of the movies he watched. (He may or may not be able to recall other details about these movies: but either he doesn’t think to volunteer this information and the police don’t ask for it, or the police choose not to record inconvenient facts in an attempt to close the case cleanly while technically telling the truth.)
This hypothesis makes sense of the paramedic’s claim about the type of knife, makes sense of the silent evidence of neither the accused nor the corpse having any injuries mentioned aside from the single stab wound (a person comfortable with violence yells an explicit verbal warning at another person comfortable with violence, and then stabs him to death, but there’s no sign of a struggle?), and is supported by base rates (suicide is significantly more common than homicide in first-world nations).
. . . to be clear, I’d still say murder is much more likely, but I consider the above possibility just possible enough to be conflicted about the reasonableness of reasonable doubt in this case.
I’m curious what other LW users think.
Can’t believe I missed that; edited; ty!
Equations Mean Things
True. But if things were opened up this way, realistically more than one person would want to get in on it. (Enough to cover an entire percentage point of the bid? I have no idea.)
. . . Is there a way a random punter could kick in, say, $100k towards Elon’s bid? Either they end up spending $100k on shares valued at somewhere between $100k and $150k; or, more likely, they make the seizure of OpenAI $100k harder at no cost to themselves.
I once saw an advert claiming that a pregnancy test was “over 99% accurate”. This inspired me to invent an only-slightly-worse pregnancy test, which is over 98% accurate. My invention is a rock with “NOT PREGNANT” scrawled on it: when applied to a randomly selected human being, it is right more than 98% of the time. It is also cheap, non-invasive, endlessly reusable, perfectly consistent, immediately effective and impossible to apply incorrectly; this massive improvement in cost and convenience is obviously worth the ~1% decrease in accuracy.
I can’t tell if this post is a request for more feedback for you in future, or trying to open a more general discussion about what norms and conventions exist around giving feedback, or if it’s about you wanting to see people give more love to other creators.
I was trying to do all of these things simultaneously.
This seems to imply there are better and worse times of day to try and get immediate feedback. If so, what are they?