Multiplying Matrices Without Multiplying

Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm for this task that greatly outperforms existing methods. Experiments using hundreds of matrices from diverse domains show that it often runs 100× faster than exact matrix products and 10× faster than current approximate methods. In the common case that one matrix is known ahead of time, our method also has the interesting property that it requires zero multiply-adds. These results suggest that a mixture of hashing, averaging, and byte shuffling—–the core operations of our method—–could be a more promising building block for machine learning than the sparsified, factorized, and/or scalar quantized matrix products that have recently been the focus of substantial research and hardware investment. 2021: Davis W. Blalock, J. Guttag https://arxiv.org/pdf/2106.10860v1.pdf