A LUT-based matrix multiplication using neural networks

Matrix multiplication is a prime operation in linear algebra and scientific computations. In this paper, Artificial Neural Network-based matrix multiplication is introduced to create a completely new horizon in matrix multiplication technique, due to having non-linear, non-parametric characteristics of Neural Network. The time complexity of the proposed matrix multiplication algorithm based on neural networks is O(log n(n+n
²
+ n2/2 + log
₂
n)), whereas the time complexity of the best known matrix multiplication algorithm is O(n
³
/p), where n is the dimension of the matrix and p is the number of processing elements. Besides, Artificial Neural Network being the powerful data-driven, self-adaptive tool, it provides the resultant matrix multiplication with a high degree of accuracy. Through supervised learning, the neural network completes multiplication through addition operation instead of multiplication in solution prediction stage, which evidently reduces required number of Look-Up Table (LUT). The proposed design achieves an improvement of 43.88% and 50.17% over the best known existing approach in terms of number of LUTs and slices required, respectively.