Efficient Convolutional Neural Networks Utilizing Fine-Grained Fast Fourier Transforms †

Abstract

Convolutional Neural Networks (CNNs) are among the most prevalent deep learning techniques employed across various domains. The computational complexity of CNNs is largely attributed to the convolution operations. These operations are computationally demanding and significantly impact overall model performance. Traditional CNN implementations convert convolutions into matrix operations via the im2col (image to column) technique, facilitating parallelization through advanced BLAS libraries. This study identifies and investigates a significant yet intricate pattern of data redundancy within the matrix-based representation of convolutions, a pattern that, while complex, presents opportunities for optimization. Through meticulous analysis of the redundancy inherent in the im2col approach, this paper introduces a mathematically succinct matrix representation for convolution, leading to the development of an optimized FFT-based convolution with finer FFT granularity. Benchmarking demonstrates that our approach achieves an average speedup of 14 times and a maximum speedup of 17 times compared to the regular FFT convolution. Similarly, it outperforms the Im2col+GEMM approach from NVIDIA’s cuDNN library, achieving an average speedup of three times and a maximum speedup of five times. Our FineGrained FFT convolution approach, when integrated into Caffe, a widely used deep learning framework, leads to significant performance gains. Evaluations using synthetic CNNs designed for real-world applications show an average speedup of 1.67 times. Furthermore, a modified VGG network variant achieves a speedup of 1.25 times.