# Dilated Convolution with Learnable Spacings: beyond bilinear interpolation

arXiv: https://arxiv.org/abs/2306.00817 · HTML: https://mlsanity.com/paper/2306.00817/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 16 of 16)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [InternImage: Exploring Large-Scale Vision Foundation Models with Deformable Convolutions](https://mlsanity.com/paper/2211.05778/) (2022)
- [Scaling Up Your Kernels to 31x31: Revisiting Large Kernel Design in CNNs](https://mlsanity.com/paper/2203.06717/) (2022)
- [MetaFormer Baselines for Vision](https://mlsanity.com/paper/2210.13452/) (2022)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes](https://mlsanity.com/paper/2110.08059/) (2021)
- [Structured Receptive Fields in CNNs](https://mlsanity.com/paper/1605.02971/) (2016)
- [Resolution learning in deep convolutional networks using scale-space theory](https://mlsanity.com/paper/2106.03412/) (2021)
- [Dilated convolution with learnable spacings](https://mlsanity.com/paper/2112.03740/) (2021)
- [Blurring the Line Between Structure and Learning to Optimize and Adapt Receptive Fields](https://mlsanity.com/paper/1904.11487/) (2019)
- [SMPConv: Self-moving Point Representations for Continuous Convolution](https://mlsanity.com/paper/2304.02330/) (2023)
- [Understanding Gaussian Attention Bias of Vision Transformers Using Effective Receptive Fields](https://mlsanity.com/paper/2305.04722/) (2023)
- [Gaussian Mixture Convolution Networks](https://mlsanity.com/paper/2202.09153/) (2022)

## Built on by (most cited first, 4 of 4)

- [Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings](https://mlsanity.com/paper/2306.17670/) (2023)
- [Audio classification with Dilated Convolution with Learnable Spacings](https://mlsanity.com/paper/2309.13972/) (2023)
- [Dilated Convolution with Learnable Spacings makes visual models more aligned with humans: a Grad-CAM study](https://mlsanity.com/paper/2408.03164/) (2024)
- [mGRADE: Minimal Recurrent Gating Meets Delay Convolutions for Lightweight Sequence Modeling](https://mlsanity.com/paper/2507.01829/) (2025)

## Abstract (arXiv)

Dilated Convolution with Learnable Spacings (DCLS) is a recently proposed variation of the dilated convolution in which the spacings between the non-zero elements in the kernel, or equivalently their positions, are learnable. Non-integer positions are handled via interpolation. Thanks to this trick, positions have well-defined gradients. The original DCLS used bilinear interpolation, and thus only considered the four nearest pixels. Yet here we show that longer range interpolations, and in particular a Gaussian interpolation, allow improving performance on ImageNet1k classification on two state-of-the-art convolutional architectures (ConvNeXt and Conv-Former), without increasing the number of parameters. The method code is based on PyTorch and is available at https://github.com/K-H-Ismail/Dilated-Convolution-with-Learnable-Spacings-PyTorch