  Fast convolutions via transforms, either Winograd or FFT, had emerged as a
preferred way of performing the computation of convolutional layers, as it
greatly reduces the number of required operations. Recent work shows that, for
many layer structures, a well--designed implementation of fast convolutions can
greatly utilize modern CPUs, significantly reducing the compute time. However,
the generous amount of shared L3 cache present on modern CPUs is often
neglected, and the algorithms are optimized solely for the private L2 cache. In
this paper we propose an efficient `L3 Fusion` algorithm that is specifically
designed for CPUs with significant amount of shared L3 cache. Using the
hierarchical roofline model, we show that in many cases, especially for layers
with fewer channels, the `L3 fused` approach can greatly outperform standard 3
stage one provided by big vendors such as Intel. We validate our theoretical
findings, by benchmarking our `L3 fused` implementation against publicly
available state of the art.
