Our paper "Can Neural Networks Distinguish High-school Level Mathematical Concepts?" has been accepted at ICDM
12.09.2023In our paper "Can Neural Networks Distinguish High-school Level Mathematical Concepts?" we evaluate the ability of various neural networks to classify the relationship between two mathematical expressions. For example, two expressions can be equivalent or one could be a derivative of the other. We show that neural networks are able to learn the underlying mathematical patterns and outperform rule-based systems.
Abstract:
Processing symbolic mathematics algorithmically is an important field of research.
It has applications in computer algebra systems and supports researchers as well as applied mathematicians in their daily work.
Recently, exploring the ability of neural networks to grasp mathematical concepts has received special attention.
One particularly complex task for neural networks is to understand the relation of two mathematical expressions to each other.
Despite the advances in learning mathematical relationships, previous studies are limited by small-scale datasets, relatively simple formula construction by few axiomatic rules and even artifacts in the data.
With this work, we aim at overcoming these limitations and provide a deeper insight into the representation power of neural networks for classifying mathematical relations.
We introduce a novel data generation algorithm to allow for more complex formula compositions and fully include mathematical fields up to high-school level.
We research several tree-based and sequential neural architectures for classifying mathematical relations and conduct a systematic analysis of the models against rule-based as well as neural baselines with a focus on varying data set complexity, generalization abilities, and understanding of syntactical patterns.
Our findings highlight the effectiveness of tree-structured models for this task and show the potential of deep learning models to distinguish high-school level mathematical concepts.
