We introduce a new method for discovering matrix multiplication schemes based on random walks in a certain graph, which we call the flip graph. Using this method, we were able to reduce the number of multiplications for the matrix formats (4, 4, 5) and (5, 5, 5), both in characteristic two and for arbitrary ground fields.

翻译：我们引入了一种新的方法来发现基于在某个图表中随机行走的矩阵乘法。 我们称之为翻转图。 使用这种方法,我们减少了矩阵格式(4、4、5)和(5、5、5)的乘法数量,包括特性二和任意地面的乘法数量。