Related papers: AlephZero and Mathematical Experience
Safety assurance of automated driving systems must consider uncertain environment perception. This paper reviews literature addressing how perception testing is realized as part of safety assurance. We focus on testing for verification and…
Automated testing tools typically create test cases that are different from what human testers create. This often makes the tools less effective, the created tests harder to understand, and thus results in tools providing less support to…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Automatic verification deals with the validation by means of computers of correctness certificates. The related tools, usually called proof assistants or interactive provers, provide an interactive environment for the creation of formal…
An increasingly large number of experiments study the labor productivity effects of automation technologies such as generative algorithms. A popular question in these experiments relates to inequality: does the technology increase output…
Any act of problem-solving combines prior knowledge, local search, and a third element that is less often discussed: the extraction of information from search to update understanding. I propose a model of mathematical problem-solving as a…
Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and…
The rapid adoption of generative artificial intelligence (AI) tools in higher education is transforming how students engage with undergraduate mathematics, raising concerns about learning and assessment validity. This study examines the…
This paper offers a phenomenological reading of contemporary machine learning through Heideggerian concepts, aimed at enriching practitioners' reflexive understanding of their own practice. We argue that this philosophical lens reveals…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Algorithmic decision-making (ADM) increasingly shapes people's daily lives. Given that such autonomous systems can cause severe harm to individuals and social groups, fairness concerns have arisen. A human-centric approach demanded by…
AlphaZero, an approach to reinforcement learning that couples neural networks and Monte Carlo tree search (MCTS), has produced state-of-the-art strategies for traditional board games like chess, Go, shogi, and Hex. While researchers and…
Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the…
Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…
In this paper we aim to provide analysis and insights (often based on visualization), which explain the beneficial effects of on-line decision making on top of off-line training. In particular, through a unifying abstract mathematical…
In this lecture I will talk about three mathematical puzzles involving mathematics and computation that have preoccupied me over the years. The first puzzle is to understand the amazing success of the simplex algorithm for linear…
Agents in real-world scenarios like automated driving deal with uncertainty in their environment, in particular due to perceptual uncertainty. Although, reinforcement learning is dedicated to autonomous decision-making under uncertainty…
A significant amount of research has considered mathematical proofs, the students who learn them, and the instructors that teach them, from a variety of perspectives. This paper considers this topic from four main perspectives: students'…
Final written examination is the most important part of summative assessment in automatic control courses. Preparation of the examinations with a given number of points according to the concept of Constructive Alignment (which could be the…