Related papers: L'algorithme : pourquoi et comment le d{\'e}finir …
If an active citizen should increasingly be a computationally enlightened one, replacing the autonomy of reason with the heteronomy of algorithms, then I argue in this article that we must begin teaching the principles of critiquing the…
Research on algorithms has drastically increased in recent years. Various sub-disciplines of computer science investigate algorithms according to different objectives and standards. This plurality of the field has led to various…
A suite of impressive scientific discoveries have been driven by recent advances in artificial intelligence. These almost all result from training flexible algorithms to solve difficult optimization problems specified in advance by teams of…
Algorithmic statistics considers the following problem: given a binary string $x$ (e.g., some experimental data), find a "good" explanation of this data. It uses algorithmic information theory to define formally what is a good explanation.…
The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when…
The starting point of this paper is a collection of properties of an algorithm that have been distilled from the informal descriptions of what an algorithm is that are given in standard works from the mathematical and computer science…
In this paper we give a definition of "algorithm," "finite algorithm," "equivalent algorithms," and what it means for a single algorithm to dominate a set of algorithms. We define a derived algorithm which may have a smaller mean execution…
Algorithmic fairness has attracted increasing attention in the machine learning community. Various definitions are proposed in the literature, but the differences and connections among them are not clearly addressed. In this paper, we…
This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs,…
Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…
The words ``Programming is the second literacy'' were coined more than 40 years ago but never came to life. This paper is one in the series of papers aimed at the analysis of mathematical requirements for a merge of school mathematics with…
This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…
With the ever-growing presence of deep artificial neural networks in every facet of modern life, a growing body of researchers in educational data science -- a field consisting of various interrelated research communities -- have turned…
Artificial Intelligence - what is this? That is the question! In earlier papers we already gave a formal definition for AI, but if one desires to build an actual AI implementation, the following issues require attention and are treated…
It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems,…
Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus,…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Debates about artificial intelligence (AI) in education often portray teaching as a modular and procedural job that can increasingly be automated or delegated to technology. This brief communication paper argues that such claims depend on…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
Recent advances in Artificial Intelligence (AI) have sparked renewed interest in its potential to improve education. However, AI is a loose umbrella term that refers to a collection of methods, capabilities, and limitations-many of which…