As a total handwave, I would expect an LLM trained on formal logic and a huge corpus of proofs to produce pretty strong logic output.

And of course, if you trained a gigantic model on the entire web, then you'd get a very smooth approximation of the text in the corpus and very fluent, grammatical output. So basically, an LLM.

>> As many know and point out, this idea is now very old (40+ years?).

More like 110 years. Markov Chains were proposed in 1913 (by Markov) and popularised by Shannon in 1948 (in "A Mathematical Theory of Communication", the work that introduced information theory):

The underlying mathematics of the n-gram was first proposed by Markov (1913), who used what are now called Markov chains (bigrams and trigrams) to predict whether an upcoming letter in Pushkin’s Eugene Onegin would be a vowel or a con- sonant. Markov classified 20,000 letters as V or C and computed the bigram and trigram probability that a given letter would be a vowel given the previous one or two letters. Shannon (1948) applied n-grams to compute approximations to English word sequences. Based on Shannon’s work, Markov models were commonly used in engineering, linguistic, and psychological work on modeling word sequences by the 1950s. In a series of extremely influential papers starting with Chomsky (1956) and including Chomsky (1957) and Miller and Chomsky (1963), Noam Chomsky argued that “finite-state Markov processes”, while a possibly useful engineering heuristic, were incapable of being a complete cognitive model of human grammatical knowl- edge. These arguments led many linguists and computational linguists to ignore work in statistical modeling for decades.

https://web.archive.org/web/20220522005827/https://web.stanf...

(Note the usual shaking of angry fists at Chomsky. The NLP community continued on its path anyway, and built smooth, fluent generators of total bullshit and absolutely no progress towards a "cognitive model of human grammatical knowledge").

From a quick look, it doesn't seem to sample uniformly. w3 is added to a list for the context w1, w2, not a set. So, say word A occurs twice as often in a particular context as B, it will be in the list twice as often. So, even though a uniform choice function is used, the probability of A getting samples is twice as high.

You get a word salad because a trigram model has to little context to do anything else. This is a well-known issue with Markov and hidden Markov models.

(Fun fact: some hidden Markov model taggers switch to a different trigram distribution for V2 languages after seeing the finite verb, otherwise they often fail catastrophically in the verb cluster due to the limited context.)

Yeah, you're right. I had to squint a bit but it's like you say, the code is sampling uniformly from a list with possible multiples. Don't make me squint man! I'll get wrinkles :P

Squinting a bit more, that's not the way I know how to build n-grams. If you gave me the string (the cat sat on the bat) I'd give you bi-grams ($s the), (the cat), (cat sat), (sat on), (on the), (the bat), (bat $e). That way, after the first bigram, the next word only depends on the second word in the last bigram, because every bigram (w1 w2) is only ever followed by a bigram (w2 w3). So you're sliding a window of length 2 over the corpus, guided by the probability of the next word.

>> You get a word salad because a trigram model has to little context to do anything else. This is a well-known issue with Markov and hidden Markov models.

Yes, it's the Markov property that makes for word salad, ultimately, but you get less salad-y output if you can calculate better probabilities, and if you do it in the way I say above. And you can always build a string by selecting the next bigram that maximises the probability of the entire string. That's how I've always done it. I guess that's not Markovian any more but gives you reasonable output especially for small-ish corpora with not huge variance.

>> (Fun fact: some hidden Markov model taggers switch to a different trigram distribution for V2 languages after seeing the finite verb, otherwise they often fail catastrophically in the verb cluster due to the limited context.)

Thanks, I didn't know that.

I don't understand what you mean here, isn't that exactly what an n-gram model is already designed to achieve where n > 1? Since this is a 2-gram model isn't it already doing this?

So you're right that my comment is a bit confusing: I refer to the way you sample from a bi-gram model, so as to generate a string. Sorry!

The thing is, it's only if you buy fully into Chomskyan thinking that you think a "cognitive model of human grammatical knowledge" might even be useful. Or that it's a particularly special thing compared to any other cognitive model of human knowledge.

Then I put a demagogue politician speech through this and the results were almost like a speech that politician would have given. It was hard to tell the difference between the original and the generated.

in other words, if the public admires word salad, and someone speaks in word salad, then word salad output would not be considered as problematic by a large number of people.

"Hillary brought death and disaster to Iraq, Syria and Libya, she empowered Iran, and she unleashed ISIS. Now she wants to raise your taxes very substantially. Highest taxed nation in the world is a tenant of mine in Manhattan, so many great people. These are people that have been stolen, stolen by either very stupid politicians ask me the question, how are you going to get rid of all the emails?” “Yes, ma’am, they’re gonna stay in this country blind. My contract with the American voter begins with a plan to end government that will not protect its people is a government corruption at the State Department of Justice is trying as hard as they can to protect religious liberty"

Details at: https://successfulsoftware.net/2019/04/02/bloviate/