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SFC: Achieve Accurate Fast Convolution under Low-precision Arithmetic
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Proposes SFC, a Fourier-based fast convolution that uses symbolic DFT-4/6 transforms needing only additions plus correction terms for circular-to-linear conversion, enabling accurate int8/int6 quantized convolution.
Problem
Fast convolution algorithms (Winograd, FFT, NTT) lose accuracy under low-precision quantization because of ill-conditioned transforms or irrational coefficients, so combining them with quantization degrades model accuracy.
Approach
Extend the DFT via symbolic computation (representing irrational roots as first-order integer polynomials in s with s^2=s-1 for DFT-6) so the transforms need only additions, and add correction terms that recover valid linear-convolution outputs from the circular convolution outputs.
Key results
- SFC6(7x7,3x3) with int8 PTQ on ResNet18 reaches 69.59 top-1 (-0.17 vs fp32), versus -2.22 for channel-balanced Winograd F(4x4,3x3).
- SFC-6(6x6,3x3) reduces multiplications by 73% for 3x3 convolution, versus 2.25x (55.6%) reduction for Winograd F(2x2,3x3) per the abstract's claim of 3.68x vs 2.25x multiplication reduction.
- On FPGA, the SFC accelerator uses 1056 DSPs and reports 10.08 throughput metric versus 5.64 for Winograd and 3.48 for NTT in the synthesis table.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Wino(4×4, 3×3) quantized convolution with SFC6(7×7, 3×3) | ResNet18 · ImageNet validation int8 | Top-1 accuracy: 68.16 -> 69.59 | Helped |
| Replace Wino(4×4, 3×3) quantized convolution with SFC6(7×7, 3×3) | ResNet34 · ImageNet validation int6 | Top-1 accuracy: 68.80 -> 72.40 | Helped |
| Replace Wino(4×4, 3×3) quantized convolution with SFC6(7×7, 3×3) | ResNet50 · ImageNet validation int8 | Top-1 accuracy: 75.74 -> 76.02 | Helped |
| Use frequency-wise rather than tensor-wise activation quantization (ablation) | SFC-6(7×7, 3×3), ResNet18 · ImageNet int8 | Accuracy: 69.18 -> 69.54 | Helped |
| Use frequency-wise rather than tensor-wise activation quantization (ablation) | SFC(7×7, 3×3), ResNet18 · ImageNet int4 | Accuracy: 17.81 -> 31.10 | Helped |
| Use frequency-wise and channel-wise filter quantization rather than channel-wise filter quantization (ablation) | SFC(7×7, 3×3), ResNet18 with frequency-wise activation quantization · ImageNet int4 | Accuracy: 31.10 -> 55.82 | Helped |
| Use frequency-wise activation quantization with channel+frequency filter quantization rather than tensor activation and channel filter quantization (ablation) | Wino(4×4, 3×3), ResNet18 · ImageNet int8 | Accuracy: 57.40 -> 67.62 | Helped |
| Use frequency-wise activation and channel+frequency filter quantization rather than tensor activation and channel filter quantization (ablation) | SFC-6(7×7, 3×3), ResNet18 · ImageNet int8 | Accuracy: 69.18 -> 69.58 | Helped |
Surprising findings
- Winograd F(4x4,3x3) with int8 quantization needs frequency-wise quantization granularity to reach acceptable accuracy, whereas SFC maintains accuracy at int8 with simpler granularity.
Limitations
- Iterative convolution for large kernels only beats FFT with fewer than 3 iterations; large transform sizes introduce higher-order terms.
- Sub-int8 accuracy still degrades (int6 drops 0.96 points on ResNet18), and int4 needs frequency-wise quantization.
- Evaluation limited to image classification on ImageNet with CNN backbones.
Experimental setup
Datasets: ImageNet
Benchmarks: ImageNet
Metrics: top-1 accuracy bit-operations (BOPs) mean squared error arithmetic complexity condition number DSP count throughput
Baselines: Winograd F(4x4,3x3) Channel Balancing Full Quantization direct convolution AdaQuant
Builds on: Winograd minimal filtering Fast Fourier Transform AdaQuant Scaling Gradient Backward
Closest papers by meaning
- FlashFFTConv: Efficient Convolutions for Long Sequences with Tensor Cores (ICLR 2024 · similarity 0.86)
- FIMA-Q: Post-Training Quantization for Vision Transformers by Fisher Information Matrix Approximation (CVPR 2025 · similarity 0.83)
- GPLQ: A General, Practical, and Lightning QAT Method for Vision Transformers (NeurIPS 2025 · similarity 0.83)
- FrameQuant: Flexible Low-Bit Quantization for Transformers (ICML 2024 · similarity 0.82)
- Data-Free Group-Wise Fully Quantized Winograd Convolution via Learnable Scales (CVPR 2025 · similarity 0.82)
- The Quantization Benefits of Residual-Free Transformers (NeurIPS 2026 · similarity 0.82)
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