[nabla9]

You saw name "Noam Chomsky" and that started a process in your mind that generated the standard spiel about Syntactic Structures.

Chomsky Hierarchy is his more fundamental work that joins computer science and linguistics. It was published in IRE Transactions on Information Theory. Chomsky, Noam (1956). "Three models for the description of language" https://chomsky.info/wp-content/uploads/195609-.pdf

Type-3 grammar ≡ finite-state automaton

Type-2 grammar ≡ Non-deterministic pushdown automaton

Type-1 grammar ≡ Linear-bounded non-deterministic Turing machine

Type-0 grammar ≡ Turing machine

ps. Chomsky was already aware of Finite State Automata and Turing Machines and understood that they match Type-3 and Type-0. Pushdown Automata was invented later, and connection between Type-1 grammar and Linear Bounded Automata was made few years later.

[PaulHoule]

An LLM is not type 0. It always finishes in finite time so it is not Turing complete.

I asked Copilot

   answer yes or no,  is the following Java method syntactically well formed
   
   static int aMethod() { return "5"; }

and got what I thought was the wrong answer

   No.
   It’s syntactically valid as Java code, but it will not compile because it returns a String where 
   an int is required.

because I hadn't specified clearly that I was talking about the type 2 CFG of the parser as opposed to the type 1 behavior of the compiler as a whole. [1] I had a good conversation with copilot about it and I'm sure I'd get better results with a better prompt... It would make a good arXiv paper to pose an LLM grammatical recognition problems by prompting

   here is a set of rules: ...  is the production ... in the grammar?

with a wide range of cases. Somebody who just tries a few examples might be impressed by its capability but if you were rigorous about it you would conclude that an LLM pretends to be able to recognize grammars but can't actually do it.

And that's true about everything they do, one could argue that "in an exact sense, LLM can't do anything at all") They'll make a try at a weird question like

   what percent of North Americans would recognize the kitsune hand gesture?

which is a public opinion research question similar in character to

   what is lowest mass eigenstate of the neutrino?

in that it could be answered rigorously (but still in terms of probability, even hep results have p-values)

[1] javac implements type 1 behavior in the java language which is a substrate

[lostmsu]

> It always finishes in finite time so it is not Turing complete.

This is incorrect. The simplest LLM inference is basically a `do { choose_word(...); } until (word == '<special stop word>');` loop. That loop may never stop.

[xg15]

I think it could be useful to combine the two paradigms to maybe get a better understanding of what transformers can and cannot learn.

E.g. would it be possible to create an algorithm that takes a grammar (and maybe a desired context window size) as input and constructs a transformer network that generates sentences exactly from that grammar?

("Construct" meaning directly setting the weights, without any iterative training process)

[nabla9]

They are combined. Chomsky Hierarchies are the core of modern Computer science because they map perfectly into automata theory. They are always taught together in computer science.

>E.g. would it be possible to create an algorithm that takes a grammar (and maybe a desired context window size) as input and constructs a transformer network that generates sentences exactly from that grammar?

You don't need transformers for what you describe. That's 101 theory of computation class where you learn about automata, grammars, parsers, and generators.

[xg15]

Yeah, I know the theory of formal grammars and automata that the Chomsky hierarchy is part of. What I meant is that language models and specifically transformer networks are usually entirely separate from that theory, so it would be useful to build a bridge between "modern" language processing using GPTs/LLMs and the classical formal theory.

The most obvious overlap in usage is with programming languages: LLMs can parse and generate code in formal languages, but their processing model is completely different from syntax trees and parsers. So the question is, how do they store the formal structure of a programming language and could this be mapped back in any way to a grammar or automaton?

[PaulHoule]

The way I see it is that attention is graph structured -- this token here is connected to that token there and so forth by the attention lighting up or also in the sense that there are a bunch of places in the document where people are talking about "Noam" or "Chomsky" or "Noam Chomsky" or "The Author" or "him", etc.

Alternately if you were looking it from a semantic web perspective the knowledge expressed in a document is a graph and that graph structure is more fundamental than the tree structure of a text because you could express the same knowledge in different orders. Serialization fundamentally requires putting things in some specific order which might specifically be chronological (work from 2005 to the present as a play with many acts) or could be organized around some conceptual hierarchy (kitsune legends, self psychology, character acting, animal and human behavior and physiology, ...) or the minimization or elimination of backward references (whatever it is that the C spec does a touch wrong but post-Common Lisp specs do right) , etc. Ultimately the graph is pruned away into a tree where the remaining links are denoted by syntactic features in the local scale of the document, you're kinda left filling in the rest of the links with some combination of pragmatics, logical inference, something like SAT solving, etc,

A conventional parsing point of view sees a Java program as a tree but for ordinary purposes it does not matter what order you put the fields and methods in and even though procedural programs are allegedly a sequence of operations done in a certain order it is frequently the case that it does not matter at all if you run line 71 or line 75 first so it is often the case that the graph is the real thing and the trees that we're so comfortable with are the shadows on the walls of the cave.

[yongjik]

Chomsky Hierarchy pertains to "languages" defined in the theory of computation: i.e., it is a subset of the set of all finite sequence of alphabets (for some fixed notion of "alphabets"). If a sentence (a particular finite sequence of alphabets) is in the subset, then it is a "valid" sentence of the language. Otherwise it is invalid.

It should be already clear from this that this notion of language is rather different from natural languages. For example, if there is a formal language that contains "Good morning" and "My hovercraft is full of eels" as valid sentences, then nothing distinguishes these sentences any more. (Of course you could add annotations and build semantic values but they are not essential to the discussion of formal languages.)

It gets a bit more ridiculous when you try to connect LLMs to the Chomsky hierarchy. Modern LLMs do not really operate on the principle of "is this a valid sentence?" yet provide vastly superior results when it comes to generating naturally sounding sentences.

I think LLMs have put an end to any hope that formal language theory (in the style of Chomsky Hierarchy) will be relevant to understanding human languages.

[littlestymaar]

> For example, if there is a formal language that contains "Good morning" and "My hovercraft is full of eels" as valid sentences, then nothing distinguishes these sentences any more.

Mind explaining a bit? Because I've no idea what you mean.

[Legend2440]

The trouble is that english doesn’t fit neatly into any of these categories. It has features that make it at least a context-free language, but can’t handle other features of context-free languages like unlimited nesting.

Ultimately these are categories of formal languages, and natural language is an entirely different kind of thing.

[nabla9]

Strictly speaking natural languages fit into Context-Sensitive (Type-1) in Chomsky Hierarchy, but that's too broad to be useful.

In practice they are classified into MCSL (Mildly Context-Sensitive) subcategory defined by Aravind K. Joshi.

[krnlclnl]

Sure, if you accept and agree with Joshi.

No reason to do that though, except to validate some random persons perspective on language. The sky will not open and smash us with a giant foot if we reject such an obligation.

[nabla9]

Natural languages being in MCSL (Mildly Context-Sensitive) is the consensus among linguistics, not some random individual's viewpoint.

[krnlclnl]

OK? What concrete human problems human biology faces are resolved by this groups consensus? Obsession with notation does little to improve crop yields, or improve working conditions for the child labor these academic geniuses rely on.

Sure, linguists, glad you found some semantics that fit your obsession. Happy for you!

Most people will never encounter their work and live their lives never knowing such an event happened.

[suddenlybananas]

You can also reject quantum physics and the sky will not open and smash us with a giant foot. However, to do so without serious knowledge of physics would be quite dumb.

[krnlclnl]

Apples and oranges. Language emerges from human biology which emerges from the physical realm. In the end language emerges then from the physical realm. Trying to de-couple it from physical nature and make it an abstract thought bubble is akin to bike shedding in programming.

[suddenlybananas]

You could say this about literally anything.