Nowadays, convolutional neural networks are among the most widely used types of deep learning networks thanks to their usefulness in many application domains. There are many efforts to find methods to increase their training and inference performance and efficiency. One of the most widely used technique to implement convolution consists of flattening tensors into 2D matrices and carrying out the operation through a matrix-matrix multiplication routine, which has highly optimized implementations in high-performance libraries. However, this kind of approach uses extra time and memory to transform and store the tensors involved. For this reason, direct convolution is becoming increasingly popular. Direct convolution can be implemented as a series of nested loops iterating over tensor dimensions and it does not require extra memory. In this work, we evaluate on various multi-core CPUs the performance and scalability effects deriving from different parallelization strategies, loop organizations, and SIMD-vectorization approaches with different compilers in relation with architectural aspects. We discuss each parameter thoroughly and distill our findings in a set of heuristics that can be used to quickly achieve a high-performance implementation in accordance to the underlying hardware and the characteristics of the convolutional layer at hand. By adopting a per-layer approach, we increase performance up to 60-70% compared to a static implementation for all the layers. Moreover, our results are comparable, or even better (up to $1.67\times $ speedup) than matrix-matrix multiplication-based convolution in a multi-core system.
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