  Winograd convolution is widely used in deep neural networks (DNNs). Existing
work for DNNs considers only the subset Winograd algorithms that are equivalent
to Toom-Cook convolution. We investigate a wider range of Winograd algorithms
for DNNs and show that these additional algorithms can significantly improve
floating point (FP) accuracy in many cases. We present results for three FP
formats: fp32, fp16 and bf16 (a truncated form of fp32) using 2000 inputs from
the ImageNet dataset. We found that in fp16 this approach gives us up to 6.5
times better image recognition accuracy in one important case while maintaining
the same number of elementwise multiplication operations in the innermost loop.
In bf16 the convolution can be computed using 5% fewer innermost loop
multiplications than with currently used Winograd algorithms while keeping the
accuracy of image recognition the same as for direct convolution method.
