Error Analysis and Improving the Accuracy of Winograd Convolution for Deep Neural Networks
This work addresses a critical bottleneck in optimizing deep neural network performance for practitioners, but it is incremental as it builds on existing Winograd methods to improve accuracy rather than introducing a new paradigm.
The paper tackles the problem of reduced floating-point numerical accuracy in Winograd convolution algorithms for deep neural networks, which are widely used to speed up convolutions but at the cost of accuracy, and shows that proposed methods like canonical evaluation ordering and point selection can significantly reduce error, allowing for larger block sizes and reduced computation.
Popular deep neural networks (DNNs) spend the majority of their execution time computing convolutions. The Winograd family of algorithms can greatly reduce the number of arithmetic operations required and is present in many DNN software frameworks. However, the performance gain is at the expense of a reduction in floating point (FP) numerical accuracy. In this paper, we analyse the worst case FP error and prove the estimation of norm and conditioning of the algorithm. We show that the bound grows exponentially with the size of the convolution, but the error bound of the \textit{modified} algorithm is smaller than the original one. We propose several methods for reducing FP error. We propose a canonical evaluation ordering based on Huffman coding that reduces summation error. We study the selection of sampling "points" experimentally and find empirically good points for the most important sizes. We identify the main factors associated with good points. In addition, we explore other methods to reduce FP error, including mixed-precision convolution, and pairwise summation across DNN channels. Using our methods we can significantly reduce FP error for a given block size, which allows larger block sizes and reduced computation.