Related papers: Submodule approach to creative telescoping
Creative telescoping is an algorithmic method initiated by Zeilberger to compute definite sums by synthesizing summands that telescope, called certificates. We describe a creative telescoping algorithm that computes telescopers for definite…
We present a new algorithm to compute minimal telescopers for rational functions in two discrete variables. As with recent reduction-based approaches, our algorithm has the important feature that the computation of a telescoper is…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Hermite reduction is a classical algorithmic tool in symbolic integration. It is used to decompose a given rational function as a sum of a function with simple poles and the derivative of another rational function. We extend Hermite…
In robotic task planning, symbolic planners using rule-based representations like PDDL are effective but struggle with long-sequential tasks in complicated environments due to exponentially increasing search space. Meanwhile, LLM-based…
In this note we reinvestigate the task of computing creative telescoping relations in differential-difference operator algebras. Our approach is based on an ansatz that explicitly includes the denominators of the delta parts. We contribute…
Creative telescoping is a powerful computer algebra paradigm -initiated by Doron Zeilberger in the 90's- for dealing with definite integrals and sums with parameters. We address the mixed continuous-discrete case, and focus on the…
We present a new algorithm for constructing minimal telescopers for rational functions in three discrete variables. This is the first discrete reduction-based algorithm that goes beyond the bivariate case. The termination of the algorithm…
We show that the problem of constructing telescopers for functions of m variables is equivalent to the problem of constructing telescopers for algebraic functions of m -1 variables and present a new algorithm to construct telescopers for…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
We present a reduction algorithm that simultaneously extends Hermite's reduction for rational functions and the Hermite-like reduction for hyperexponential functions. It yields a unique additive decomposition and allows to decide…
We propose a way to split a given bivariate P-recursive sequence into a summable part and a non-summable part in such a way that the non-summable part is minimal in some sense. This decomposition gives rise to a new reduction-based creative…
The software compilation process has a tendency to obscure the original design of the system and makes it difficult both to identify individual components and discern their purpose simply by examining the resulting binary code. Although…
Creative telescoping algorithms compute linear differential equations satisfied by multiple integrals with parameters. We describe a precise and elementary algorithmic version of the Griffiths-Dwork method for the creative telescoping of…
In recent times, spatial light modulators have become a common tool in optics laboratories as well as industrial environment to shape the spatial structure of a beam. Although these devices are often easy to use, they usually come at a high…
Inference scaling methods for LLMs often rely on decomposing problems into steps (or groups of tokens), followed by sampling and selecting the best next steps. However, these steps and their sizes are often predetermined or manually…
Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial…
Speculative decoding accelerates LLM inference by utilizing otherwise idle computational resources during memory-to-chip data transfer. Current speculative decoding methods typically assume a considerable amount of available computing…
We showcase a collection of practical strategies to deal with a problem arising from an analysis of integral estimators derived via quasi-Monte Carlo methods. The problem reduces to a triple binomial sum, thereby enabling us to open up the…
Few-shot prompting is a surprisingly powerful way to use Large Language Models (LLMs) to solve various tasks. However, this approach struggles as the task complexity increases or when the individual reasoning steps of the task themselves…