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Neural Networks for Mathematical Reasoning – Evaluations, Capabilities, and Techniques
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Neural Networks for Mathematical Reasoning – Evaluations, Capabilities, and Techniques
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Dissertation
Neural Networks for Mathematical Reasoning – Evaluations, Capabilities, and Techniques
2024
Overview
This thesis investigates the potential of neural networks as a powerful approach to reasoning. It argues that neural networks can effectively leverage statistical structures to learn useful heuristics and model arbitrary action distributions, making them well-suited for reasoning tasks. To test this claim, the thesis focuses on mathematical reasoning as a well-defined domain with broad applications. The author sets up various benchmarks to define the problem and measure progress in this emerging field. Through extensive experimentation, the thesis demonstrates that neural networks can perform non-trivial mathematical reasoning tasks in both abduction and induction. Additionally, the author shows that various techniques, such as improved inductive bias design, high-level proof sketching, and self-supervised learning, can enhance neural networks' mathematical reasoning capabilities. Overall, this thesis provides compelling evidence that neural networks are a promising tool for mathematical reasoning, with the potential to surpass existing methods in the field.
Publisher
ProQuest Dissertations & Theses
ISBN
9798382192932
