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One-dimensional Path Convolution
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Proposes PathConv, a pure 1D-operator CNN that traverses images along shifted Hilbert/Z-order paths (three paths) with path-aware channel attention, reaching ResNet-level accuracy with about 1/3 the parameters on CIFAR-10, SVHN and ImageNet-64.
Problem
Flattening 2D images into 1D pixel streams for 1D-only CNNs disrupts spatial locality, and standard Hilbert/Z-order traversal paths trade off locality between pixels, degrading accuracy relative to 2D CNNs.
Approach
Path shifting samples shifted Hilbert/Z-order paths from spatially expanded variants so that every pixel is closer to its neighbors than in raster scan in at least one of three paths (set cover via randomized rounding); a path-aware channel attention module (intra-path and inter-path) then handles multiple parallel paths within a 1D-only CNN.
Key results
- PathConvB-HC*s reaches 93.97% on CIFAR-10 with 7.82M params vs ResNet-50 at 93.95% with 25.55M params.
- PathConvS-HC*s reaches 62.26% on ImageNet-64 with 3.76M params (4.58G FLOPs), vs ResNet-18 at 63.43% with 11.68M params, and above WRN-40-2 at 61.23%.
- Using raster scan paths instead of shifted Hilbert/Z-order paths drops PathConvB accuracy by about 3.9% on CIFAR-10 and 8.0% on ImageNet-64 relative to ResNet.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace raster scanning with three shifted Hilbert paths | PathConvS · CIFAR-10 | top-1 accuracy: 89.56% -> 92.45% | Helped |
| Replace raster scanning with three shifted Z-order paths | PathConvB · ImageNet-64 | top-1 accuracy: 60.40% -> 68.83% | Helped |
| Use six shifted Hilbert paths instead of the default three (ablation) | PathConvB · ImageNet-64 | top-1 accuracy: 68.46% -> 62.23% | Hurt |
| Use one unshifted Hilbert path instead of three shifted paths (ablation) | PathConvB · ImageNet-64 | top-1 accuracy: 68.46% -> 60.53% | Hurt |
| Use six shifted Z-order paths instead of the default three (ablation) | PathConvB · ImageNet-64 | top-1 accuracy: 68.83% -> 63.07% | Hurt |
| Use one unshifted Z-order path instead of three shifted paths (ablation) | PathConvB · ImageNet-64 | top-1 accuracy: 68.83% -> 60.01% | Hurt |
| Add PACA (ablation) | PathConvB-HC* · CIFAR-10 | top-1 accuracy: 90.13% -> 93.97% | Helped |
| Add positional encoding (ablation) | PathConvB-HC* · CIFAR-10 | top-1 accuracy: 92.34% -> 93.97% | Helped |
| Add PACA (ablation) | PathConvB-HC* · SVHN | top-1 accuracy: 94.20% -> 97.12% | Helped |
| Add positional encoding (ablation) | PathConvB-HC* · SVHN | top-1 accuracy: 95.91% -> 97.12% | Helped |
| Add PACA (ablation) | PathConvB-HC* · ImageNet-64 | top-1 accuracy: 60.93% -> 68.46% | Helped |
| Add positional encoding (ablation) | PathConvB-HC* · ImageNet-64 | top-1 accuracy: 63.85% -> 68.46% | Helped |
Surprising findings
- Using a single unshifted path (P=1) gave slightly better CIFAR-10 accuracy than the three-path configuration, suggesting fewer paths converge better on small datasets.
Limitations
- Evaluated only on low-resolution datasets (32x32 and 64x64), not larger-resolution images.
- Path traversal requires traversing the image once per path, adding overhead, and the NP set cover configuration search is approximate.
- Performance drops with more paths (P=6) on large datasets and PACA is needed to mitigate convergence issues.
Experimental setup
Datasets: CIFAR-10 SVHN ImageNet-64
Benchmarks: CIFAR-10 SVHN ImageNet-64
Metrics: top-1 accuracy parameter count FLOPs locality measurements (total distance, Psd)
Baselines: ResNet-18 ResNet-50 WRN-40-2 WRN-40-5 PathConv with raster scan paths
Builds on: ResNet ConvNeXt efficient channel attention randomized rounding MobileNetV2 inverted bottleneck
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