  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.
