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Learning word embeddings using distributional information is a task that has been studied by many researchers, and a lot of studies are reported in the literature. On the contrary, less studies were done for the case of multiple languages.…
We derive asymptotics for the moments as well as the weak limit of the height distribution of watermelons with p branches with wall. This generalises a famous result of de Bruijn, Knuth and Rice on the average height of planted plane trees,…
In this paper, we compute the distribution of the first letter statistic on nine avoidance classes of permutations corresponding to two pairs of patterns of length four. In particular, we show that the distribution is the same for each…
Reciprocity is a second-order correlation that has been recently detected in all real directed networks and shown to have a crucial effect on the dynamical processes taking place on them. However, no current theoretical model generates…
Design-based inference, also known as randomization-based or finite-population inference, provides a principled framework for trustworthy statistical inference by attributing randomness solely to the design mechanism (e.g., treatment…
Reciprocity, or the tendency of individuals to mirror behavior, is a key measure that describes information exchange in a social network. Users in social networks tend to engage in different levels of reciprocal behavior. Differences in…
In this paper, we introduce the notion of a grammatical labeling to describe a recursive process of generating combinatorial objects based on a context-free grammar. For example, by labeling the ascents and descents of a Stirling…
Distributed representations of sentences have been developed recently to represent their meaning as real-valued vectors. However, it is not clear how much information such representations retain about the polarity of sentences. To study…
Reduplication and repetition, though similar in form, serve distinct linguistic purposes. Reduplication is a deliberate morphological process used to express grammatical, semantic, or pragmatic nuances, while repetition is often…
By studying the reciprocity property of linear Diophantine systems in light of Malcev-Neumann series, we present in this paper a new approach to and a generalization of Stanley's monster reciprocity theorem. A formula for the "error term"…
The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…
Universal Cycles, or U-cycles, as originally defined by de Bruijn, are an efficient method to exhibit a large class of combinatorial objects in a compressed fashion, and with no repeats. de Bruijn's theorem states that U-cycles for $n$…
We study a sorting procedure (run-sorting) on permutations, where runs are rearranged in lexicographic order. We describe a rather surprising bijection on permutations on length $n$, with the property that it sends the set of peak-values to…
We investigate language interpretations of two extensions of the Lambek calculus: with additive conjunction and disjunction and with additive conjunction and the unit constant. For extensions with additive connectives, we show that…
Most recent approaches use the sequence-to-sequence model for paraphrase generation. The existing sequence-to-sequence model tends to memorize the words and the patterns in the training dataset instead of learning the meaning of the words.…
The autoregressive decoding for text generation in large language models (LLMs), while widely used, is inherently suboptimal due to the lack of a built-in mechanism to perform refinement and/or correction of the generated content. In this…
We develop the technique of reduced word manipulation to give a range of results concerning reduced words and permutations more generally. We prove a broad connection between pattern containment and reduced words, which specializes to our…
Recent neural sequence-to-sequence models with a copy mechanism have achieved remarkable progress in various text generation tasks. These models addressed out-of-vocabulary problems and facilitated the generation of rare words. However, the…
Neural machine translation (NMT) models are usually trained with the word-level loss using the teacher forcing algorithm, which not only evaluates the translation improperly but also suffers from exposure bias. Sequence-level training under…
We sketch the construction of a derived enhancement of the reciprocity isomorphism of class field theory. Details will appear in a forthcoming joint paper of the authors with A. Raksit.