Related papers: On the mechanical creation of mathematical concept…
Understanding of free-format multi-step arithmetic word problems with extraneous information is discussed. A model including a full set of general skills necessary for understanding such problems was developed and computer implemented. The…
Concept-based explainable approaches have emerged as a promising method in explainable AI because they can interpret models in a way that aligns with human reasoning. However, their adaption in the text domain remains limited. Most existing…
Explanations are hypothesized to improve human understanding of machine learning models and achieve a variety of desirable outcomes, ranging from model debugging to enhancing human decision making. However, empirical studies have found…
Aligning human-interpretable concepts with the internal representations learned by modern machine learning systems remains a central challenge for interpretable AI. We introduce a geometric framework for comparing supervised human concepts…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
We argue how AI can assist mathematics in three ways: theorem-proving, conjecture formulation, and language processing. Inspired by initial experiments in geometry and theoretical physics in 2017, we summarize how this emerging field has…
Recent years have seen the dramatic rise of the usage of AI algorithms in pure mathematics and fundamental sciences such as theoretical physics. This is perhaps counter-intuitive since mathematical sciences require the rigorous definitions,…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
A plausible definition of "reasoning" could be "algebraically manipulating previously acquired knowledge in order to answer a new question". This definition covers first-order logical inference or probabilistic inference. It also includes…
Machine learning models that first learn a representation of a domain in terms of human-understandable concepts, then use it to make predictions, have been proposed to facilitate interpretation and interaction with models trained on…
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…
Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue…
Questions concerning origin of mathematical knowledge and roles of language and intuition (imagery) in mathematical thoughts are long standing and widely debated. By introspection, mathematicians usually have some beliefs regarding these…
I think that the main reason why we do not understand the general principles of how knowledge works (and probably also the reason why we have not yet designed and built efficient machines capable of artificial intelligence), is not the…
Machine learning models that incorporate concept learning as an intermediate step in their decision making process can match the performance of black-box predictive models while retaining the ability to explain outcomes in human…
Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…
Explainability is needed to establish confidence in machine learning results. Some explainable methods take a post hoc approach to explain the weights of machine learning models, others highlight areas of the input contributing to…
Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without…
Prior work on generating explanations in a planning and decision-making context has focused on providing the rationale behind an AI agent's decision making. While these methods provide the right explanations from the explainer's…