Multiplying Matrices Without Multiplying

• URL: http://arxiv.org/abs/2106.10860v1
• Date: Mon, 21 Jun 2021 05:08:54 GMT
• Title: Multiplying Matrices Without Multiplying
• Authors: Davis Blalock, John Guttag
• Abstract summary: Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. We introduce a learning-based algorithm for this task that greatly outperforms existing methods.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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