SFC: Achieve Accurate Fast Convolution under Low-precision Arithmetic

Liulu He, Yufei Zhao, Rui Gao, Yuan Du, Li Du
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:18081-18093, 2024.

Abstract

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 3.68× multiplication reduction for 3×3 convolution, while the Winograd algorithm only achieves a 2.25× 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-he24m, title = {{SFC}: Achieve Accurate Fast Convolution under Low-precision Arithmetic}, author = {He, Liulu and Zhao, Yufei and Gao, Rui and Du, Yuan and Du, Li}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {18081--18093}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/he24m/he24m.pdf}, url = {https://proceedings.mlr.press/v235/he24m.html}, abstract = {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 3.68× multiplication reduction for 3×3 convolution, while the Winograd algorithm only achieves a 2.25× 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.} }
Endnote
%0 Conference Paper %T SFC: Achieve Accurate Fast Convolution under Low-precision Arithmetic %A Liulu He %A Yufei Zhao %A Rui Gao %A Yuan Du %A Li Du %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-he24m %I PMLR %P 18081--18093 %U https://proceedings.mlr.press/v235/he24m.html %V 235 %X 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 3.68× multiplication reduction for 3×3 convolution, while the Winograd algorithm only achieves a 2.25× 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.
APA
He, L., Zhao, Y., Gao, R., Du, Y. & Du, L.. (2024). SFC: Achieve Accurate Fast Convolution under Low-precision Arithmetic. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:18081-18093 Available from https://proceedings.mlr.press/v235/he24m.html.

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