Title: Language Design and Renormalization,
Abstract: Here we consider some well-known facts in syntax from a physics perspective,
which allows us to establish some remarkable equivalences. Specifically, 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, i.e., probability distributions over word sequences, widely
used in natural language processing as well as other ambits. In this setting,
MERGE corresponds to a 3-index probability tensor implementing a
coarse-graining, akin to a probabilistic context-free grammar. The probability
vectors of meaningful sentences are naturally given by stochastic tensor
networks (TN) that are mostly loop-free, such as Tree Tensor Networks and
Matrix Product States. These structures have short-ranged correlations in the
syntactic distance by construction and, because of the peculiarities of human
language, they are extremely efficient to manipulate computationally. We also
propose how to obtain such language models from probability distributions of
certain TN quantum states, which we show to be efficiently preparable by a
quantum computer. Moreover, using tools from entanglement theory, we use these
quantum states to prove classical lower bounds on the perplexity of the
probability distribution for a set of words in a sentence. Implications of
these results are discussed in the ambits of theoretical and computational
linguistics, artificial intelligence, programming languages, RNA and protein
sequencing, quantum many-body systems, and beyond. Our work shows how many of
the key linguistic ideas from the last century, including developments in
computational linguistics, fit perfectly with known physical concepts linked to
renormalization.