高效的矩阵乘法：稀疏2次幂分解
Efficient Matrix Multiplication: The Sparse Power-of-2 Factorization
摘要：
我们提出了一个算法，以减少计算工作量的一个给定的矩阵与一个未知的列向量的乘法。该算法利用稀疏恢复的原理，将给定的矩阵分解为元素为零或2的整数次幂的矩阵的乘积。虽然经典的低分辨率量化达到了6 dB每比特的精度，我们的方法可以实现许多倍以上的大矩阵。数值证据表明，改善实际上增长与矩阵的大小无界。由于稀疏性，该算法甚至允许每个矩阵条目的量化级别低于1位，同时实现对大矩阵的高度精确的近似。应用包括但不限于神经网络，以及用于大规模MIMO和毫米波应用的全数字波束形成。
英文摘要：
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.
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