Multiplying Matrices Without Multiplying
Abstract
Multiplying matrices is among the most fundamental and computeintensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learningbased algorithm for this task that greatly outperforms existing methods. Experiments using hundreds of matrices from diverse domains show that it often runs $100\times$ faster than exact matrix products and $10\times$ 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 multiplyadds. 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 arXiv:
 arXiv:2106.10860
 Bibcode:
 2021arXiv210610860B
 Keywords:

 Computer Science  Machine Learning;
 Computer Science  Hardware Architecture;
 Computer Science  Performance;
 Statistics  Machine Learning
 EPrint:
 To appear at ICML 2021