针对大型矩阵奇异值分解(singular value decomposition,SVD)时使用经典算法时间复杂度较高,以及已有的量子SVD算法要求待分解的矩阵必须具有非稀疏低秩的性质,并且在计算过程中构造任意大小酉矩阵对目前的量子计算机来说实现起来并不容易等问题,提出基于QR迭代的量子SVD。QR迭代使用的是Householder变换,通过量子矩阵乘法运算完成经典矩阵乘法运算过程。实验结果表明,该方法能够得到所求矩阵的奇异值及奇异矩阵,使大型矩阵的SVD具有可行性。
Quantized training has been proven to be a prominent method to achieve deep neural network training under limited computational resources.It uses low bit-width arithmetics with a proper scaling factor to achieve negligible accuracy loss.Cambricon-Q is the ASIC design proposed to efficiently support quantized training,and achieves significant performance improvement.However,there are still two caveats in the design.First,Cambricon-Q with different hardware specifications may lead to different numerical errors,resulting in non-reproducible behaviors which may become a major concern in critical applications.Second,Cambricon-Q cannot leverage data sparsity,where considerable cycles could still be squeezed out.To address the caveats,the acceleration core of Cambricon-Q is redesigned to support fine-grained irregular data processing.The new design not only enables acceleration on sparse data,but also enables performing local dynamic quantization by contiguous value ranges(which is hardware independent),instead of contiguous addresses(which is dependent on hardware factors).Experimental results show that the accuracy loss of the method still keeps negligible,and the accelerator achieves 1.61×performance improvement over Cambricon-Q,with about 10%energy increase.
