> The company says that the drug was generally well tolerated, but that’s on the oncology scale.
> ...
> He’s been on daraxonrasib since early this year, and describes it this way: “. . .it’s a nasty drug. It causes crazy stuff like my body can’t grow skin and so I bleed all out of a whole bunch of parts of me that shouldn’t be bleeding” If you go to that link above, be prepared, because he also looks like he’s had aqua regia thrown all over him (and apparently feels a bit like that, too). But his tumor volume has gone down by about 75%, and there’s a very strong chance that he wouldn’t still be alive at all without having gone on the drug.
There's eg https://summit.sfu.ca/item/11130 from a Tamara Smyth and Frederick Scott; Google scholar shows some citations but not necessarily conical brass in particular. That link is about trombones, so also not conical. (I read that and tried to implement some stuff in it, see https://nuchi.github.io/trombone/ for a browser-based playable version.)
Conical and cylindrical bores definitely differ but I don't see why they'd be different specifically with respect to the lip interaction, can you say more about that part?
I have no idea, but I wouldn't expect so unless it was by coincidence? Not sure what chords have to do with any of this. There's a canonical way to choose 4 points uniformly and independently at random on the circle, and it's got nothing to do with chords.
Right, I was taking it as given that the problem of choosing a hemisphere canonically for a point meant "such that the argument works in the same way as for the circle".
Bertrand paradox just doesn't apply here, there's a natural measure on the circle and all higher dimensional spheres. I wouldn't expect an article on this subject to need to make that clarification unless it's dealing with chords or some other situation without a natural measure.
> The same decomposition works in higher dimensions.
I don't think the same argument works in higher dimensions. On a circle, we can canonically pick a semicircle corresponding to each point (we have two choices, let's say we pick the clockwise one).
In higher dimensions there's no canonical choice of half-sphere. In odd dimensions one could pick a canonical half-sphere per point but it might turn out that some other non-chosen half-sphere for that point contains all the other points. In even dimensions there isn't even a way to canonically pick a half-sphere for each point (this is a consequence of the Hairy Ball Theorem).
(For all I know the actual numbers might turn out to be the same, I don't know. I'm just saying that the argument doesn't work.)
I remember being very taken with this story when I first read it, and it's striking how obsolete it reads now. At the time it was written, "simulated humans" seemed a fantastical suggestion for how a future society might do scaled intellectual labor, but not a ridiculous suggestion.
But now with modern LLMs it's just too impossible to take it seriously. It was a live possibility then; now, it's just a wrong turn down a garden path.
A high variance story! It could have been prescient, instead it's irrelevant.
> Codex uses apply_patch: It takes a string as input, which is essentially an OpenAI-flavored diff, and instead of relying on a structured schema, the harness just expects this blob to follow a strict set of rules. Since OpenAI folks are without a doubt smart, I’m sure the token selection process is biased to fit this structure at the LLM gateway for the Codex variants of GPT, similar to how other constraints like JSON schemas or required tool calls work.
It still has to work to get an exact match, or at least I didn't read the code to see if there's any fuzzy matching used.
Note the two codex models were the only ones doing worse with the author's proposed format. The author found them doing better with replace than with apply patch, but since the author appears to be unaware that they use a schema for constrained sampling, I think a more realistic benchmark should enable constrained sampling for the apply test.
They don't appear to care about the images of the immersions or their complements, aside from them not being related by an isometry of R^3. They're not doing any topology with the image.
In other works, they have two immersions from the torus to R^3, whose induced metric and mean curvature are the same, and whose images are not related by an isometry of R^3. I didn't see anything about the topology of the images per se, that doesn't seem to be the point here.
yeah I have, but I think only when it gets stuck in a loop and outputs a (for example) array that goes on forever. a truncated array is obviously not valid JSON. but it'd be hard to miss that if you're looking at the outputs.
Can anyone explain (or link) what they mean by "injection", at a level of explanation that discusses what layers they're modifying, at which token position, and when?
Are they modifying the vector that gets passed to the final logit-producing step? Doing that for every output token? Just some output tokens? What are they putting in the KV cache, modified or unmodified?
It's all well and good to pick a word like "injection" and "introspection" to describe what you're doing but it's impossible to get an accurate read on what's actually being done if it's never explained in terms of the actual nuts and bolts.
Oh now I understand. I thought your ab and ba were single tokens (even though that doesn't make sense in context). Once you point out they're separate tokens, I follow you. Thank you!
Edit: that's a great example
Edit 2: even more fun: training data is [ab, ab, ba, bb, bb, bb]. Then constrained sampling flips your likelihood from 1:2 to 2:1
You know, it only just now occurs to me to wonder if the blackjack story is the public sanitized version of "how I got $24k because I'm not allowed to tell you the real version"
Sorry to actually your actually, but the derivative of a function f from a space A to a space B at the point a is a linear function Df_a from the tangent space of A at a to the tangent space of B at b = f(a).
When the spaces are Euclidean spaces then we conflate the tangent space with the space itself because they're identical.
By the way, this makes it easy to remember the chain rule formula in 1 dimension. There's only one logical thing it could be between spaces of arbitrary dimensions m, n, p: composition of linear transformations from T_a A to T_f(a) B to T_g(f(a)) C. Now let m = n = p = 1, and composition of linear transformations just becomes multiplication.
> ...
> He’s been on daraxonrasib since early this year, and describes it this way: “. . .it’s a nasty drug. It causes crazy stuff like my body can’t grow skin and so I bleed all out of a whole bunch of parts of me that shouldn’t be bleeding” If you go to that link above, be prepared, because he also looks like he’s had aqua regia thrown all over him (and apparently feels a bit like that, too). But his tumor volume has gone down by about 75%, and there’s a very strong chance that he wouldn’t still be alive at all without having gone on the drug.