Core Viewpoint - The article discusses a new algorithm called RXTX for matrix multiplication, which significantly improves efficiency in terms of energy and time consumption, with potential applications in data analysis, chip design, wireless communication, and large language model training [3][8]. Group 1: Algorithm Overview - RXTX is a new algorithm that combines machine learning search methods and combinatorial optimization techniques to enhance the efficiency of calculating the product of a matrix and its transpose [8]. - The algorithm's recursive relationship is defined as R(n) = 8R(n/4) + 26M(n/4), which contrasts with the previous state-of-the-art algorithm's relationship S(n) = 4S(n/2) + 2M(n/2) [16]. - RXTX achieves a reduction in the asymptotic multiplication constant to approximately 0.6341, which is about 5% lower than the previous algorithm's constant of approximately 0.6667 [17]. Group 2: Performance Analysis - Experimental data indicates that RXTX's multiplication count is 5% lower than the original algorithm when n is a power of 4, and this advantage persists as n increases [21]. - For matrices of size 6144×6144, RXTX's average runtime is 2.524 seconds, outperforming the default implementation of BLAS by 9% in 99% of tests [27]. - The total computational complexity of RXTX is lower than that of the original algorithm when n is greater than or equal to 256, and it shows significant superiority over naive algorithms when n is greater than or equal to 1024 [24]. Group 3: Methodology - The discovery of RXTX leverages a combination of machine learning and combinatorial optimization, inspired by the approach of AlphaTensor but with a focus on reducing computational complexity [28]. - The algorithm involves generating candidate rank-1 bilinear products through reinforcement learning, followed by mixed-integer linear programming (MILP) to enumerate and filter these candidates [31].