Lorxus

Karma: 278

Mathematician, alignment researcher, doctor. Reach out to me on Discord and tell me you found my profile on LW if you’ve got something interesting to say; you have my explicit permission to try to guess my Discord handle if so. You can’t find my old abandoned LW account but it’s from 2011 and has 280 karma.

A Lorxus Favor is worth (approximately) one labor-day’s worth of above-replacement-value specialty labor, given and received in good faith, and used for a goal approximately orthogonal to one’s desires, and I like LessWrong because people here will understand me if I say as much.

Apart from that, and the fact that I am under no NDAs, including NDAs whose existence I would have to keep secret or lie about, you’ll have to find the rest out yourself.

Lorxus 29 Aug 2024 15:14 UTC
3 points
0
on: Why Large Bureaucratic Organizations?
I’m gonna leave my thoughts on the ramifications for academia, where a major career step is to repeatedly join and leave different large bureaucratic organizations for a decade, as an exercise to the reader.

Like, in a world where the median person is John Wentworth (“Wentworld”), I’m pretty sure there just aren’t large organizations of the sort our world has.

I have numerous thoughts on how Lorxusverse Polity handles this problem but none of it is well-worked out enough to share. In sum though: Probably cybernetics (in the Beer sense) got discovered way earlier and actually ever used as stated and that was that, no particular need for dominance-status as glue or desire for it as social-good. (We’d be way less social overall, though, too, and less likely to make complex enduring social arrangements. There would be careful Polity-wide projects for improving social-contact and social-nutrition. They would be costly and weird. Whether that’s good or bad on net, I can’t say.)

Lorxus 28 Aug 2024 15:22 UTC
1 point
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in reply to: M. Y. Zuo’s comment on: Shifting Headspaces—Transitional Beast-Mode
Sure, but you obviously don’t (and can’t even in principle) turn that up all the way! The key is to make sure that that mode still exists and that you don’t simply amputate and cauterize it.

Lorxus 28 Aug 2024 15:16 UTC
1 point
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in reply to: TsviBT’s comment on: Wei Dai’s Shortform
[2.] maybe one could go faster by trying to more directly cleave to the core philosophical problems.
...
An underemphasized point that I should maybe elaborate more on: a main claim is that there’s untapped guidance to be gotten from our partial understanding—at the philosophical level and for the philosophical level. In other words, our preliminary concepts and intuitions and propositions are, I think, already enough that there’s a lot of progress to be made by having them talk to each other, so to speak.
OK but what would this even look like?\gen
Toss away anything amenable to testing and direct empirical analysis; it’s all too concrete and model-dependent.
Toss away mathsy proofsy approaches; they’re all too formalized and over-rigid and can only prove things from starting assumptions we haven’t got yet and maybe won’t think of in time.
Toss away basically all settled philosophy, too; if there were answers to be had there rather than a few passages which ask correct questions, the Vienna Circle would have solved alignment for us.
What’s left? And what causes it to hang together? And what causes it not to vanish up its own ungrounded self-reference?

Lorxus 28 Aug 2024 15:09 UTC
1 point
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in reply to: Wei Dai’s comment on: Wei Dai’s Shortform
Clearly academia has some blind spots, but how big? Do I just have a knack for finding ideas that academia hates, or are the blind spots actually enormous?
From someone who left a corner of it: the blindspots could be arbitrarily large as far as I know, because there seemed to me to be no real explicit culture of Hamming questions/metalooking for anything neglected. You worked on something vaguely similar/related to your advisor’s work, because otherwise you can’t get connections to people who know how to attack the problem.

Lorxus 28 Aug 2024 14:57 UTC
1 point
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in reply to: TsviBT’s comment on: Wei Dai’s Shortform
As my reacts hopefully implied, this is exactly the kind of clarification I needed—thanks!
Like, bro, I’m saying it can’t think. That’s the tweet. What thinking is, isn’t clear, but That thinking is should be presumed, pending a forceful philosophical conceptual replacement!
Sure, but you’re not preaching to the choir at that point. So surely the next step in that particular dance is to stick a knife in the crack and twist?
That is -
“OK, buddy:
Here’s property P (and if you’re good, Q and R and...) that [would have to]/[is/are obviously natural and desirable to]/[is/are pretty clearly a critical part if you want to] characterize ‘thought’ or ‘reasoning’ as distinct from whatever it is LLMs do when they read their own notes as part of a new prompt and keep chewing them up and spitting the result back as part of the new prompt for itself to read.
Here’s thing T (and if you’re good, U and V and...) that an LLM cannot actually do, even in principle, which would be trivially easy for (say) an uploaded (and sane, functional, reasonably intelligent) human H could do, even if H is denied (almost?) all of their previously consolidated memories and just working from some basic procedural memory and whatever Magical thing this ‘thinking’/‘reasoning’ thing is.”
And if neither you nor anyone else can do either of those things… maybe it’s time to give up and say that this ‘thinking’/‘reasoning’ thing is just philosophically confused? I don’t think that that’s where we’re headed, but I find it important to explicitly acknowledge the possibility; I don’t deal in more than one epiphenomenon at a time and I’m partial to Platonism already. So if this ‘reasoning’ thing isn’t meaningfully distinguishable in some observable way from what LLMs do, why shouldn’t I simply give in?

Lorxus 25 Aug 2024 6:02 UTC
1 point
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on: Announcing ILIAD — Theoretical AI Alignment Conference
> https://www.lesswrong.com/posts/r7nBaKy5Ry3JWhnJT/announcing-iliad-theoretical-ai-alignment-conference#whqf4oJoYbz5szxWc
you didn’t invite me so you don’t get to have all the nice things, but I did leave several good artifacts and books I recommend lying around. I invite you to make good use of them!

Lorxus 15 Aug 2024 18:01 UTC
3 points
2
on: Dialogue on What It Means For Something to Have A Function/Purpose
(Minor quibble: I’d be careful about using “should” here, as in “the heart should pump blood”, because “should” is often used in a moral sense. For instance, the COVID-19 spike protein presumably has some function involving sneaking into cells, it “should” do that in the teleological sense, but in the moral sense COVID-19 “should” just die out. I think that ambiguity makes a sentence like “but it might be another thing to say, that the heart should pump blood” sound deeper/more substantive than it is, in this context.
This puts me in mind of what I’ve been calling “the engineer’s ‘should’” vs “the strategist’s ‘should’” vs “the preacher’s ‘should’”. Teleological/mechanistic, systems-predictive, is-ought. Really, these ought to all be different words, but I don’t really have a good way to cleanly/concisely express the difference between the first two.

Lorxus 15 Aug 2024 7:15 UTC
6 points
0
in reply to: Mike Gupta’s comment on: Shifting Headspaces—Transitional Beast-Mode
To paraphrase:

Want and have. See and take. Run and chase. Thirst and slake. And if you’re thwarted in pursuit of your desire… so what? That’s just the way of things, not always getting what you hunger for. The desire itself is still yours, still pure, still real, so long as you don’t deny it or seek to snuff it out.

Lorxus 14 Aug 2024 17:55 UTC
1 point
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in reply to: Lorxus’s comment on: tlevin’s Shortform
@habryka Forgot to comment on the changes you implemented for soundscape at LH during the mixer—possibly you may want to put a speaker in the Bayes window overlooking the courtyard firepit. People started congregating/pooling there (and notably not at the other firepit next to it!) because it was the locally-quietest location, and then the usual failure modes of an attempted 12-person conversation ensued.

Lorxus 8 Aug 2024 19:22 UTC
7 points
0
on: A rough and incomplete review of some of John Wentworth’s research
any finite-entropy function $f (X)$
Uh...
1. $\forall x \in X,$ $P [X = x] > 0$ .
2. $\sum_{X} P [X = x] = 1.$
3. By “oh, no, the $(σ)$ s have to be non-repeating”, $| X | \geq | N | .$ Thus by the nth term test, $\forall ϵ > 0,$ $\exists x \in X : P [X = x] < ϵ$ .
4. By properties of logarithms, $- log (P [X = x])$ has no upper bound over $x \in X$ . In particular, $- P [X = x] log (P [X = x])$ has no upper bound over $x \in X$ .
5. I’m not quite clear on how @johnswentworth defines a “finite-entropy function”, but whichever reasonable way he does that, I’m pretty sure that the above means that the set of all such functions over our $X$ as equipped with distribution $P [X]$ of finite entropy is in fact the empty set. Which seems problematic. I do actually want to know how John defines that. Literature searches are mostly turning up nothing for me. Notably, many kinds of reasonable-looking always-positive distributions over merely countably-large sample spaces have infinite Shannon entropy.
(h/t to @WhatsTrueKittycat for spotlighting this for me!)

Lorxus 6 Aug 2024 17:36 UTC
2 points
0
on: We’re not as 3-Dimensional as We Think
most of them are small and probably don’t have the mental complexity required to really grasp three dimensions
Foxes and ferrets strike me as two obvious exceptions here, and indeed, we see both being incredibly good at getting into, out of, and around spaces, sometimes in ways that humans might find unexpected.

Lorxus 2 Aug 2024 16:46 UTC
1 point
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on: Davidad’s Bold Plan for Alignment: An In-Depth Explanation
, and here]
This overleaf link appears to be restricted-access-only?

Lorxus 31 Jul 2024 19:03 UTC
3 points
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in reply to: habryka’s comment on: tlevin’s Shortform
As someone who’s spent meaningful amounts of time at LH during parties, absolutely yes. You successfully made it architecturally awkward to have large conversations, but that’s often cashed out as “there’s a giant conversation group in and totally blocking [the Entry Hallway Room of Aumann]/[the lawn between A&B]/[one or another firepit and its surrounding walkways]; that conversation group is suffering from the obvious described failure modes, but no one in it is sufficiently confident or agentic or charismatic to successfully break out into a subgroup/subconversation.

I’d recommend quiet music during parties? Or maybe even just a soundtrack of natural noises—birdsong and wind? rain and thunder? - to serve the purpose instead.

Lorxus 31 Jul 2024 5:24 UTC
1 point
0
on: Whiteboard Pen Magazines are Useful
I liked this post so much that I made my own better Lesser Scribing Artifact and I’m preparing a post meant to highlight the differences between my standard and yours. Cheers!

Lorxus 21 Jul 2024 22:10 UTC
1 point
0
in reply to: TsviBT’s comment on: Koan: divining alien datastructures from RAM activations

Why do you need to be certain? Say there’s a screen showing a nice “high-level” interface that provides substantial functionality (without directly revealing the inner workings, e.g. there’s no shell). Something like that should be practically convincing.

Then whatever that’s doing is a constraint in itself, and I can start off by going looking for patterns of activation that correspond to e.g. simple-but-specific mathematical operations that I can actuate in the computer.

I’m unsure about that, but the more pertinent questions are along the lines of “is doing so the first (in understanding-time) available, or fastest, way to make the first few steps along the way that leads to these mathematically precise definitions? The conjecture here is “yes”.

Maybe? But I’m definitely not convinced. Maybe for idealized humanesque minds, yes, but for actual humans, if your hypothesis were correct, Euler would not have had to invent topology in the 1700s, for instance.

Lorxus 21 Jul 2024 19:50 UTC
4 points
0
on: A simple model of math skill
I don’t have much to say except that this seems broadly correct and very important in my professional opinion. Generating definitions is hard, and often depends subtly/finely on the kinds of theorems you want to be able to prove (while still having definitions that describe the kind of object you set out to describe, and not have them be totally determined by the theorem you want—that would make the objects meaningless!). Generating frameworks out of whole cloth is harder yet; understanding them is sometimes easiest of all.

Lorxus 21 Jul 2024 4:57 UTC
1 point
0
on: Koan: divining alien datastructures from RAM activations
Thinking about it more, I want to poke at the foundations of the koan. Why are we so sure that this is a computer at all? What permits us this certainty, that this is a computer, and that it is also running actual computation rather than glitching out?

B: Are you basically saying that it’s a really hard science problem?

From a different and more conceit-cooperative angle: it’s not just that this is a really hard science problem, it might be a maximally hard science problem. Maybe too hard for existing science to science at! After all, hash functions are meant to be maximally difficult, computationally speaking, to invert (and in fact impossible in the general case but merely very hard to generate hash collisions).

Another prompt: Suppose you leave Green alone for six months, and when you come back, it turns out ze’s figured out what hash tables are. What do you suppose might have happened that led to zer figuring out hash tables?

That Green has figured out how to probe the RAM properly, and how to assign meaning to the computations, and that zer Alien Computer is doing the same-ish thing that mine is?

Although you never do figure out what algorithm is running on the alien computer, it happens to be the case that in the year 3000, the algorithm will be called “J-trees”.

It would follow, to me, that I should be looking for treelike patterns of activation, and in particular that maybe this is some application of the principles inherent to hash sort or radix sort to binary self-balancing trees, likely in memory address assignment, as might be necessary/worthwhile in a computer of a colossal scale such as we won’t even get until Y3k?

B: It sounds nice, but it kind of just sounds like you’re recommending mindfulness or something.

I’d disagree with Blue here! To clean and oil a machine and then run a quick test of function than setting it running to carefully watch it do its thing!

...However, we can put the metaphysicist’s ramblings in special quotes:

Doing so still never gets you to the idea of a homology sphere, and it isn’t enough to point towards the mathematically precise definition of an infinite 3-manifold without boundary.

Lorxus 20 Jul 2024 21:20 UTC
1 point
0
in reply to: Lorxus’s comment on: Lorxus’s Shortform
EDIT: I and the person who first tried to render this SHAPE for me misunderstood its nature.

Lorxus 20 Jul 2024 1:39 UTC
1 point
0
in reply to: faul_sname’s comment on: Lorxus’s Shortform
You maybe got stuck in some of the many local optima that Nurmela 1995 runs into. Genuinely, the best sphere code for 9 points in 4 dimensions is known to have a minimum angular separation of ~1.408 radians, for a worst-case cosine similarity of about 0.162.
You got a lot further than I did with my own initial attempts at random search, but you didn’t quite find it, either.

Lorxus 19 Jul 2024 21:24 UTC
24 points
2
on: Lorxus’s Shortform
On @TsviBT’s recommendation, I’m writing this up quickly here.
re: the famous graph from https://transformer-circuits.pub/2022/toy_model/index.html#geometry with all the colored bands, plotting “dimensions per feature in a model with superposition”, there look to be 3 obvious clusters outside of any colored band and between 2/5 and 1/2, the third of which is directly below the third inset image from the right. All three of these clusters are at 1/(1-S) ~ 4.
A picture of the plot, plus a summary of my thought processes for about the first 30 seconds of looking at it from the right perspective:
In particular, the clusters appear to correspond to dimensions-per-feature of about 0.44~0.45, that is, ⁴⁄₉. Given the Thomson problem-ish nature of all the other geometric structures displayed, and being professionally dubious that there should be only such structures of subspace dimension 3 or lower, my immediate suspicion since last week when I first thought about this is that the uncolored clusters should be packing 9 vectors as far apart from each other as possible on the surface of a 3-sphere in some 4D subspace.
In particular, mathematicians have already found a 23-celled 4-tope with 9 vertices (which I have made some sketches of) where the angular separation between vertices is ~80.7° : http://neilsloane.com/packings/index.html#I . Roughly, the vertices are: the north pole of S^3; on a slice just (~9°) north of the equator, the vertices of a tetrahedron “pointing” in some direction; on a slice somewhat (~19°) north of the south pole, the vertices of a tetrahedron “pointing” dually to the previous tetrahedron. The edges are given by connecting vertices in each layer to the vertices in the adjacent layer or layers. Cross sections along the axis I described look like growing tetrahedra, briefly become various octahedra as we cross the first tetrahedon, and then resolve to the final tetrahedron before vanishing.
I therefore predict that we should see these clusters of 9 embedding vectors lying roughly in 4D subspaces taking on pretty much exactly the 23-cell shape mathematicians know about, to the same general precision as we’d find (say) pentagons or square antiprisms, within the model’s embedding vectors, when S ~ ³⁄₄.
Potentially also there’s other 3/f, 4/f, and maybe 5/f; given professional experience I would not expect to see 6+/f sorts of features, because 6+ dimensions is high-dimensional and the clusters would (approximately) factor as products of lower-dimensional clusters already listed. There’s a few more clusters that I suspect might correspond to ³⁄₇ (a pentagonal bipyramid?) or ⁵⁄₁₂ (some terrifying 5-tope with 12 vertices, I guess), but I’m way less confident in those.
A hand-drawn rendition of the 23-cell in whiteboard marker: