Related papers: $O_n$ is an $n$-MCFL
Ambiguity is an intrinsic feature of natural language. Managing ambiguity is a key part of human language understanding, allowing us to anticipate misunderstanding as communicators and revise our interpretations as listeners. As language…
Morphological tasks use large multi-lingual datasets that organize words into inflection tables, which then serve as training and evaluation data for various tasks. However, a closer inspection of these data reveals profound…
The uniform one-dimensional fragment of first-order logic was introduced a few years ago as a generalization of the two-variable fragment of first-order logic to contexts involving relations of arity greater than two. Quantifiers in this…
Let $\bar{a}_s(n)$ denote the number of partitions of $n$, wherein each odd part is multicolored (atmost $s\ge 1$ colors) and the first appearance of parts may be overlined. In this paper, we establish new families of congruences modulo…
In "Embers of Autoregression" (McCoy et al., 2023), we showed that several large language models (LLMs) have some important limitations that are attributable to their origins in next-word prediction. Here we investigate whether these issues…
Instead of pretraining multilingual language models from scratch, a more efficient method is to adapt existing pretrained language models (PLMs) to new languages via vocabulary extension and continued pretraining. However, this method…
A permutation of n letters is k-prolific if each (n-k)-subset of the letters in its one-line notation forms a unique pattern. We present a complete characterization of k-prolific permutations for each k, proving that k-prolific permutations…
We are interested in contractible n-manifolds M which "split" as M = A union B where A,B, and A intersect B are all homeomorphic to Euclidean n-space (such M are called open n-splitters) or A,B, and A intersect B are all homeomorphic to the…
Scaling existing applications and solutions to multiple human languages has traditionally proven to be difficult, mainly due to the language-dependent nature of preprocessing and feature engineering techniques employed in traditional…
We define invariants of words in arbitrary groups, measuring how letters in a word are interleaving, perfectly detecting the dimension series of a group. These are the letter-braiding invariants. On free groups, braiding invariants coincide…
Humans acquire language through implicit learning, absorbing complex patterns without explicit awareness. While LLMs demonstrate impressive linguistic capabilities, it remains unclear whether they exhibit human-like pattern recognition…
We study the dynamic membership problem for regular languages: fix a language L, read a word w, build in time O(|w|) a data structure indicating if w is in L, and maintain this structure efficiently under letter substitutions on w. We…
Most current large language models (LLMs) support a wide variety of languages in addition to English, including high-resource languages (e.g. German, Chinese, French), as well as low-resource ones (e.g. Swahili, Telugu). In addition they…
Fragments of first-order logic over words can often be characterized in terms of finite monoids or finite semigroups. Usually these algebraic descriptions yield decidability of the question whether a given regular language is definable in a…
Enterprise modeling deals with the increasing complexity of processes and systems by operationalizing model content and by linking complementary models and languages, thus amplifying the model-value beyond mere comprehensible pictures. To…
We investigate the $\phi^{2n}$ deformations of the O($N$)-symmetric (generalized) free theories with a flat boundary, where $n\geqslant 2$ is an integer. The generalized free theories refer to the $\Box^k$ free scalar theories with a…
GF(2)-grammars are a recently introduced grammar family with some unusual algebraic properties. They are closely connected to unambiguous grammars. By using the method of formal power series, we establish strong conditions that are…
Multilingual sentence encoders have seen much success in cross-lingual model transfer for downstream NLP tasks. Yet, we know relatively little about the properties of individual languages or the general patterns of linguistic variation that…
We study FO+, a fragment of first-order logic on finite words, where monadic predicates can only appear positively. We show that there is an FO-definable language that is monotone in monadic predicates but not definable in FO+. This…
Detecting out of policy speech (OOPS) content is important but difficult. While machine learning is a powerful tool to tackle this challenging task, it is hard to break the performance ceiling due to factors like quantity and quality…