ArConv Layers: Efficient 2D Feature Extraction

Updated 12 October 2025

ArConv layers are a novel CNN component that decomposes 2D convolutions into sequential 1D passes with intermediate transpositions to capture spatial features efficiently.
They reduce parameter count from K² to 2K (or K when shared), achieving over 66% parameter savings compared to standard 2D convolutions, ideal for resource-constrained devices.
In retinal disease detection, ArConvNet demonstrated superior accuracy (0.9328) with only ~1.3 million parameters, highlighting its practical benefits in medical imaging.

ArConv layers are a novel architectural component for convolutional neural networks that achieve two-dimensional (2D) feature extraction by reusing one-dimensional (1D) convolutional kernels in a sequential and transpositional fashion. This design allows for significant parameter reduction compared to standard 2D convolutional layers, with the specific goal of improving model accessibility, reducing computational and memory footprint, and enhancing deployment feasibility for resource-constrained environments, such as mobile devices. The ArConv approach was introduced in the context of retinal disease detection, where the resulting ArConvNet exhibited superior accuracy and parameter efficiency compared to widely-used lightweight models (Kasani et al., 5 Oct 2025).

1. Structural Design and Computational Scheme

The core design of an ArConv layer is based on the decomposition of a 2D convolution into two separate 1D convolutional passes, interleaved with matrix transposition. The process can be described as follows:

Row-wise 1D Depthwise Convolution: For an input tensor $X \in \mathbb{R}^{H \times W \times C}$ , a 1D convolution kernel $k \in \mathbb{R}^{K}$ operates along the width (columns) for each channel $c$ , yielding

$Y(i, j, c) = \sum_{p=1}^{K} k[p] \cdot X(i, j+p, c)\ .$

Spatial Transposition: The intermediate output $Y$ is transposed along the spatial axes, swapping rows and columns to obtain $Y^\top$ .
Column-wise 1D Depthwise Convolution: The same 1D kernel $k$ is applied again (on the now row-wise dimension, which corresponds to the original columns),

$Z(i, j, c) = \sum_{p=1}^{K} k[p] \cdot Y^\top(i, j+p, c)\ .$

Transpose to Original Orientation: The result $Z$ is transposed back to recover the original spatial correspondence.

Formally, for each channel, the entire ArConv operation is succinctly

$\text{Output} = ( (X * k_1)^\top * k_2 )^\top$

where $k_1$ and $k_2$ may be shared or separately parameterized 1D kernels.

2. Parameter and Memory Efficiency

By substituting a $K \times K$ spatial kernel (standard in 2D convolution, requiring $K^2$ parameters per channel) with a pair of 1D kernels of length $K$ reused across two axes, the parameter count per filter is reduced from $K^2$ to $2K$, or $K$ if the kernel is shared. The reported reduction in total parameter count exceeds 66% compared to conventional 2D convolutional layers. This directly leads to a smaller model file size and reduced memory requirements at inference time.

Such reduction has several practical advantages:

Lower memory footprint enables deployment on edge devices and smartphones.
Reduced parameterization mitigates the risk of overfitting, especially critical for applications with limited training data.
Smaller models are more amenable to rapid prototyping and transfer learning.

3. Feature Extraction Dynamics

The sequential application and reuse of the 1D kernel enable the ArConv layer to extract spatial dependencies from both axes iteratively. The process is not merely separable convolution, as the two-step sequence with intervening transpositions ensures that feature information propagates along orthogonal directions, capturing structured spatial relationships.

Experimental analysis in the cited paper shows that the behavior of an ArConv layer is better approximated by another ArConv layer than by a traditional 2D convolution, indicating that this architecture supports nuanced and efficient representation of image features, especially those relevant in medical imaging where spatial patterns may have complex alignments.

4. Empirical Results in Retinal Disease Detection

In the context of the RfMiD dataset for retinal disease diagnosis, models constructed using ArConv layers (e.g., ArConvNet) show quantitative and qualitative benefits:

With only $\sim$ 1.3 million parameters, ArConvNet achieved an accuracy of 0.9328 on the RfMiD test set.
By contrast, MobileNetV2 (utilizing standard depthwise separable 2D convolutions) used $\sim$ 2.2 million parameters and achieved an accuracy of 0.9266 under identical training and evaluation protocols.

This improvement demonstrates a tighter trade-off between parameter efficiency and predictive performance for ArConv layers.

Model	Parameter Count	RfMiD Accuracy
ArConvNet	1,319,488	0.9328
MobileNetV2	2,260,544	0.9266

The neural network with ArConv layers thus matches or surpasses performance of widely adopted lightweight models while achieving substantial parameter savings.

5. Computational Characteristics and Deployment

While ArConv achieves substantial reductions in parameter and model size, the sequential nature of the two-step operation introduces a slight increase in per-inference time relative to a single 2D convolution (0.51 seconds per batch for ArConv versus 0.30 seconds for a conventional 2D convolution, as reported for the same task and hardware). However, the trade-off is favorable for memory-constrained or mobile platforms, as the time overhead is minimal and far outweighed by the savings in both parameters and memory access requirements.

The lightweight footprint and independence from hardware-specific convolution accelerators further facilitate deployment in mobile medical screening applications.

ArConv layers differ fundamentally from conventional separable convolutions (which perform 1D convolutions along each axis independently and sum the results) by their reusing and sequential application of a single 1D kernel, combined with an explicit transposition between operations. This approach does not correspond exactly to a separable 2D filter, and experimental evidence suggests distinctive feature extraction dynamics.

No evidence in the data suggests that ArConv, as introduced in (Kasani et al., 5 Oct 2025), uses adaptive sampling, analytic kernels, or attention-based adaptivity (as seen, for example, in "Adaptive Rectangular Convolution" (Wang et al., 1 Mar 2025) or the analytic kernel strategies of (Cui et al., 3 Jul 2024)).

7. Applicability and Future Directions

The principal application domain addressed is medical image analysis via retinal disease detection, but the parameter reduction and extraction dynamics of ArConv layers suggest broader relevance for tasks where:

Model weight size is the limiting factor
Spatial patterns are crucial and might vary in orientation or continuity
Overfitting is a concern due to limited data

Further exploration may include hybridization with attention mechanisms, integration into architectures for broader image understanding tasks, or adaptation for non-image sequential data.

In conclusion, ArConv layers provide a principled, efficient, and effective alternative to standard 2D convolutions, optimizing parameter usage and facilitating high-performance medical image analysis in resource-constrained environments (Kasani et al., 5 Oct 2025).