相关论文: Extended Rate, more GFUN

This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…

Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…

We show that the statistics of the continued fraction expansion of a randomly chosen rational in the unit interval, with a fixed large denominator $q$, approaches the Gauss-Kuzmin statistics with polynomial rate in $q$. This improves on…

A common recent approach to semantic parsing augments sequence-to-sequence models by retrieving and appending a set of training samples, called exemplars. The effectiveness of this recipe is limited by the ability to retrieve informative…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

This article describes the REDUCE package ZEILBERG implemented by Gregor St\"olting and the author. The REDUCE package ZEILBERG is a careful implementation of the Gosper and Zeilberger algorithms for indefinite, and definite summation of…

In this article we show the rough outline of a computer algorithm to generate lower bounds on the exponential function of (in principle) arbitrary precision. We implemented this to generate all necessary analytic terms for the Boltzmann…

We develop a synthesis of Turing's paradigm of computation and von Neumann's quantum logic to serve as a model for quantum computation with recursion, such that potentially non-terminating computation can take place, as in a quantum Turing…

The celebrated Zeilberger algorithm which finds holonomic recurrence equations for definite sums of hypergeometric terms $F(n,k)$ is extended to certain nonhypergeometric terms. An expression $F(n,k)$ is called a hypergeometric term if both…

There has recently been a concerted effort to derive mechanisms in vision and machine learning systems to offer uncertainty estimates of the predictions they make. Clearly, there are enormous benefits to a system that is not only accurate…

Summation formulas, such as the Euler-Maclaurin expansion or Gregory's quadrature, have found many applications in mathematics, ranging from accelerating series, to evaluating fractional sums and analyzing asymptotics, among others. We show…

It is natural for probabilistic programs to use conditionals to express alternative substructures in models, and loops (recursion) to express repeated substructures in models. Thus, probabilistic programs with conditionals and recursion…

We construct a new scheme of approximation of any multivalued algebraic function $f(z)$ by a sequence $\{r_{n}(z)\}_{n\in \mathbb{N}}$ of rational functions. The latter sequence is generated by a recurrence relation which is completely…

Motivated by the optimal continued fractions studied independently by Selenius and Bosma, we define and introduce algorithms producing superoptimal continued fraction expansions of irrationals. The convergents of these expansions…

This paper establishes a novel role for Gaussian-mixture models (GMMs) as functional approximators of Q-function losses in reinforcement learning (RL). Unlike the existing RL literature, where GMMs play their typical role as estimates of…

We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…

Lin and Lin have recently shown how starting with a classical query algorithm (decision tree) for a function, we may find upper bounds on its quantum query complexity. More precisely, they have shown that given a decision tree for a…

In this paper we present two efficient methods for reconstructing a rational number from several residue-modulus pairs, some of which may be incorrect. One method is a natural generalization of that presented by Wang, Guy and Davenport in…

Scaling inference compute in large language models (LLMs) through repeated sampling consistently increases the coverage (fraction of problems solved) as the number of samples increases. We conjecture that this observed improvement is…