Related papers: Approximation theory for distant Bang calculus
Kohn-Sham density functional theory (DFT) is the workhorse of quantum chemistry, offering an attractive balance between accuracy and computational cost. Although exact in principle, DFT in practice relies on an approximation to the unknown…
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
In the folklore of linear logic, a common intuition is that the structure of finiteness spaces, introduced by Ehrhard, semantically reflects the strong normalization property of cut-elimination. We make this intuition formal in the context…
Distributional semantics offers new ways to study the semantics of morphology. This study focuses on the semantics of noun singulars and their plural inflectional variants in English. Our goal is to compare two models for the…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers of small coupling parameters, which as a…
Rule-based machine translation is more data efficient than the big data-based machine translation approaches, making it appropriate for languages with low bilingual corpus resources -- i.e., minority languages. However, the rule-based…
Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting. In this paper, the technique is applied to a typed, call-by-value, lambda-calculus.…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
The expansions of tree-level amplitudes for one theory into amplitudes for another theory, which have been studied in various recent literatures, exhibit hidden connections between different theories that are invisible in traditional…
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…
Recognizing similarities among entities is central to both human cognition and computational intelligence. Within this broader landscape, Entity Set Expansion is one prominent task aimed at taking an initial set of (tuples of) entities and…
String diagrammatic calculi have become increasingly popular in fields such as quantum theory, circuit theory, probabilistic programming, and machine learning, where they enable resource-sensitive and compositional algebraic analysis.…
Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…
Recent advancements in cognitive science and multi-round reasoning techniques for Large Language Models (LLMs) suggest that iterative thinking processes improve problem-solving performance in complex tasks. Inspired by this, approaches like…
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $\lambda$-calculus, the process representations yield (at best) non-extensional $\lambda $-theories (i.e., $\beta$…
State-of-the-art performance in QA tasks is currently achieved by systems employing Large Language Models (LLMs), however these models tend to hallucinate information in their responses. One approach focuses on enhancing the generation…
We present a new and surprisingly simple analysis of random-shift decompositions -- originally proposed by Miller, Peng, and Xu [SPAA'13]: We show that decompositions for exponentially growing scales $D = 2^0, 2^1, \ldots,…
The enriched effect calculus (EEC) is an extension of Moggi's computational metalanguage with a selection of primitives from linear logic. This paper explores the enriched effect calculus as a target language for continuation-passing-style…