  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.
