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Winograd-based convolution has quickly gained traction as a preferredapproach to implement convolutional neural networks (ConvNet) on varioushardware platforms because it requires fewer floating point operations thanFFT-based or direct convolutions.  This paper compares three highly optimized implementations (regular FFT--,Gauss--FFT--, and Winograd--based convolutions) on modern multi-- andmany--core CPUs. Although all three implementations employed the sameoptimizations for modern CPUs, our experimental results with two popularConvNets (VGG and AlexNet) show that the FFT--based implementations generallyoutperform the Winograd--based approach, contrary to the popular belief.  To understand the results, we use a Roofline performance model to analyze thethree implementations in detail, by looking at each of their computation phasesand by considering not only the number of floating point operations, but alsothe memory bandwidth and the cache sizes. The performance analysis explainswhy, and under what conditions, the FFT--based implementations outperform theWinograd--based one, on modern CPUs.

FFT Convolutions are Faster than Winograd on Modern CPUs, Here is Why