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Phasor-Driven Acceleration for FFT-based CNNs

Eduardo Reis, Thangarajah Akilan, Mohammed Khalid

TL;DR

This work tackles the computational bottleneck of FFT-based CNNs by replacing the conventional rectangular complex multiplication in the spectral domain with a phasor (polar) representation. The phasor approach reduces spectral-domain operations to a single real multiplication and a single real addition per element, while leveraging Real FFT for real-valued inputs. The authors implement the method in PyTorch with an OverrideConv2d mechanism and evaluate across six architectures on CIFAR-10 and CIFAR-100, reporting speedups up to about 1.376x during training and 1.390x during inference on CIFAR-10, with similar gains on CIFAR-100 and maintained accuracy. The method is modular and platform-agnostic, suggesting practical impact for accelerating FFT-based CNNs in both research and edge deployments, and it can be combined with other FFT-optimization techniques in future work.

Abstract

Recent research in deep learning (DL) has investigated the use of the Fast Fourier Transform (FFT) to accelerate the computations involved in Convolutional Neural Networks (CNNs) by replacing spatial convolution with element-wise multiplications on the spectral domain. These approaches mainly rely on the FFT to reduce the number of operations, which can be further decreased by adopting the Real-Valued FFT. In this paper, we propose using the phasor form, a polar representation of complex numbers, as a more efficient alternative to the traditional approach. The experimental results, evaluated on the CIFAR-10, demonstrate that our method achieves superior speed improvements of up to a factor of 1.376 (average of 1.316) during training and up to 1.390 (average of 1.321) during inference when compared to the traditional rectangular form employed in modern CNN architectures. Similarly, when evaluated on the CIFAR-100, our method achieves superior speed improvements of up to a factor of 1.375 (average of 1.299) during training and up to 1.387 (average of 1.300) during inference. Most importantly, given the modular aspect of our approach, the proposed method can be applied to any existing convolution-based DL model without design changes.

Phasor-Driven Acceleration for FFT-based CNNs

TL;DR

This work tackles the computational bottleneck of FFT-based CNNs by replacing the conventional rectangular complex multiplication in the spectral domain with a phasor (polar) representation. The phasor approach reduces spectral-domain operations to a single real multiplication and a single real addition per element, while leveraging Real FFT for real-valued inputs. The authors implement the method in PyTorch with an OverrideConv2d mechanism and evaluate across six architectures on CIFAR-10 and CIFAR-100, reporting speedups up to about 1.376x during training and 1.390x during inference on CIFAR-10, with similar gains on CIFAR-100 and maintained accuracy. The method is modular and platform-agnostic, suggesting practical impact for accelerating FFT-based CNNs in both research and edge deployments, and it can be combined with other FFT-optimization techniques in future work.

Abstract

Recent research in deep learning (DL) has investigated the use of the Fast Fourier Transform (FFT) to accelerate the computations involved in Convolutional Neural Networks (CNNs) by replacing spatial convolution with element-wise multiplications on the spectral domain. These approaches mainly rely on the FFT to reduce the number of operations, which can be further decreased by adopting the Real-Valued FFT. In this paper, we propose using the phasor form, a polar representation of complex numbers, as a more efficient alternative to the traditional approach. The experimental results, evaluated on the CIFAR-10, demonstrate that our method achieves superior speed improvements of up to a factor of 1.376 (average of 1.316) during training and up to 1.390 (average of 1.321) during inference when compared to the traditional rectangular form employed in modern CNN architectures. Similarly, when evaluated on the CIFAR-100, our method achieves superior speed improvements of up to a factor of 1.375 (average of 1.299) during training and up to 1.387 (average of 1.300) during inference. Most importantly, given the modular aspect of our approach, the proposed method can be applied to any existing convolution-based DL model without design changes.
Paper Structure (16 sections, 13 equations, 3 figures, 4 tables, 2 algorithms)

This paper contains 16 sections, 13 equations, 3 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Fourier Transform
  5. Complex Representation
  6. Spectral Domain Product
  7. Experimental Analysis
  8. Environment Configuration
  9. Baseline
  10. Implementation Details
  11. Problem Domain, Dataset, and DCNN Architectures
  12. Batch Execution Speedup
  13. Transfer Learning (TL) Speedup
  14. Additional Resources
  15. Discussion
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Overview of the proposed method using phasor product to reduce the number of operations between $X_{\mathcal{F}}$ and $W_{\mathcal{F}}$.
  • Figure 2: Training loss comparison of the proposed model w.r.t. the baseline, based on Mathieu2014, for six different networks on CIFAR-10.
  • Figure 3: Training loss comparison of the proposed model w.r.t. the baseline, based on Mathieu2014, for six different networks on CIFAR-100.