Language model

A language model is a probabilistic model of a natural language.^[1] In 1980, the first significant statistical language model was proposed, and during the decade IBM performed ‘Shannon-style’ experiments, in which potential sources for language modeling improvement were identified by observing and analyzing the performance of human subjects in predicting or correcting text.^[2]

Language models are useful for a variety of tasks, including speech recognition^[3] (helping prevent predictions of low-probability (e.g. nonsense) sequences), machine translation,^[4] natural language generation (generating more human-like text), optical character recognition, route optimization,^[5] handwriting recognition,^[6] grammar induction,^[7] and information retrieval.^[8]^[9]

Large language models, currently their most advanced form, are a combination of larger datasets (frequently using words scraped from the public internet), feedforward neural networks, and transformers. They have superseded recurrent neural network-based models, which had previously superseded the pure statistical models, such as word n-gram language model.

Pure statistical models

Models based on word n-grams

A word n-gram language model is a purely statistical model of language. It has been superseded by recurrent neural network–based models, which have been superseded by large language models.^[10] It is based on an assumption that the probability of the next word in a sequence depends only on a fixed size window of previous words. If only one previous word is considered, it is called a bigram model; if two words, a trigram model; if n − 1 words, an n-gram model.^[11] Special tokens are introduced to denote the start and end of a sentence $\langle s\rangle$ and $\langle /s\rangle$ .

To prevent a zero probability being assigned to unseen words, each word's probability is slightly lower than its frequency count in a corpus. To calculate it, various methods were used, from simple "add-one" smoothing (assign a count of 1 to unseen n-grams, as an uninformative prior) to more sophisticated models, such as Good–Turing discounting or back-off models.

Exponential

Maximum entropy language models encode the relationship between a word and the n-gram history using feature functions. The equation is

$P(w_{m}\mid w_{1},\ldots ,w_{m-1})={\frac {1}{Z(w_{1},\ldots ,w_{m-1})}}\exp(a^{T}f(w_{1},\ldots ,w_{m}))$

where $Z(w_{1},\ldots ,w_{m-1})$ is the partition function, $a$ is the parameter vector, and $f(w_{1},\ldots ,w_{m})$ is the feature function. In the simplest case, the feature function is just an indicator of the presence of a certain n-gram. It is helpful to use a prior on $a$ or some form of regularization.

The log-bilinear model is another example of an exponential language model.

Skip-gram model

Skip-gram language model is an attempt at overcoming the data sparsity problem that the preceding model (i.e. word n-gram language model) faced. Words represented in an embedding vector were not necessarily consecutive anymore, but could leave gaps that are skipped over.^[12]

Formally, a $k$ -skip- $n$ -gram is a length- $n$ subsequence where the components occur at distance at most $k$ from each other.

For example, in the input text:

the rain in Spain falls mainly on the plain

the set of 1-skip-2-grams includes all the bigrams (2-grams), and in addition the subsequences

the in, rain Spain, in falls, Spain mainly, falls on, mainly the, and on plain.

In skip-gram model, semantic relations between words are represented by linear combinations, capturing a form of compositionality. For example, in some such models, if $v$ is the function that maps a word $w$ to its $n$ -d vector representation, then

$v(\mathrm {king} )-v(\mathrm {male} )+v(\mathrm {female} )\approx v(\mathrm {queen} )$

where ≈ is made precise by stipulating that its right-hand side must be the nearest neighbor of the value of the left-hand side.^[13]^[14]

Neural models

Recurrent neural network

Continuous representations or embeddings of words are produced in recurrent neural network-based language models (known also as continuous space language models).^[15] Such continuous space embeddings help to alleviate the curse of dimensionality, which is the consequence of the number of possible sequences of words increasing exponentially with the size of the vocabulary, furtherly causing a data sparsity problem. Neural networks avoid this problem by representing words as non-linear combinations of weights in a neural net.^[16]

Large language models

A large language model (LLM) is a type of computational model designed for natural language processing tasks such as language generation. As language models, LLMs acquire these abilities by learning statistical relationships from vast amounts of text during a self-supervised and semi-supervised training process.^[17]

The largest and most capable LLMs are artificial neural networks built with a decoder-only transformer-based architecture, enabling efficient processing and generation of large-scale text data. Modern models can be fine-tuned for specific tasks, or be guided by prompt engineering.^[18] These models acquire predictive power regarding syntax, semantics, and ontologies^[19] inherent in human language corpora, but they also inherit inaccuracies and biases present in the data on which they are trained.^[20]

Although sometimes matching human performance, it is not clear whether they are plausible cognitive models. At least for recurrent neural networks, it has been shown that they sometimes learn patterns that humans do not, but fail to learn patterns that humans typically do.^[21]

Evaluation and benchmarks

Evaluation of the quality of language models is mostly done by comparison to human created sample benchmarks created from typical language-oriented tasks. Other, less established, quality tests examine the intrinsic character of a language model or compare two such models. Since language models are typically intended to be dynamic and to learn from data they see, some proposed models investigate the rate of learning, e.g., through inspection of learning curves.^[22]

Various data sets have been developed for use in evaluating language processing systems.^[23] These include:

Corpus of Linguistic Acceptability^[24]
GLUE benchmark^[25]
Microsoft Research Paraphrase Corpus^[26]
Multi-Genre Natural Language Inference
Question Natural Language Inference
Quora Question Pairs^[27]
Recognizing Textual Entailment^[28]
Semantic Textual Similarity Benchmark
SQuAD question answering Test^[29]
Stanford Sentiment Treebank^[30]
Winograd NLI
BoolQ, PIQA, SIQA, HellaSwag, WinoGrande, ARC, OpenBookQA, NaturalQuestions, TriviaQA, RACE, MMLU (Massive Multitask Language Understanding), BIG-bench hard, GSM8k, RealToxicityPrompts, WinoGender, CrowS-Pairs.^[31] (LLaMa Benchmark)

References

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