Related papers: Enriching a Linear/Non-linear Lambda Calculus: A P…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
We propose Quantum-informed Tensor Adaptation (QuanTA), a novel, easy-to-implement, fine-tuning method with no inference overhead for large-scale pre-trained language models. By leveraging quantum-inspired methods derived from quantum…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
This paper presents a novel framework for high-dimensional nonlinear quantum computation that exploits tensor products of amplified vector and matrix encodings to efficiently evaluate multivariate polynomials. The approach enables the…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
Large language models (LLMs) have demonstrated remarkable capabilities across various domains, yet their application to relational deep learning (RDL) remains underexplored. Existing approaches adapt LLMs by traversing relational links…
We propose a quantum programming language that generalizes the $\lambda$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of…
As the core component of Natural Language Processing (NLP) system, Language Model (LM) can provide word representation and probability indication of word sequences. Neural Network Language Models (NNLMs) overcome the curse of dimensionality…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
Monoidal algebraic structures consist of operations that can have multiple outputs as well as multiple inputs, which have applications in many areas including categorical algebra, programming language semantics, representation theory,…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
We refine a model for linear logic based on two well-known ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic…
In this paper, we propose a sequential neural encoder with latent structured description (SNELSD) for modeling sentences. This model introduces latent chunk-level representations into conventional sequential neural encoders, i.e., recurrent…
Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…
With the advent of powerful neural language models over the last few years, research attention has increasingly focused on what aspects of language they represent that make them so successful. Several testing methodologies have been…
Rich textual and topological information of textual graphs need to be modeled in real-world applications such as webpages, e-commerce, and academic articles. Practitioners have been long following the path of adopting a shallow text encoder…
Quantum computing is rapidly evolving in both physics and computer science, offering the potential to solve complex problems and accelerate computational processes. The development of quantum chips necessitates understanding the…
We study a \emph{QDisCoCirc}-inspired, chunked diagram-to-circuit quantum natural language processing (QNLP) model for three-class sentiment classification of financial texts. In our classical simulations, we keep the Hilbert-space…