相关论文: Extended Rate, more GFUN

Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…

Recurrent neural networks such as the GRU and LSTM found wide adoption in natural language processing and achieve state-of-the-art results for many tasks. These models are characterized by a memory state that can be written to and read from…

We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…

We present mathematical and conceptual foundations for the task of robust amplitude estimation using engineered likelihood functions (ELFs), a framework introduced in Wang et al. [PRX Quantum 2, 010346 (2021)] that uses Bayesian inference…

The numerical reasoning in the financial domain -- performing quantitative analysis and summarizing the information from financial reports -- can greatly increase business efficiency and reduce costs of billions of dollars. Here, we propose…

The integration of retrieval-augmented techniques with LLMs has shown promise in improving performance across various domains. However, their utility in tasks requiring advanced reasoning, such as generating and evaluating mathematical…

This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic…

A numerical program is presented which facilitates a computation pertaining to the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such…

A general rate estimation method is proposed that is based on studying the in-sample evolution of appropriately chosen diverging/converging statistics. The proposed rate estimators are based on simple least squares arguments, and are shown…

Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed…

Algorithms for the numerical evaluation of the incomplete gamma function ratios $P(a,x)=\gamma(a,x)/\Gamma(a)$ and $Q(a,x)=\Gamma(a,x)/\Gamma(a)$ are described for positive values of $a$ and $x$. Also, inversion methods are given for…

Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA and greedy Thiele algorithms have sparked renewed interest…

Retrieval-Augmented Generation (RAG) architectures have recently garnered significant attention for their ability to improve truth grounding and coherence in natural language processing tasks. However, the reliability of RAG systems in…

Generative Flow Networks (GFlowNets; GFNs) are a class of generative models that learn to sample compositional objects proportionally to their a priori unknown value, their reward. We focus on the case where the reward has a specified,…

The reciprocal square root is an important computation for which many very sophisticated algorithms exist (see for example \cite{863046,863031} and the references therein). In this paper we develop a simple differential compensation (much…

We present QBAL, an extension of Girard, Scedrov and Scott's bounded linear logic. The main novelty of the system is the possibility of quantifying over resource variables. This generalization makes bounded linear logic considerably more…

Many possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel…

A rational function $f(x)$ is rationally summable if there exists a rational function $g(x)$ such that $f(x)=g(x+1)-g(x)$. Detecting whether a given rational function is summable is an important and basic computational subproblem that…

Rational approximations are introduced and studied in granular graded rough sets and generalizations thereof by the first author in recent research papers. The concept of rationality is determined by related ontologies and coherence between…

This article introduces GuessCompx which is an R package that performs an empirical estimation on the time and memory complexities of an algorithm or a function. It tests multiple increasing-sizes samples of the user's data and attempts to…