Related papers: A Chomsky-Sch\"utzenberger representation for weig…
We develop a constructive theory of finite multisets in Homotopy Type Theory, defining them as free commutative monoids. After recalling basic structural properties of the free commutative-monoid construction, we formalise and establish the…
Cross-language learning allows us to use training data from one language to build models for a different language. Many approaches to bilingual learning require that we have word-level alignment of sentences from parallel corpora. In this…
We introduce tree stack automata as a new class of automata with storage and identify a restricted form of tree stack automata that recognises exactly the multiple context-free languages.
We study the problem of multilingual masked language modeling, i.e. the training of a single model on concatenated text from multiple languages, and present a detailed study of several factors that influence why these models are so…
Reversible weighted automata are introduced and considered in a specific setting where the weights are taken from a nontrivial locally finite commutative ring such as a finite field. It is shown that the supports of series realised by such…
This paper seeks to model human language by the mathematical framework of quantum physics. With the well-designed mathematical formulations in quantum physics, this framework unifies different linguistic units in a single complex-valued…
Here we announce the construction and properties of a big commutative subalgebra of the Kirillov algebra, called big algebra, attached to a finite dimensional irreducible representation of a complex semisimple Lie group. They are…
Parikh theorem was originally stated and proved by Rohkit Parikh in MIT research report in 1961. Many different proofs of this classical theorems were produced then; our goal is to give another proof using Chomsky-Schutzenberger…
We study the relation between weighted pluripotential on a compact set E in C^N and the pluripotential theory of an associated circed set Z in C^(N+1)
Linear embedding transformation has been shown to be effective for zero-shot cross-lingual transfer tasks and achieve surprisingly promising results. However, cross-lingual embedding space mapping is usually studied in static word-level…
We propose a scalable framework for deciding, proving, and explaining (in-)equivalence of context-free grammars. We present an implementation of the framework and evaluate it on large data sets collected within educational support systems.…
Multimodal models have been proven to outperform text-based models on learning semantic word representations. Almost all previous multimodal models typically treat the representations from different modalities equally. However, it is…
We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove…
In this paper, we prove that the weighted BMO space as follows $${\rm BMO}^{p}(\omega)=\Big\{f\in L^{1}_{\rm loc}:\sup_{Q}\|\chi_{Q}\|^{-1}_{L^{p}(\omega)}\big\|(f-f_{Q})\omega^{-1}\chi_{Q}\big\|_{L^{p}(\omega)}<\infty\Big\}$$ is…
This work provides a smooth and everywhere well-defined extension of Bondi-Metzner-Sachs (BMS) supertranslations into the bulk of Minkowski space. The supertranslations lead to physically distinct spacetimes, all isometric to Minkowski…
We study totally bounded subsets in weighted variable exponent amalgam and Sobolev spaces. Moreover, this paper includes several detailed generalized results of some compactness criterions in these spaces.
Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any strongly truncated Riesz space is isomorphic to a uniformly…
Multilingual Word Embeddings (MWEs) represent words from multiple languages in a single distributional vector space. Unsupervised MWE (UMWE) methods acquire multilingual embeddings without cross-lingual supervision, which is a significant…
The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable…
By fundamental results of Sch\"utzenberger, McNaughton and Papert from the 1970s, the classes of first-order definable and aperiodic languages coincide. Here, we extend this equivalence to a quantitative setting. For this, weighted automata…