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The output is "word salad" because the probabilities of the model are uniform, albeit implicitly- eyballing the python, it selects the next n-gram uniformly at

The output is "word salad" because the probabilities of the model are uniform, albeit implicitly- eyballing the python, it selects the next n-gram uniformly at random. A better n-gram model would calculate the probability of an n-gram following another n-gram according to their frequency in the training corpus. With a larger corpus and better training techniques (some smoothing for one thing) you'd get much more coherent 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.stanford.edu/~jurafsky/slp3/3.pdf 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").

shawnz 3y ago
> A better n-gram model would calculate the probability of an n-gram following another n-gram according to their frequency in the training corpus. With a larger corpus and better training techniques (some smoothing for one thing) you'd get much more coherent output. 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?
- YeGoblynQueenne 3y ago
  That's right, but a bi-gram model is just a big table of bi-grams and their probabilities (which are really their frequencies in a corpus normalised over the number of all bigrams in the corpus). You can use those probabilities in two ways: to calculate the probability of a string, by taking the bigrams in the string and multiplying their probabilities together; or by starting with some bigram (e.g. a search term entered by a user) and then selecting the next bigram according to its probability (i.e. its frequency in the corpus), or according to the probability of the entire string so-far (which you get by multiplying the probabilities of the bigrams so far); and repeat until you reach some maximum string-length. 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!
microtonal 3y ago
The output is "word salad" because the probabilities of the model are uniform, albeit implicitly- eyballing the python, it selects the next n-gram uniformly at random. 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.)
- deleted 3y ago
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- YeGoblynQueenne 3y ago
  >> 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. 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.
jameshart 3y ago
> absolutely no progress towards a "cognitive model of human grammatical knowledge" 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.

shawnz 3y ago

> A better n-gram model would calculate the probability of an n-gram following another n-gram according to their frequency in the training corpus. With a larger corpus and better training techniques (some smoothing for one thing) you'd get much more coherent output. 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?

YeGoblynQueenne 3y ago
That's right, but a bi-gram model is just a big table of bi-grams and their probabilities (which are really their frequencies in a corpus normalised over the number of all bigrams in the corpus). You can use those probabilities in two ways: to calculate the probability of a string, by taking the bigrams in the string and multiplying their probabilities together; or by starting with some bigram (e.g. a search term entered by a user) and then selecting the next bigram according to its probability (i.e. its frequency in the corpus), or according to the probability of the entire string so-far (which you get by multiplying the probabilities of the bigrams so far); and repeat until you reach some maximum string-length. 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!

microtonal 3y ago

The output is "word salad" because the probabilities of the model are uniform, albeit implicitly- eyballing the python, it selects the next n-gram uniformly at random. 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.)

deleted 3y ago
[deleted]
YeGoblynQueenne 3y ago
>> 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. 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.

jameshart 3y ago

> absolutely no progress towards a "cognitive model of human grammatical knowledge" 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.