Related papers: Limits of an AI program for solving college math p…
Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we…
Deep learning relies on a very specific kind of neural networks: those superposing several neural layers. In the last few years, deep learning achieved major breakthroughs in many tasks such as image analysis, speech recognition, natural…
Artificial Neural Networks are computational network models inspired by signal processing in the brain. These models have dramatically improved the performance of many learning tasks, including speech and object recognition. However,…
This paper studies deep neural networks for solving extremely large linear systems arising from highdimensional problems. Because of the curse of dimensionality, it is expensive to store both the solution and right-hand side vector in such…
Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of…
Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies \emph{representational}…
The widespread availability of generative artificial intelligence tools poses new challenges for school mathematics education, particularly regarding the formative role of traditional mathematical tasks. In post-AI educational contexts,…
Artificial intelligence (AI) tools such as large language models (LLMs) are already altering student learning. Unlike previous technologies, LLMs can independently solve problems regardless of student understanding, yet are not always…
Advocates for Neuro-Symbolic Artificial Intelligence (NeSy) assert that combining deep learning with symbolic reasoning will lead to stronger AI than either paradigm on its own. As successful as deep learning has been, it is generally…
The ability to explain decisions made by AI systems is highly sought after, especially in domains where human lives are at stake such as medicine or autonomous vehicles. While it is often possible to approximate the input-output relations…
The lack of interpretability has hindered the large-scale adoption of AI technologies. However, the fundamental idea of interpretability, as well as how to put it into practice, remains unclear. We provide notions of interpretability based…
Artificial intelligence (AI) has demonstrated impressive progress in mathematical reasoning, yet its integration into the practice of mathematical research remains limited. In this study, we investigate how the AI Mathematician (AIM) system…
Math anxiety is a clinical pathology impairing cognitive processing in math-related contexts. Originally thought to affect only inexperienced, low-achieving students, recent investigations show how math anxiety is vastly diffused even among…
As demonstrated in many areas of real-life applications, neural networks have the capability of dealing with high dimensional data. In the fields of optimal control and dynamical systems, the same capability was studied and verified in many…
The mathematical capabilities of AI systems are complex and multifaceted. Most existing research has predominantly focused on the correctness of AI-generated solutions to mathematical problems. In this work, we argue that beyond producing…
This work attempts to explain the types of computation that neural networks can perform by relating them to automata. We first define what it means for a real-time network with bounded precision to accept a language. A measure of network…
Detecting assistance from artificial intelligence is increasingly important as they become ubiquitous across complex tasks such as text generation, medical diagnosis, and autonomous driving. Aid detection is challenging for humans,…
One of the most fundamental questions in Biology or Artificial Intelligence is how the human brain performs mathematical functions. How does a neural architecture that may organise itself mostly through statistics, know what to do? One…
Recent advancements in artificial intelligence have propelled the capabilities of Large Language Models, yet their ability to mimic nuanced human reasoning remains limited. This paper introduces a novel conceptual enhancement to LLMs,…
When AI systems interact with humans in the loop, they are often called on to provide explanations for their plans and behavior. Past work on plan explanations primarily involved the AI system explaining the correctness of its plan and the…