An input-adaptive and in-place approach to dense tensor-times-matrix multiply

This paper describes a novel framework, called I
n
T
ens
L
i
("intensely"), for producing fast single-node implementations of dense tensor-times-matrix multiply (T
tm
) of arbitrary dimension. Whereas conventional implementations of T
tm
rely on explicitly converting the input tensor operand into a matrix---in order to be able to use any available and fast general matrix-matrix multiply (G
emm
) implementation---our framework's strategy is to carry out the T
tm

in-place
, avoiding this copy. As the resulting implementations expose tuning parameters, this paper also describes a heuristic empirical model for selecting an optimal configuration based on the T
tm
's inputs. When compared to widely used single-node T
tm
implementations that are available in the Tensor Toolbox and Cyclops Tensor Framework (C
tf
), In-TensLi's in-place and input-adaptive T
tm
implementations achieve 4× and 13× speedups, showing Gemm-like performance on a variety of input sizes.