Reduced-Complexity Algorithms for Tessarine Neural Networks.

Abstract

The brief presents the results of synthesizing efficient algorithms for implementing the basic data-processing macro operations used in tessarine-valued neural networks. These macro operations primarily include the macro operation of multiplication of two tessarines: the macro operation of calculating the inner product of two tessarine-valued vectors and the macro operation of multiple multiplications of one tessarine by the set of different tessarines. When synthesizing the discussed algorithms, we use the fact that tessarine multiplications can be interpreted as matrix-vector products. In each of these cases, the matrices have a specific block structure, which allows them to be efficiently factorized. This factorization provides a reduction in the multiplicative complexity of computing the product of two tessarines. In what follows, we use the optimized tessarine multiplication algorithm to synthesize reduced-complexity algorithms for the inner product of two tessarine-valued vectors as well as to compute multiple tessarine multiplication. Also, to further decrease the computational complexity of the inner product of two tessarine-valued vectors and multiple tessarine multiplication, we take into account that the selective sets of operations in the computations of all partial matrix-vector multiplications participating in these macro operations are the same. Accounting for this fact provides an additional reduction in computation complexity.