%0 Generic %1 blalock2021multiplying %A Blalock, Davis %A Guttag, John %D 2021 %K 2021 matrix %T Multiplying Matrices Without Multiplying %U http://arxiv.org/abs/2106.10860 %X 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 $100\times$ 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 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.

@misc{blalock2021multiplying, abstract = {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 $100\times$ 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 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.}, added-at = {2021-09-04T13:47:43.000+0200}, author = {Blalock, Davis and Guttag, John}, biburl = {https://www.bibsonomy.org/bibtex/26c4b52435a2abfca7769233390a58be6/analyst}, description = {[2106.10860] Multiplying Matrices Without Multiplying}, interhash = {94ed2cd5ff9821fa265cfdedeb31fb47}, intrahash = {6c4b52435a2abfca7769233390a58be6}, keywords = {2021 matrix}, note = {cite arxiv:2106.10860Comment: To appear at ICML 2021}, timestamp = {2021-09-04T13:47:43.000+0200}, title = {Multiplying Matrices Without Multiplying}, url = {http://arxiv.org/abs/2106.10860}, year = 2021 }