The Chomsky hierarchy is a classification of grammars. So it's about Syntax.
GPT is purely about semantics, about truth. To the extent that I think it can be said to be fundamentally informal in its dedication to truth, since it can easily be prompted to produce syntactically incorrect output - wrt the syntax of whatever language whose semantics determine the truth GPT is asked to reflect.
So I think this is a categorically incorrect question.
I mean, what is the fundamental syntax of the output of an LLM? It would have to be that any sequence of utf8 chars is valid.
LLMs have absolutely nothing to do with truth. If anything the analogy is closer to syntax as LLMs are pure form, just language in absence of any context or reference.
LLMs tell you one thing and not its negation, this choice is semantic. "just language in absence of any context or reference" is a set that includes every valid text. The usefulness of LLMs is their ability to mostly respect whatever semantics you establish in the prompt in their choice of output.
The article shows one, the kind of double torus - though I do not understand how neighbourhoods that intersect the line of contact between the 2 "tubes" can be mapped to R².
Ok I see, it's a 2D shape in 3D space, you actually need the 3th dimension to contain this shape... At least I find that there's s distinction between a 2D shape you can draw on a 2D screen (like a filled rectangle or a disk), and a shape that's a 2D surface itself but requires 3-dimensional space to sit in (like a torus/donut or a non-filled 2-sphere)
So I guess the 126-dimensional shape actually also is in 127-dimensional space then
But the article says "Over the years, mathematicians found that the twisted shapes exist in dimensions 2, 6, 14, 30 and 62.".
To me "Exists in dimension 2" sounds like a shape in 2D space, not in 3D space, but apparently that's not what they mean and the way I understand this language is wrong
> So I guess the 126-dimensional shape actually also is in 127-dimensional space then
Sometimes you need more dimensions to embed the manifold. For a 2-dimencional object, the most famous example is the Klein bottle https://en.wikipedia.org/wiki/Klein_bottle You can construct one of them in 3-dimmension only if you cheat. Yhey look nice and you can buy a few cheating-versions. But you can embed the Klein bottle in 4-dimensions (without cheating).
For the manifold in the article, I'm not sure how many additional dimensions you need. Perhaps 127 (n+1) is enough or perhaps you need 252 (2n) or perhaps something in between. You can always embed an n-dimensional manifold in the 2n space, but that is the worst case. https://en.wikipedia.org/wiki/Whitney_embedding_theorem
Oh, you got me. Too casual a read, and you switched to acronyms so I didn’t catch my association. It’s great that you’re exploring these ideas, though it still feels like the computer is tabulating.
An attempt at understanding the difference that makes the sorting problem (the problem solved by sorting algorithms), but not the travelling salesman problem, efficiently solvable, looking at the topologies of their solution spaces.
Sorting has a simple local optimum implies global optimum property. If a list is sorted than any (not necessarily sequential) sublist is sorted, and the converse. No such property applies to TSP.
I think that the best way to think about why some combinatorial problems are hard and others easy isn't to ask what makes a problem hard, but rather what makes a problem easy. Combinatorial problems seem to be hard by default. It takes some special simplifying property to make them easy.
The idea here is not to understand why some combinatorial problems are hard and others easy, but rather to just be able to distinguish between them. So, instead of understanding why the measure functions structure the solution spaces the way they do, treating them as black boxes and examining the structure they provide to the solution space.
As far as I understand (I'm not a physicist), to be able to say that the universe is isotropic across space, you need a point of view that just doesn't exist. You cannot speak about an absolute synchronicity among events happening in locations scattered among an arbitrary subset of the set of all visible galaxies, and without that, you cannot abstract time out of the picture, which you'd need to do to speak about isotropicity across space.
I don't think that, in this regard, you can say much more than "the universe is not isotropic across space-time".
You cannot speak about an absolute synchronicity among events happening in locations scattered among an arbitrary subset of the set of all visible galaxies
The cosmic microwave background gives you a physical realization of just that (but of course only approximately so), at least as far as cosmologists are concerned. The rules of relativity of course still apply, making this particular synchronicity convention just one of many others...
But the cosmic microwave background refers to one single event, that has echoes everywhere, right? If I understand correctly, you don't need to synchronize anything to have echoes everywhere.
But the cosmic microwave background refers to one single event, that has echoes everywhere, right?
An event is a single point in spacetime, whereas photon decoupling happens everywhere, defining a spacelike hypersurface we use for synchronization (in the idealized scenario).
Subsequently, the CMB allows us to single out a particular reference frame (the one where it looks isotropic) and provides a measure of expansion via its redshift/temperature which we can then translate to cosmological time (ie time since the big bang as measured by an observer following the Hubble flow) via our cosmological models.
Yode (the POC 4 years before) itself only worked with a (JavaScript) AST to create seditors. Tree-sitter would have helped here to provide an AST for different programming languages uniformly directly in NeoVim. Yode-Nvim is more powerful than the first version because it operates on lines to create seditors. In this respect Tree-sitter doesn't matter for Yode-Nvim. If someone uses Tree-sitter to select code in visual mode, he can easily create seditors for code objects like functions. This is also possible without Tree-sitter, but you have to select the function yourself.
> Years ago he was a springboard for me to read further on various topics, each time leading me to conclude he doesn't give a shit about presenting the truth if it gets in the way of his story. :(
If everyone were like her or him, it would be fine to write sloppyly and engagingly about science and history posing as if you were a real authority. But that doesnt seem to be the case (this is HN).
With uindex, you provide a Parsing Expression Grammar (PEG) [1], and you obtain a database that can hold, as data, unicode strings structured according to the top production of the provided PEG. You can then query the db for tokens corresponding to any of the (sub-) productions in the grammar.
This is a work in progress; for example, at the moment, dbs exist only in memory. In my opinion it shows promise, since as I show in the linked README, it performs in the league of in-memory SQLite.
Do you think it is worth investing more effort on this?
I would say that you are mixing up "parsing" and "calendaring (or something of the sort)". As far as I understand parsing is syntactic analysis, i.e. going from a linear structure to a more complex structure (usually a tree); it should not add to the tree anything that was not in the linear structure. It shouldn't consider a semantic context (such as the current date) to produce an ast.
By parsing I mean it in the usual sense for a date... strptime, Date.Parse, etc... i.e. turning a string to a date (or multiple dates). You can call it something else if you'd like.
GPT is purely about semantics, about truth. To the extent that I think it can be said to be fundamentally informal in its dedication to truth, since it can easily be prompted to produce syntactically incorrect output - wrt the syntax of whatever language whose semantics determine the truth GPT is asked to reflect.
So I think this is a categorically incorrect question.
I mean, what is the fundamental syntax of the output of an LLM? It would have to be that any sequence of utf8 chars is valid.