Binomial and toric ideal data for learning a performance metric of Buchberger's algorithm

This data set consists of randomly generated binomial and toric ideals. It was used for predicting a certain complexity measure of Buchberger's algorithm for toric and binomial ideals in small number of variables. See also the corresponding code on GitHub and the Involve journal paper available on arXiv, which explains in detail the models used to generate the data. 

From the article:

What can be (machine) learned about the performance of Buchberger's algorithm?

Given a system of polynomials, Buchberger's algorithm computes a Gr\"obner basis of the ideal these polynomials generate using an iterative procedure based on multivariate long division. The runtime of each step of the algorithm is typically dominated by a series of polynomial additions, and the total number of these additions is a hardware-independent performance metric that is often used to evaluate and optimize various implementation choices. In this work we attempt to predict, using just the starting input, the number of polynomial additions that take place during one run of Buchberger's algorithm. Good predictions are useful for quickly estimating difficulty and understanding what features make a Gr\"obner basis computation hard. Our features and methods could also be used for value models in the reinforcement learning approach to optimize Buchberger's algorithm introduced in the second author's thesis. 

We show that a multiple linear regression model built from a set of easy-to-compute ideal generator statistics can predict the number of polynomial additions somewhat well, better than an uninformed model, and better than regression models built on some intuitive commutative algebra invariants that are more difficult to compute. We also train a simple recursive neural network that outperforms these linear models. Our work serves as a proof of concept, demonstrating that predicting the number of polynomial additions in Buchberger's algorithm is a feasible problem from the point of view of machine learning.