[2106.10860] Multiplying Matrices Without Multiplying

arxiv.org · 6,179 words · saved by 1 readers

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.

Multiplying Matrices Without Multiplying Davis Blalock 1 2 John Guttag 2 Abstract is minimizing the amount of compute time required to ap- proximate linear operations with a given level of fidelity. Multiplying matrices is among the most fundamental…

[2106.10860] Multiplying Matrices Without Multiplying

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