相关论文: An Invitation to Algorithmic Information Theory

Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…

AI business process applications automate high-stakes business decisions where there is an increasing demand to justify or explain the rationale behind algorithmic decisions. Business process applications have ordering or constraints on…

In this paper, we propose a new mixed-integer linear programming (MILP) model ontology and a novel constraint typology of MILP formulations. MILP is a commonly used mathematical programming technique for modelling and solving real-life…

Machine learning interatomic potentials (MLIPs) enable atomistic simulations with near ab initio accuracy at significantly reduced computational cost, but their broader adoption is often limited by fragmented tooling, limited scalability,…

Computing theory analyzes abstract computational models to rigorously study the computational difficulty of various problems. Introductory computing theory can be challenging for undergraduate students, and the main goal of our research is…

The interest in explainability in artificial intelligence (AI) is growing vastly due to the near ubiquitous state of AI in our lives and the increasing complexity of AI systems. Answer-set Programming (ASP) is used in many areas, among them…

Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous…

Large language models (LLMs) have been explored in a variety of reasoning tasks including solving of mathematical problems. Each math dataset typically includes its own specially designed evaluation script, which, while suitable for its…

Numerical investigations are an important research tool in quantum information theory. There already exists a wide range of computational tools for quantum information theory implemented in various programming languages. However, there is…

Large-scale, high-quality data is essential for advancing the reasoning capabilities of large language models (LLMs). As publicly available Internet data becomes increasingly scarce, synthetic data has emerged as a crucial research…

This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…

We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…

Constraints on entropies are considered to be the laws of information theory. Even though the pursuit of their discovery has been a central theme of research in information theory, the algorithmic aspects of constraints on entropies remain…

The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…

I give an introduction to algorithmic uses of the principle of inclusion-exclusion. The presentation is intended to be be concrete and accessible, at the expense of generality and comprehensiveness.

The paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of…

The paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of…

Research efforts of the past fifty years have led to a development of linear integer programming as a mature discipline of mathematical optimization. Such a level of maturity has not been reached when one considers nonlinear systems subject…

A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…