# Active Convolution: Learning the Shape of Convolution for Image Classification

arXiv: https://arxiv.org/abs/1703.09076 · HTML: https://mlsanity.com/paper/1703.09076/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2017.

## Built on by (most cited first, 24 of 24)

- [Deformable ProtoPNet: An Interpretable Image Classifier Using Deformable Prototypes](https://mlsanity.com/paper/2111.15000/) (2021)
- [Involution: Inverting the Inherence of Convolution for Visual Recognition](https://mlsanity.com/paper/2103.06255/) (2021)
- [LargeKernel3D: Scaling up Kernels in 3D Sparse CNNs](https://mlsanity.com/paper/2206.10555/) (2022)
- [PIT: Position-Invariant Transform for Cross-FoV Domain Adaptation](https://mlsanity.com/paper/2108.07142/) (2021)
- [SRWarp: Generalized Image Super-Resolution under Arbitrary Transformation](https://mlsanity.com/paper/2104.10325/) (2021)
- [Modelling Long Range Dependencies in ND: From Task-Specific to a General Purpose CNN](https://mlsanity.com/paper/2301.10540/) (2023)
- [FisheyeHDK: Hyperbolic Deformable Kernel Learning for Ultra-Wide Field-of-View Image Recognition](https://mlsanity.com/paper/2203.07255/) (2022)
- [Orientation and Context Entangled Network for Retinal Vessel Segmentation](https://mlsanity.com/paper/2207.11396/) (2022)
- [Deformation-Invariant Neural Network and Its Applications in Distorted Image Restoration and Analysis](https://mlsanity.com/paper/2310.02641/) (2023)
- [Convolutional Neural Networks with Gated Recurrent Connections](https://mlsanity.com/paper/2106.02859/) (2021)
- [Pooling Revisited: Your Receptive Field is Suboptimal](https://mlsanity.com/paper/2205.15254/) (2022)
- [Convolution kernel adaptation to calibrated fisheye](https://mlsanity.com/paper/2402.01456/) (2024)
- [Event-Driven Dynamic Scene Depth Completion](https://mlsanity.com/paper/2505.13279/) (2025)
- [Adapting CNNs for Fisheye Cameras without Retraining](https://mlsanity.com/paper/2404.08187/) (2024)
- [Metric Convolutions: A Unifying Theory to Adaptive Image Convolutions](https://mlsanity.com/paper/2406.05400/) (2024)
- [Integrating Large Circular Kernels into CNNs through Neural Architecture Search](https://mlsanity.com/paper/2107.02451/) (2021)
- [GMConv: Modulating Effective Receptive Fields for Convolutional Kernels](https://mlsanity.com/paper/2302.04544/) (2023)
- [Log-Polar Space Convolution for Convolutional Neural Networks](https://mlsanity.com/paper/2107.11943/) (2021)
- [Deformably-Scaled Transposed Convolution](https://mlsanity.com/paper/2210.09446/) (2022)
- [Space-Time Attention with Shifted Non-Local Search](https://mlsanity.com/paper/2309.16849/) (2023)
- [Quasi-Conformal Convolution : A Learnable Convolution for Deep Learning on Simply Connected Open Surfaces](https://mlsanity.com/paper/2502.01356/) (2025)
- [Active Learning Methods for Efficient Data Utilization and Model Performance Enhancement](https://mlsanity.com/paper/2504.16136/) (2025)
- [Intriguing Properties of Dynamic Sampling Networks](https://mlsanity.com/paper/2511.20800/) (2025)
- [Learning Task-Aware Sampling with Shared Saliency through Density-Equalizing Mappings](https://mlsanity.com/paper/2606.12869/) (2026)

## Abstract (arXiv)

In recent years, deep learning has achieved great success in many computer vision applications. Convolutional neural networks (CNNs) have lately emerged as a major approach to image classification. Most research on CNNs thus far has focused on developing architectures such as the Inception and residual networks. The convolution layer is the core of the CNN, but few studies have addressed the convolution unit itself. In this paper, we introduce a convolution unit called the active convolution unit (ACU). A new convolution has no fixed shape, because of which we can define any form of convolution. Its shape can be learned through backpropagation during training. Our proposed unit has a few advantages. First, the ACU is a generalization of convolution; it can define not only all conventional convolutions, but also convolutions with fractional pixel coordinates. We can freely change the shape of the convolution, which provides greater freedom to form CNN structures. Second, the shape of the convolution is learned while training and there is no need to tune it by hand. Third, the ACU can learn better than a conventional unit, where we obtained the improvement simply by changing the conventional convolution to an ACU. We tested our proposed method on plain and residual networks, and the results showed significant improvement using our method on various datasets and architectures in comparison with the baseline.