kman

Karma: 1,212

kman Mar 24, 2025, 5:39 PM
2 points
0
on: kman’s Shortform
I’m looking for recommendations for frameworks/tools/setups that could facilitate machine checked math manipulations.
More details:
- My current use case is to show that an optimized reshuffling of a big matrix computation is equivalent to the original unoptimized expression
  - Need to be able to index submatrices of an arbitrary sized matrices
- I tried doing the manipulations with some CASes (SymPy and Mathematica), which didn’t work at all
  - IIUC the main reason they didn’t work is that they couldn’t handle the indexing thing
- I have very little experience with proof assistants, and am not willing/able to put the effort into becoming fluent with them
- The equivalence proof doesn’t need to be a readable by me if e.g. an AI can cook up a complicated equivalence proof
  - So long as I can trust that it didn’t cheat e.g. by sneaking in extra assumptions

kman Mar 19, 2025, 6:47 PM
2 points
1
in reply to: Anrol L’s comment on: How to Make Superbabies
I agree with this critique; I think washing machines belong on the “light bulbs and computers” side of the analogy. The analogy has the form:

”germline engineering for common diseases and important traits” : “gene therapy for a rare disease” :: “widespread, transformation uses of electricity” : x
So x should be some very expensive, niche use of electricity that provides a very large benefit to its tiny user base (and doesn’t arguably indirectly lead to large future benefits, e.g. via scientific discovery for a niche scientific instrument).

kman Mar 18, 2025, 1:08 AM
4 points
2
in reply to: faul_sname’s comment on: kman’s Shortform
I think you’re mixing up max with argmax?

kman’s Shortform

kmanMar 17, 2025, 10:52 PM

6 points

6 comments1 min readLW link

kman Mar 17, 2025, 10:52 PM
22 points
8
on: kman’s Shortform
Something I didn’t realize until now: P = NP would imply that finding the argmax of arbitrary polynomial time (P-time) functions could be done in P-time.
Proof sketch
Suppose you have some polynomial time function f: N → Q. Since f is P-time, if we feed it an n-bit input x it will output a y with at most max_output_bits(n) bits as output, where max_output_bits(n) is at most polynomial in n. Denote y_max and y_min as the largest and smallest rational numbers encodable in max_output_bits(n) bits.
Now define check(x, y) := f(x) >= y, and argsat(y) := x such that check(x, y) else None. argsat(y) is in FNP, and thus runs in P-time if P = NP. Now we can find argmax(f(x)) by running a binary search over all values y in [y_min, y_max] on the function argsat(y). The binary search will call argsat(y) at most max_output_bits(n) times, and P x P = P.
I’d previously thought of argmax as necessarily exponential time, since something being an optimum is a global property of all evaluations of the function, rather than a local property of one evaluation.

kman Mar 3, 2025, 12:35 AM
19 points
1
on: Statistical Challenges with Making Super IQ babies
1. The biggest discontinuity is applied at the threshold between spike and slab. Imagine we have mutations that before shrinkage have the values +4 IQ, +2 IQ, +1.9 IQ, and 1.95 is our spike vs. slab cutoff. Furthermore, let’s assume that the slab shrinks 25% of the effect. Then we get 4→3, 2→1.5, 1.9→0, meaning we penalize our +2 IQ mutation much less than our +1.9 mutation, despite their similar sizes, and we penalize our +4 IQ effect size more than the +2 IQ effect size, despite it having the biggest effect, this creates an arbitrary cliff where similar-sized effects are treated completely differently based on which side of the cutoff they fall on, and where the one that barely makes it, is the one we are the least skeptical off”
There isn’t any hard effect size cutoff like this in the model. The model just finds whatever configurations of spikes have high posteriors given the assumption of sparse normally distributed nonzero effects. I.e., it will keep adding spikes until further spikes can no longer offset their prior improbability via higher likelihood (note this isn’t a hard cutoff, since we’re trying to approximate the true posterior over all spike configurations; some lower probability configurations with extra spikes will be sampled by the search algorithm).

kman Feb 28, 2025, 9:44 PM
2 points
0
in reply to: momom2’s comment on: How to Make Superbabies
My guess is that peak intelligence is a lot more important than sheer numbers of geniuses for solving alignment. At the end of the day someone actually has to understand how to steer the outcome of ASI, which seems really hard and no one knows how to verify solutions. I think that really hard (and hard to verify) problem solving scales poorly with having more people thinking about it.
Sheer numbers of geniuses would be one effect of raising the average, but I’m guessing the “massive benefits” you’re referring to are things like coordination ability and quality of governance? I think those mainly help with alignment via buying time, but if we’re already conditioning on enhanced people having time to grow up I’m less worried about time, and also think that sufficiently widespread adoption to reap those benefits would take substantially longer (decades?).

kman Feb 25, 2025, 7:13 PM
2 points
0
in reply to: Donald Hobson’s comment on: How to Make Superbabies
Emotional social getting on with people vs logic puzzle solving IQ.
Not sure I buy this, since IQ is usually found to positively correlate with purported measures of “emotional intelligence” (at least when any sort of ability (e.g. recognizing emotions) is tested; the correlation seems to go away when the test is pure self reporting, as in a personality test). EDIT: the correlation even with ability-based measures seems to be less than I expected.
Also, smarter people seem (on average) better at managing interpersonal issues in my experience (anecdotal, I don’t have a reference). But maybe this isn’t what you mean by “emotional social getting on with people”.
There could have been a thing where being too far from the average caused interpersonal issues, but very few people would have been far from the average, so I wouldn’t expect this to have prevented selection if IQ helped on the margin.
Engineer parents are apparently more likely to have autistic children. This looks like a tradeoff to me. To many “high IQ” genes and you risk autism.
Seems somewhat plausible. I don’t think that specific example is good since engineers are stereotyped as aspies in the first place; I’d bet engineering selects for something else in addition to IQ that increases autism risk (systematizing quotient, or something). I have heard of there being a population level correlation between parental IQ and autism risk in the offspring, though I wonder how much this just routes through paternal age, which has a massive effect on autism risk.
This study found a relationship after controlling for paternal age (~30% risk increase when father’s IQ > 126), though the IQ test they used had a “technical comprehension” section, which seems unusual for an IQ test (?), and which seems to have driven most of the association.
How many angels can dance on the head of a pin. In the modern world, we have complicated elaborate theoretical structures that are actually correct and useful. In the pre-modern world, the sort of mind that now obsesses about quantum mechanics would be obsessing about angels dancing on pinheads or other equally useless stuff.
So I think there’s two possibilities here to keep distinct. (1) is that ability to think abstractly wasn’t very useful (and thus wasn’t selected for) in the ancestral environment. (2) Is that it was actively detrimental to fitness, at least above some point. E.g. because smarter people found more interesting things to do than reproduce, or because they cared about the quality of life of their offspring more than was fitness-optimal, or something (I think we do see both of these things today, but I’m not sure about in the past).
They aren’t mutually exclusive possibilities; in fact if (2) were true I’d expect (1) to probably be true also. (2) but not (1) seems unlikely since IQ being fitness-positive on the margin near the average would probably outweigh negative effects from high IQ outliers.

kman Feb 25, 2025, 6:15 PM
4 points
0
in reply to: jbash’s comment on: How to Make Superbabies
So on one hand, I sort of agree with this. For example, I think people giving IQ tests to LLMs and trying to draw strong conclusions from that (e.g. about how far off we are from ASI) is pretty silly. Human minds share an architecture that LLMs don’t share with us, and IQ tests measure differences along some dimension within the space of variation of that architecture, within our current cultural context. I think an actual ASI will have a mind that works quite differently and will quickly blow right past the IQ scale, similar to your example of eagles and hypersonic aircraft.
On the other hand, humans just sort of do obviously vary a ton in abilities, in a way we care about, despite the above? Like, just look around? Read about Von Neumann? Get stuck for days trying to solve a really (subjectively) hard math problem, and then see how quickly someone a bit smarter was able to solve it? One might argue this doesn’t matter if we can’t feasibly find anyone capable of solving alignment inside the variation of the human architecture. But Yudkowsky, and several others, with awareness and understanding of the problem, exist; so why not see what happens if we push a bit further? I sort of have this sense that once you’re able to understand a problem, you probably don’t need to be that much smarter to solve it, if it’s the sort of problem that’s amenable to intelligence at all.
On another note: I can imagine that, from the perspective of evolution in the ancestral environment, that maybe human intelligence variation appeared “small”, in that it didn’t cache out in much fitness advantage; and it’s just in the modern environment that IQ ends up conferring massive advantages in ability to think abstractly or something, which actually does cache out in stuff we care about.

kman Feb 25, 2025, 4:36 AM
2 points
0
in reply to: Donald Hobson’s comment on: How to Make Superbabies
I’m sort of confused by the image you posted? Von Neumann existed, and there are plenty of very smart people well beyond the “Nerdy programmer” range.
But I think I agree with your overall point about IQ being under stabilizing selection in the ancestral environment. If there was directional selection, it would need to have been weak or inconsistent; otherwise I’d expect the genetic low hanging fruit we see to have been exhausted already. Not in the sense of all current IQ-increasing alleles being selected to fixation, but in the sense of the tradeoffs becoming much more obvious than they appear to us currently. I can’t tell what the tradeoffs even were: apparently IQ isn’t associated with the average energy consumption of the brain? The limitation of birth canal width isn’t a good explanation either since IQ apparently also isn’t associated with head size at birth (and adult brain size only explains ~10% of the variance in IQ).

kman Feb 25, 2025, 4:04 AM
4 points
0
in reply to: TsviBT’s comment on: How to Make Superbabies
Don’t have much to say on it right now, I really need to do a deep dive into this at some point.

kman Feb 25, 2025, 12:10 AM
5 points
0
in reply to: LGS’s comment on: How to Make Superbabies
You should show your calculation or your code, including all the data and parameter choices. Otherwise I can’t evaluate this.
The code is pretty complicated and not something I’d expect a non-expert (even a very smart one) to be able to quickly check over; it’s not just a 100 line python script. (Or even a very smart expert for that matter, more like anyone who wasn’t already familiar with our particular codebase.) We’ll likely open source it at some point in the future, possibly soon, but that’s not decided yet. Our finemapping (inferring causal effects) procedure produces ~identical results to the software from the paper I linked above when run on the same test data (though we handle some additional things like variable per-SNP sample sizes and missing SNPs which that finemapper doesn’t handle, which is why we didn’t just use it).
The parameter choices which determine the prior over SNP effects are the number of causal SNPs (which we set to 20,000) and the SNP heritability of the phenotype (which we set to 0.19, as per the GWAS we used). The erroneous effect size adjustment was done at the end to convert from the effect sizes of the GWAS phenotype (low reliability IQ test) to the effect sizes corresponding to the phenotype we care about (high reliability IQ test).
We want to publish a more detailed write up of our methods soon(ish), but it’s going to be a fair bit of work so don’t expect it overnight.
It’s natural in your position to scrutinize low estimates but not high ones.
Yep, fair enough. I’ve noticed myself doing this sometimes and I want to cut it out. That said, I don’t think small-ish predictable overestimates to the effect sizes are going to change the qualitative picture, since with good enough data and a few hundred to a thousand edits we can boost predicted IQ by >6 SD even with much more pessimistic assumptions, which probably isn’t even safe to do (I’m not sure I expect additivity to hold that far). I’m much more worried about basic problems with our modelling assumptions, e.g. the assumption of sparse causal SNPs with additive effects and no interactions (e.g. what if rare haplotypes are deleterious due to interactions that don’t show up in GWAS since those combinations are rare?).

kman Feb 24, 2025, 10:27 PM
6 points
0
in reply to: CRISPY’s comment on: How to Make Superbabies
I know the answers to those questions. But I’m not the audience that needs to be convinced.
The audience that needs to be convinced isn’t the target audience of this post. But overall your point is taken.

kman Feb 24, 2025, 7:25 PM
2 points
0
in reply to: Kris Moore’s comment on: How to Make Superbabies
I’ll need to do a deep dive to understand the methods of the first paper, but isn’t this contradicted by the recent Tan et. al. paper you linked finding SNP heritability of 0.19 for both direct and population effects of intelligence (which matches Savage Jansen 2018)? They also found ~perfect LDSC correlation between direct and population effects, which would imply the direct and population SNP heritabilities are tagging the exact same genetic effects. (Also interesting that 0.19 is the exactly in the middle of 0.24 and 0.14, not sure what to make of that if anything).

kman Feb 24, 2025, 5:14 PM
3 points
0
in reply to: LGS’s comment on: How to Make Superbabies
With a method similar to this. You can easily compute the exact likelihood function P(GWAS results | SNP effects), which when combined with a prior over SNP effects (informed by what we know about the genetic architecture of the trait) gives you a posterior probability of each SNP being causal (having nonzero effect), and its expected effect size conditional on being causal (you can’t actually calculate the full posterior since there are 2^|SNPs| possible combinations of SNPs with nonzero effects, so you need to do some sort of MCMC or stochastic search). We may make a post going into more detail on our methods at some point.

kman Feb 24, 2025, 3:09 AM
2 points
0
in reply to: LGS’s comment on: How to Make Superbabies
This is based on inferring causal effects conditional on this GWAS. The assumed heritability affects the prior over SNP effect sizes.

kman Feb 24, 2025, 3:07 AM
10 points
0
in reply to: Donald Hobson’s comment on: How to Make Superbabies
If evolution has already taken all the easy wins, why do humans vary so much in intelligence in the first place? I don’t think the answer is mutation-selection balance, since a good chunk of the variance is explained by additive effects from common SNPs. Further, if you look at the joint distribution over effect sizes and allele frequencies among SNPs, there isn’t any clear skew towards rarer alleles being IQ-decreasing.
For example, see the plot below of minor allele frequency vs the effect size of the minor allele. (This is for Educational Attainment, a highly genetically correlated trait, rather than IQ, since the EA GWAS is way larger and has way more hits.)
If we do a Bayesian adjustment of the effect sizes for observation noise, assuming EA has a SNP heritability of 0.2 and 20,000 causal variants with normally distributed effects:
I’ve repeated this below for an IQ GWAS:
You can see that the effect sizes look roughly symmetrically distributed about zero, even for fairly rare SNPs with MAF < 1%.

kman Feb 23, 2025, 10:36 PM
3 points
0
in reply to: LGS’s comment on: How to Make Superbabies
But isn’t the R^2 the relevant measure?
Not for this purpose! The simulation pipeline is as follows: the assumed h^2 and number of causal variants is used to generate the genetic effects → generate simulated GWASes for a range of sample sizes → infer causal effects from the observed GWASes → select top expected effect variants for up to N (expected) edits.

kman Feb 23, 2025, 3:26 PM
5 points
0
in reply to: LGS’s comment on: How to Make Superbabies
The paper you called largest ever GWAS gave a direct h^2 estimate of 0.05 for cognitive performance. How are these papers getting 0.2? I don’t understand what they’re doing. Some type of meta analysis?
You’re mixing up h^2 estimates with predictor R^2 performance. It’s possible to get an estimate of h^2 with much less statistical power than it takes to build a predictor that good.
The test-retest reliability you linked has different reliabilities for different subtests. The correct adjustment depends on which subtests are being used. If cognitive performance is some kind of sumscore of the subtests, its reliability would be higher than for the individual subtests.
“Fluid IQ” was the only subtest used.
Also, I don’t think the calculation 0.2*(0.9/0.6)^2 is the correct adjustment. A test-retest correlation is already essentially the square of a correlation of the test with an underlying latent factor
Good catch, we’ll fix this when we revise the post.

kman Feb 23, 2025, 3:28 AM
4 points
0
in reply to: LGS’s comment on: How to Make Superbabies
I don’t quite understand your numbers in the OP but it feels like you’re inflating them substantially. Is the full calculation somewhere?
Not quite sure which numbers you’re referring to, but if it’s the assumed SNP heritability, see the below quote of mine from another comment talking about missing heritability for IQ:
The SNP heritability estimates for IQ of (h^2 = ~0.2) are primarily based on a low quality test that has a test-retest reliability of 0.6, compared to ~0.9 for a gold-standard IQ test. So a simple calculation to adjust for this gets you a predicted SNP heritability of 0.2 * (0.9 / 0.6)^2 = 0.45 for a gold standard IQ test, which matches the SNP heritability of height. As for the rest of the missing heritability: variants with frequency less than 1% aren’t accounted for by the SNP heritability estimate, and they might contribute a decent bit if there are lots of them and their effects sizes are larger.
The h^2 = 0.19 estimate from this GWAS should be fairly robust to stratification, because of how the LDSC estimator works. (To back this up: a recent study that actually ran a small GWAS on siblings, based on the same cognitive test, also found h^2 = 0.19 for direct effects.)