Related papers: Mathematical intuition, deep learning, and Robbins…
Neuroscience research is undergoing a minor revolution. Recent advances in machine learning and artificial intelligence (AI) research have opened up new ways of thinking about neural computation. Many researchers are excited by the…
Since Artificial Intelligence (AI) software uses techniques like deep lookahead search and stochastic optimization of huge neural networks to fit mammoth datasets, it often results in complex behavior that is difficult for people to…
This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…
Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem…
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.…
Sound deductive reasoning -- the ability to derive new knowledge from existing facts and rules -- is an indisputably desirable aspect of general intelligence. Despite the major advances of AI systems in areas such as math and science,…
Continual learning is an emerging subject in machine learning that aims to solve multiple tasks presented sequentially to the learner without forgetting previously learned tasks. Recently, many deep learning based approaches have been…
AI for Mathematics (AI4Math) is not only intriguing intellectually but also crucial for AI-driven discovery in science, engineering, and beyond. Extensive efforts on AI4Math have mirrored techniques in NLP, in particular, training large…
I review the works of G\"ardenfors (1990) and Scorzato (2013) and show that their combination provides an elegant solution of Goodman's new riddle of induction. The solution is based on two main ideas: (1) clarifying what is expected from a…
The problem of replicating the flexibility of human common-sense reasoning has captured the imagination of computer scientists since the early days of Alan Turing's foundational work on computation and the philosophy of artificial…
Mathematical modelling (MM) is a key competency for solving complex real-world problems, yet many students struggle with abstraction, representation, and iterative reasoning. Artificial intelligence (AI) has been proposed as a support for…
Artificial Intelligence (AI) is a discipline of computer science that deals with machine intelligence. It is essential to bring AI into the context of learning because it helps in analysing the enormous amounts of data that is collected…
Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…
Solutions relying on artificial intelligence are devised to predict data patterns and answer questions that are clearly defined, involve an enumerable set of solutions, clear rules, and inherently binary decision mechanisms. Yet, as they…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
Artificial Intelligence is a field that lives many lives, and the term has come to encompass a motley collection of scientific and commercial endeavours. In this paper, I articulate the contours of a rather neglected but central scientific…
Deep learning based on artificial neural networks is a powerful machine learning method that, in the last few years, has been successfully used to realize tasks, e.g., image classification, speech recognition, translation of languages,…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The purpose of this paper is to report on the most recent developments in our ongoing investigation of the representation and manipulation of uncertainty in automated reasoning systems. In our earlier studies (Tong and Shapiro, 1985) we…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…