Fast convolution algorithms, including Winograd and FFT, can efficiently accelerate convolution operations in deep models. However, these algorithms depend on high-precision arithmetic to maintain inference accuracy, which conflicts with the model quantization. To resolve this conflict and further improve the efficiency of quantized convolution, we proposes SFC, a new algebra transform for fast convolution by extending the Discrete Fourier Transform (DFT) with symbolic computing, in which only additions are required to perform the transformation at specific transform points, avoiding the calculation of irrational number and reducing the requirement for precision. Additionally, we enhance convolution efficiency by introducing correction terms to convert invalid circular convolution outputs of the Fourier method into effective ones. The numerical error analysis is presented for the first time in this type of work and proves that our algorithms can provide a 3.68x multiplication reduction for 3x3 convolution, while the Winograd algorithm only achieves a 2.25x reduction with similarly low numerical errors. Experiments carried out on benchmarks and FPGA show that our new algorithms can further improve the computation efficiency of quantized models while maintaining accuracy, surpassing both the quantization-alone method and existing works on fast convolution quantization.

通过采用符号计算扩展离散傅里叶变换(DFT)的SFC，只需要在特定转换点执行加法运算，从而避免了计算无理数并降低了对精度的要求，同时通过引入修正项将傅里叶方法的无效循环卷积输出转换为有效输出，首次提出了数值误差分析，证明了我们算法在三维卷积上可以实现3.68倍的乘法减少，而Winograd算法只能达到2.25倍减少，同时在基准和FPGA实验中表明我们的新算法可以进一步提高量子化模型的计算效率并保持准确性，超过了仅量子化方法和现有的快速卷积量化研究。

SFC：在低精度算术下实现准确快速卷积