论文标题
有效的矩阵乘法：稀疏2分解功率
Efficient Matrix Multiplication: The Sparse Power-of-2 Factorization
论文作者
论文摘要
我们提出了一种算法，以减少给定矩阵与未知列向量的乘法的计算工作。该算法将给定的矩阵分解为矩阵的产物，其条目是使用稀疏恢复原理的两个矩阵的矩阵或两个整数幂。尽管经典低分辨率量化的准确性每位6 dB，但我们的方法比大型矩阵可以取得的成就多倍。数值证据表明，随着基质大小，改进实际上是无限的。由于稀疏性，该算法甚至允许每个矩阵输入1位的量化水平，同时实现高度准确的大矩阵近似值。应用程序包括但不限于神经网络，以及用于大规模MIMO和毫米波应用的完全数字梁形成。
We present an algorithm to reduce the computational effort for the multiplication of a given matrix with an unknown column vector. The algorithm decomposes the given matrix into a product of matrices whose entries are either zero or integer powers of two utilizing the principles of sparse recovery. While classical low resolution quantization achieves an accuracy of 6 dB per bit, our method can achieve many times more than that for large matrices. Numerical evidence suggests that the improvement actually grows unboundedly with matrix size. Due to sparsity, the algorithm even allows for quantization levels below 1 bit per matrix entry while achieving highly accurate approximations for large matrices. Applications include, but are not limited to, neural networks, as well as fully digital beam-forming for massive MIMO and millimeter wave applications.
