Improving matrix-vector multiplication via lossless grammar-compressed matrices

As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming paramount importance. In this article we propose a new lossless compression scheme for real-valued matrices which achieves efficient performance in terms ratio time linear-algebra operations. Experiments show that, as compressor, our tool clearly superior gzip it usually within 20% xz ratio. addition, compressed format supports matrix-vector multiplications space proportional size representation, unlike that require full decompression matrix. To knowledge compressor first one achieving complexities match theoretical limit expressed by k -th order statistical entropy input. achieve further time/space reductions, column-reordering algorithms hinging on novel column-similarity score. Our experiments various sets ML column reordering can yield reduction up 16% peak memory usage during multiplication. Finally, compare proposal against state-of-the-art Compressed Linear Algebra (CLA) approach showing ours runs always at least twice faster (in multi-thread setting), better occupancy usage. This experimentally confirms provably effective bounds compressed-matrix approach.