Related papers: On the mechanical creation of mathematical concept…
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
Concept discovery is one of the open problems in the interpretability literature that is important for bridging the gap between non-deep learning experts and model end-users. Among current formulations, concepts defines them by as a…
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…
The rapid evolution of artificial intelligence has led to expectations of transformative impact on science, yet current systems remain fundamentally limited in enabling genuine scientific discovery. This perspective contends that progress…
Concept-based explainability methods provide insight into deep learning systems by constructing explanations using human-understandable concepts. While the literature on human reasoning demonstrates that we exploit relationships between…
Can artificial intelligence discover, from raw experience and without human supervision, concepts that humans have discovered? One challenge is that human concepts themselves are fluid: conceptual boundaries can shift, split, and merge as…
Feedback on student answers and even during intermediate steps in their solutions to open-ended questions is an important element in math education. Such feedback can help students correct their errors and ultimately lead to improved…
Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an…
Providing explanations along with predictions is crucial in some text processing tasks. Therefore, we propose a new self-interpretable model that performs output prediction and simultaneously provides an explanation in terms of the presence…
In this article, we tackle the math word problem, namely, automatically answering a mathematical problem according to its textual description. Although recent methods have demonstrated their promising results, most of these methods are…
The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from…
Math word problems form a natural abstraction to a range of quantitative reasoning problems, such as understanding financial news, sports results, and casualties of war. Solving such problems requires the understanding of several…
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…
The interpretation of deep neural networks (DNNs) has become a key topic as more and more people apply them to solve various problems and making critical decisions. Concept-based explanations have recently become a popular approach for…
The highest level of mathematics research is traditionally seen as a solitary activity. Yet new innovations by mathematicians themselves are starting to harness the power of social computation to create new modes of mathematical production.…
Knowledge is the most precious asset of humankind. People extract the experience from the data that provide for us the reality through the feelings. Generally speaking, it is possible to see the analogy of knowledge elaboration between…
Explainable artificial intelligence techniques are developed at breakneck speed, but suitable evaluation approaches lag behind. With explainers becoming increasingly complex and a lack of consensus on how to assess their utility, it is…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
Modern information systems are changing the idea of "data processing" to the idea of "concept processing", meaning that instead of processing words, such systems process semantic concepts which carry meaning and share contexts with other…
The maturity of deep learning techniques has led in recent years to a breakthrough in object recognition in visual media. While for some specific benchmarks, neural techniques seem to match if not outperform human judgement, challenges are…