# Modelling Long Range Dependencies in ND: From Task-Specific to a General Purpose CNN

arXiv: https://arxiv.org/abs/2301.10540 · HTML: https://mlsanity.com/paper/2301.10540/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 65 references that are in the map.
- First posted on arXiv 25 Jan 2023.

## Builds on (most cited first, 30 of 48)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [A ConvNet for the 2020s](https://mlsanity.com/paper/2201.03545/) (2022)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Perceiver: General Perception with Iterative Attention](https://mlsanity.com/paper/2103.03206/) (2021)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Long Range Arena: A Benchmark for Efficient Transformers](https://mlsanity.com/paper/2011.04006/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Harmonic Networks: Deep Translation and Rotation Equivariance](https://mlsanity.com/paper/1612.04642/) (2016)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)

## Built on by (most cited first, 18 of 18)

- [Facing Off World Model Backbones: RNNs, Transformers, and S4](https://mlsanity.com/paper/2307.02064/) (2023)
- [2-D SSM: A General Spatial Layer for Visual Transformers](https://mlsanity.com/paper/2306.06635/) (2023)
- [Slot State Space Models](https://mlsanity.com/paper/2406.12272/) (2024)
- [LoG-VMamba: Local-Global Vision Mamba for Medical Image Segmentation](https://mlsanity.com/paper/2408.14415/) (2024)
- [Orchid: Flexible and Data-Dependent Convolution for Sequence Modeling](https://mlsanity.com/paper/2402.18508/) (2024)
- [Multi-Dimensional Hyena for Spatial Inductive Bias](https://mlsanity.com/paper/2309.13600/) (2023)
- [CKGConv: General Graph Convolution with Continuous Kernels](https://mlsanity.com/paper/2404.13604/) (2024)
- [DNArch: Learning Convolutional Neural Architectures by Backpropagation](https://mlsanity.com/paper/2302.05400/) (2023)
- [Spectral Convolutional Conditional Neural Processes](https://mlsanity.com/paper/2404.13182/) (2024)
- [From Embeddings to Accuracy: Comparing Foundation Models for Radiographic Classification](https://mlsanity.com/paper/2505.10823/) (2025)
- [Continuous Convolutional Neural Networks for Disruption Prediction in Nuclear Fusion Plasmas](https://mlsanity.com/paper/2312.01286/) (2023)
- [FISBe: A real-world benchmark dataset for instance segmentation of long-range thin filamentous structures](https://mlsanity.com/paper/2404.00130/) (2024)
- [Reparameterized Multi-Resolution Convolutions for Long Sequence Modelling](https://mlsanity.com/paper/2408.09453/) (2024)
- [Learned Gridification for Efficient Point Cloud Processing](https://mlsanity.com/paper/2307.14354/) (2023)
- [Explainable Global Wildfire Prediction Models using Graph Neural Networks](https://mlsanity.com/paper/2402.07152/) (2024)
- [Scaling Continuous Kernels with Sparse Fourier Domain Learning](https://mlsanity.com/paper/2409.09875/) (2024)
- [Conditional Clifford-Steerable CNNs for PDE Modeling](https://mlsanity.com/paper/2510.14007/) (2025)
- [Revisiting Neural Processes via Fourier Transform and Volterra Series](https://mlsanity.com/paper/2606.01172/) (2026)

## Abstract (arXiv)

Performant Convolutional Neural Network (CNN) architectures must be tailored to specific tasks in order to consider the length, resolution, and dimensionality of the input data. In this work, we tackle the need for problem-specific CNN architectures. We present the Continuous Convolutional Neural Network (CCNN): a single CNN able to process data of arbitrary resolution, dimensionality and length without any structural changes. Its key component are its continuous convolutional kernels which model long-range dependencies at every layer, and thus remove the need of current CNN architectures for task-dependent downsampling and depths. We showcase the generality of our method by using the same architecture for tasks on sequential (1rm D), visual (2rm D) and point-cloud (3rm D) data. Our CCNN matches and often outperforms the current state-of-the-art across all tasks considered.