Related papers: Limits of an AI program for solving college math p…
The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here…
Artificial neural networks are algorithms which have been developed to tackle a range of computational problems. These range from modelling brain function to making predictions of time-dependent phenomena to solving hard (NP-complete)…
Accurate estimation of item (question or task) difficulty is critical for educational assessment but suffers from the cold start problem. While Large Language Models demonstrate superhuman problem-solving capabilities, it remains an open…
We propose Neural Reasoner, a framework for neural network-based reasoning over natural language sentences. Given a question, Neural Reasoner can infer over multiple supporting facts and find an answer to the question in specific forms.…
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…
One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages.…
We present NeurASP, a simple extension of answer set programs by embracing neural networks. By treating the neural network output as the probability distribution over atomic facts in answer set programs, NeurASP provides a simple and…
AI for Mathematics (AI4Math) has emerged as a distinct field that leverages machine learning to navigate mathematical landscapes historically intractable for early symbolic systems. While mid-20th-century symbolic approaches successfully…
Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks'…
A common assumption about neural networks is that they can learn an appropriate internal representations on their own, see e.g. end-to-end learning. In this work we challenge this assumption. We consider two simple tasks and show that the…
Deep learning, a branch of artificial intelligence, is a data-driven method that uses multiple layers of interconnected units or neurons to learn intricate patterns and representations directly from raw input data. Empowered by this…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
A novel approach is presented for the solution of instantaneous chemical equilibrium problems. The chemical equilibrium can be considered, due to its intrinsically local character, as a mapping of the three-dimensional parameter space…
Artificial intelligence algorithms are capable of fantastic exploits, yet they are still grossly inefficient compared with the brain's ability to learn from few exemplars or solve problems that have not been explicitly defined. What is the…
The stunning empirical successes of neural networks currently lack rigorous theoretical explanation. What form would such an explanation take, in the face of existing complexity-theoretic lower bounds? A first step might be to show that…
Two neural-network-based numerical schemes are proposed to solve the classical obstacle problems. The schemes are based on the universal approximation property of neural networks, and the cost functions are taken as the energy minimization…
This study introduces an evaluation benchmark for middle school algebra to be used in artificial intelligence(AI) based educational platforms. The goal is to support the design of AI systems that can enhance learner conceptual understanding…
Algorithms have been fundamental to recent global technological advances and, in particular, they have been the cornerstone of technical advances in one field rapidly being applied to another. We argue that algorithms possess fundamentally…
This paper explores the implications of universities' rapid adoption of large language models (LLMs) for studying, teaching, and research by analyzing the logics underpinning their representation space. It argues that by uncritically…
The philosophy of mathematical practice (PMP) looks to evidence from working mathematics to help settle philosophical questions. One prominent program under the PMP banner is the study of explanation in mathematics, which aims to understand…