SIRD: Symbolic Integration Rules Dataset

Vaibhav Sharma, abhinav nagpal, Muhammed Fatih Balin

Keywords: symbolic mathematics, integration, dataset, search

TL;DR: We propose a dataset for step by step symbolic integration of functions, and train an AI model to guide the search for the integral.

Abstract:

Advancements in neural networks and computer hardware lead to new use cases for deep learning in the natural sciences every day. Even though symbolic
mathematics tasks have been explored, symbolic integration only has a few studies using black box models and currently lacks explainability. Symbolic integration
is a challenging search problem and the final result is obtained by applying different integration rules at each step. We propose a novel and interpretable approach to perform symbolic integration using deep learning through integral rule prediction to speed up the search. We introduce the first-of-its-kind symbolic integration rules dataset comprising two million distinct functions and integration rule pairs. For complex rules
such as u-substitution and integration by parts, it also includes the expression needed for rule application.
We also train a transformer model on our proposed dataset and incorporate it into
SymPy's integral\_steps function to get guided\_integral\_steps, resulting in $6\times$ fewer branches explored by allowing our model to guide the depth-first-search procedure.

Submission Number: 39