One-dimensional Path Convolution

Xuanshu Luo, Martin Werner
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:41391-41406, 2025.

Abstract

Two-dimensional (2D) convolutional kernels have dominated convolutional neural networks (CNNs) in image processing. While linearly scaling 1D convolution provides parameter efficiency, its naive integration into CNNs disrupts image locality, thereby degrading performance. This paper presents path convolution (PathConv), a novel CNN design exclusively with 1D operations, achieving ResNet-level accuracy using only 1/3 parameters. To obtain locality-preserving image traversal paths, we analyze Hilbert/Z-order paths and expose a fundamental trade-off: improved proximity for most pixels comes at the cost of excessive distances for other sacrificed ones to their neighbors. We resolve this issue by proposing path shifting, a succinct method to reposition sacrificed pixels. Using the randomized rounding algorithm, we show that three shifted paths are sufficient to offer better locality preservation than trivial raster scanning. To mitigate potential convergence issues caused by multiple paths, we design a lightweight path-aware channel attention mechanism to capture local intra-path and global inter-path dependencies. Experimental results further validate the efficacy of our method, establishing the proposed 1D PathConv as a viable backbone for efficient vision models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-luo25m, title = {One-dimensional Path Convolution}, author = {Luo, Xuanshu and Werner, Martin}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {41391--41406}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/luo25m/luo25m.pdf}, url = {https://proceedings.mlr.press/v267/luo25m.html}, abstract = {Two-dimensional (2D) convolutional kernels have dominated convolutional neural networks (CNNs) in image processing. While linearly scaling 1D convolution provides parameter efficiency, its naive integration into CNNs disrupts image locality, thereby degrading performance. This paper presents path convolution (PathConv), a novel CNN design exclusively with 1D operations, achieving ResNet-level accuracy using only 1/3 parameters. To obtain locality-preserving image traversal paths, we analyze Hilbert/Z-order paths and expose a fundamental trade-off: improved proximity for most pixels comes at the cost of excessive distances for other sacrificed ones to their neighbors. We resolve this issue by proposing path shifting, a succinct method to reposition sacrificed pixels. Using the randomized rounding algorithm, we show that three shifted paths are sufficient to offer better locality preservation than trivial raster scanning. To mitigate potential convergence issues caused by multiple paths, we design a lightweight path-aware channel attention mechanism to capture local intra-path and global inter-path dependencies. Experimental results further validate the efficacy of our method, establishing the proposed 1D PathConv as a viable backbone for efficient vision models.} }
Endnote
%0 Conference Paper %T One-dimensional Path Convolution %A Xuanshu Luo %A Martin Werner %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-luo25m %I PMLR %P 41391--41406 %U https://proceedings.mlr.press/v267/luo25m.html %V 267 %X Two-dimensional (2D) convolutional kernels have dominated convolutional neural networks (CNNs) in image processing. While linearly scaling 1D convolution provides parameter efficiency, its naive integration into CNNs disrupts image locality, thereby degrading performance. This paper presents path convolution (PathConv), a novel CNN design exclusively with 1D operations, achieving ResNet-level accuracy using only 1/3 parameters. To obtain locality-preserving image traversal paths, we analyze Hilbert/Z-order paths and expose a fundamental trade-off: improved proximity for most pixels comes at the cost of excessive distances for other sacrificed ones to their neighbors. We resolve this issue by proposing path shifting, a succinct method to reposition sacrificed pixels. Using the randomized rounding algorithm, we show that three shifted paths are sufficient to offer better locality preservation than trivial raster scanning. To mitigate potential convergence issues caused by multiple paths, we design a lightweight path-aware channel attention mechanism to capture local intra-path and global inter-path dependencies. Experimental results further validate the efficacy of our method, establishing the proposed 1D PathConv as a viable backbone for efficient vision models.
APA
Luo, X. & Werner, M.. (2025). One-dimensional Path Convolution. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:41391-41406 Available from https://proceedings.mlr.press/v267/luo25m.html.

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