機械学習を用いたグレブナー基底の計算

抄録

The Transformer is a deep learning model employed in generative artificial intelligence, such as ChatGPT. In recent years, there have been several studies applying Transformers to mathematical calculations. This paper presents the findings of a study [6] on learning Gröbner bases. Gröbner basis is a specific type of set of polynomials that can be used to solve systems of equations. However, the computational cost of these methods is high, prompting a significant demand for faster algorithms. Machine learning is expected to facilitate the acceleration of Gröbner bases computations. To learn Gröbner bases, a large dataset must be prepared; yet, the standard method of generating Gröbner bases from non-Gröbner bases requires a significant amount of time. In the “backward” method outlined in [2], the generation of non-Gröbner bases from Gröbner bases has been demonstrated to effectively expedite dataset generation. Moreover, for specific categories of Gröbner bases, the models attained an accuracy rate exceeding 90%, indicating the potential efficacy of Transformers in the learning of Gröbner bases.