$XX^{t}$ Can Be Faster

TL;DR

The paper introduces RXTX, an efficient algorithm for computing matrix products with fewer operations, outperforming existing methods both asymptotically and for small matrices, by leveraging machine learning and combinatorial optimization.

Contribution

RXTX is a novel algorithm that reduces the number of operations for matrix transpose multiplication, combining machine learning search with combinatorial optimization.

Findings

RXTX uses 5% fewer multiplications than state-of-the-art algorithms.

The acceleration benefits are observed for both large and small matrices.

The algorithm was discovered through a hybrid machine learning and optimization approach.

Abstract

We present RXTX, a new algorithm for computing the product of matrix by its transpose $XX^{t}$ for $X\in \mathbb{R}^{n\times m}$. RXTX uses $5\%$ fewer multiplications and $5\%$ fewer operations (additions and multiplications) than State-of-the-Art algorithms. Note that the accelerations not only holds asymptotically for large matrices with $n \rightarrow \infty$, but also for small matrices including $n = 4$. The algorithm was discovered by combining Machine Learning-based search methods with Combinatorial Optimization.