Related papers: An Internal Language for Categories Enriched over …

Large Language Models (LLMs) exhibit impressive performance on a range of NLP tasks, due to the general-purpose linguistic knowledge acquired during pretraining. Existing model interpretability research (Tenney et al., 2019) suggests that a…

Multilingual large language models (LLMs) seem to generalize somewhat across languages. We hypothesize this is a result of implicit vector space alignment. Evaluating such alignment, we see that larger models exhibit very high-quality…

It is often desirable to be able to recognize when inputs to a recognition function learned in a supervised manner correspond to classes unseen at training time. With this ability, new class labels could be assigned to these inputs by a…

In this position paper, we would like to offer and defend a new template to study equivalences between programs -- in the particular framework of process algebras for concurrent computation.We believe that our layered model of development…

Large language models (LLMs) enable researchers to analyze text at unprecedented scale and minimal cost. Researchers can now revisit old questions and tackle novel ones with rich data. We provide an econometric framework for realizing this…

Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda…

We introduce new methods for estimating and evaluating embeddings of words in more than fifty languages in a single shared embedding space. Our estimation methods, multiCluster and multiCCA, use dictionaries and monolingual data; they do…

In this note we contribute to the recently developing study of "almost Boolean" quantum logics (i.e. to the study of orthomodular partially ordered sets that are naturally endowed with a symmetric difference). We call them enriched quantum…

Lexical semantics is concerned with both the multiple senses a word can adopt in different contexts, and the semantic relations that exist between meanings of different words. To investigate them, Contextualized Language Models are a…

We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we…

Quantified Boolean logic results from adding operators to Boolean logic for existentially and universally quantifying variables. This extends the reach of Boolean logic by enabling a variety of applications that have been explored over the…

Functional logic languages can solve equations over user-defined data and functions. Thus, the definition of an appropriate meaning of equality has a long history in these languages, ranging from reflexive equality in early equational logic…

We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…

Recent breakthroughs in NLP research, such as the advent of Transformer models have indisputably contributed to major advancements in several tasks. However, few works research robustness and explainability issues of their evaluation…

Following Lawvere's description of metric spaces using enriched category theory, we introduce a change in the base of enrichment that allows description of some aspects of (relativistic) causal spaces. All such spaces are Cauchy complete,…

We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also…

Qualitative relationships illustrate how changing one property (e.g., moving velocity) affects another (e.g., kinetic energy) and constitutes a considerable portion of textual knowledge. Current approaches use either semantic parsers to…

Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent…

The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having…

This paper bridges internal and external analysis approaches to large language models (LLMs) by demonstrating that geometric properties of internal model representations serve as reliable proxies for evaluating generated text quality. We…