Language Design as Information Renormalization
This work connects linguistics and physics to model language structure, offering insights for computational efficiency and neural network design, but it is incremental in applying existing physics concepts to linguistics.
The paper interprets the linguistic operation MERGE as a physical information coarse-graining, showing it can be formalized with language models using stochastic tensor networks, which imply polynomially-decaying correlations in language and provide bounds on perplexity from quantum states.
Here we consider some well-known facts in syntax from a physics perspective, allowing us to establish equivalences between both fields with many consequences. Mainly, we observe that the operation MERGE, put forward by N. Chomsky in 1995, can be interpreted as a physical information coarse-graining. Thus, MERGE in linguistics entails information renormalization in physics, according to different time scales. We make this point mathematically formal in terms of language models. In this setting, MERGE amounts to a probability tensor implementing a coarse-graining, akin to a probabilistic context-free grammar. The probability vectors of meaningful sentences are given by stochastic tensor networks (TN) built from diagonal tensors and which are mostly loop-free, such as Tree Tensor Networks and Matrix Product States, thus being computationally very efficient to manipulate. We show that this implies the polynomially-decaying (long-range) correlations experimentally observed in language, and also provides arguments in favour of certain types of neural networks for language processing. Moreover, we show how to obtain such language models from quantum states that can be efficiently prepared on a quantum computer, and use this to find bounds on the perplexity of the probability distribution of words in a sentence. Implications of our results are discussed across several ambits.