Related papers: Quantifiers on languages and codensity monads

Working in the setting of $\infty$-categories, we develop a general theory of the codensity monad $T_\mathcal{D}$ associated with a full subcategory $\mathcal{D}\subseteq \mathcal{C}$. We show that $T_\mathcal{D}$ has a canonical monad…

The vocabulary used by language models (LM) - defined by the tokenizer - plays a key role in text generation quality. However, its impact remains under-explored in radiology. In this work, we address this gap by systematically comparing…

Many real applications problems can be encoded easily as quantified formulas in SMT. However, this simplicity comes at the cost of difficulty during solving by SMT solvers. Different strategies and quantifier instantiation techniques have…

Laminar set systems consist of non-crossing subsets of a universe with set inclusion essentially corresponding to the descendant relationship of a tree, the so-called laminar tree. Laminar set systems lie at the core of many graph…

Large Vision and Language Models have exhibited remarkable human-like intelligence in tasks such as natural language comprehension, problem-solving, logical reasoning, and knowledge retrieval. However, training and serving these models…

We study monads resulting from the combination of nondeterministic and probabilistic behaviour with the possibility of termination, which is essential in program semantics. Our main contributions are presentation results for the monads,…

Quantitative algebras are $\Sigma$-algebras acting on metric spaces, where operations are nonexpanding. Mardare, Panangaden and Plotkin introduced 1-basic varieties as categories of quantitative algebras presented by quantitative equations.…

Language Modelling has been a central part of Natural Language Processing for a very long time and in the past few years LSTM-based language models have been the go-to method for commercial language modeling. Recently, it has been shown…

We show that each level of the quantifier alternation hierarchy within FO^2[<] -- the 2-variable fragment of the first order logic of order on words -- is a variety of languages. We then use the notion of condensed rankers, a refinement of…

Linguistic similarity is multi-faceted. For instance, two words may be similar with respect to semantics, syntax, or morphology inter alia. Continuous word-embeddings have been shown to capture most of these shades of similarity to some…

Sign language datasets are often not representative in terms of vocabulary, underscoring the need for models that generalize to unseen signs. Vector quantization is a promising approach for learning discrete, token-like representations, but…

We generalize linear superalgebra to higher gradings and commutation factors, given by arbitrary abelian groups and bicharacters. Our central tool is an extension, to monoidal categories of modules, of the Nekludova-Scheunert faithful…

There are many category-theoretic notions of algebraic theory, including Lawvere theories, monads, PROPs and operads. The first central notion of this thesis is a common generalisation of these, which we call a proto-theory. In order to…

We consider the terminal monad among those preserving the objects of a subcategory, and in particular preserving the image of a monad. Several common monads are shown to be uniquely characterized by the property of being terminal objects in…

Cross-lingual word embeddings encode the meaning of words from different languages into a shared low-dimensional space. An important requirement for many downstream tasks is that word similarity should be independent of language - i.e.,…

We present a straightforward embedding of quantified multimodal logic in simple type theory and prove its soundness and completeness. Modal operators are replaced by quantification over a type of possible worlds. We present simple…

We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework is reminiscent of state-sum models and lattice topological quantum field theories,…

We present three innovations in tokenization and subword segmentation. First, we propose to use unsupervised morphological analysis with Morfessor as pre-tokenization. Second, we present an algebraic method for obtaining subword embeddings…

This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism…

We set up a parametrised monadic translation for a class of call-by-value functional languages, and prove a corresponding soundness theorem. We then present a series of concrete instantiations of our translation, demonstrating that a number…