# A guide to convolution arithmetic for deep learning

arXiv: https://arxiv.org/abs/1603.07285 · HTML: https://mlsanity.com/paper/1603.07285/

## Key facts

- Cited by 185 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2016.

## Built on by (most cited first, 30 of 185)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [SimVP: Simpler yet Better Video Prediction](https://mlsanity.com/paper/2206.05099/) (2022)
- [FeatUp: A Model-Agnostic Framework for Features at Any Resolution](https://mlsanity.com/paper/2403.10516/) (2024)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Exploiting Explanations for Model Inversion Attacks](https://mlsanity.com/paper/2104.12669/) (2021)
- [Fully Hyperbolic Convolutional Neural Networks for Computer Vision](https://mlsanity.com/paper/2303.15919/) (2023)
- [PastNet: Introducing Physical Inductive Biases for Spatio-temporal Video Prediction](https://mlsanity.com/paper/2305.11421/) (2023)
- [Machine Learning in Aerodynamic Shape Optimization](https://mlsanity.com/paper/2202.07141/) (2022)
- [Hierarchical Associative Memory](https://mlsanity.com/paper/2107.06446/) (2021)
- [Eformer: Edge Enhancement based Transformer for Medical Image Denoising](https://mlsanity.com/paper/2109.08044/) (2021)
- [Unsupervised Object Learning via Common Fate](https://mlsanity.com/paper/2110.06562/) (2021)
- [RiemannONets: Interpretable Neural Operators for Riemann Problems](https://mlsanity.com/paper/2401.08886/) (2024)
- [Real-world Video Deblurring: A Benchmark Dataset and An Efficient Recurrent Neural Network](https://mlsanity.com/paper/2106.16028/) (2021)
- [Generative Modeling of Turbulence](https://mlsanity.com/paper/2112.02548/) (2021)
- [A Comprehensive Overview and Comparative Analysis on Deep Learning Models: CNN, RNN, LSTM, GRU](https://mlsanity.com/paper/2305.17473/) (2023)
- [Rethinking materials simulations: Blending direct numerical simulations with neural operators](https://mlsanity.com/paper/2312.05410/) (2023)
- [LoftUp: Learning a Coordinate-Based Feature Upsampler for Vision Foundation Models](https://mlsanity.com/paper/2504.14032/) (2025)
- [Joint Progressive and Coarse-to-fine Registration of Brain MRI via Deformation Field Integration and Non-Rigid Feature Fusion](https://mlsanity.com/paper/2109.12384/) (2021)
- [A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling](https://mlsanity.com/paper/2110.03442/) (2021)
- [FeatEnHancer: Enhancing Hierarchical Features for Object Detection and Beyond Under Low-Light Vision](https://mlsanity.com/paper/2308.03594/) (2023)
- [KXNet: A Model-Driven Deep Neural Network for Blind Super-Resolution](https://mlsanity.com/paper/2209.10305/) (2022)
- [Unsupervised Structure-Texture Separation Network for Oracle Character Recognition](https://mlsanity.com/paper/2205.06549/) (2022)
- [Anti-aliasing Deep Image Classifiers using Novel Depth Adaptive Blurring and Activation Function](https://mlsanity.com/paper/2110.00899/) (2021)
- [Certified Zeroth-order Black-Box Defense with Robust UNet Denoiser](https://mlsanity.com/paper/2304.06430/) (2023)
- [Multigrid-Augmented Deep Learning Preconditioners for the Helmholtz Equation using Compact Implicit Layers](https://mlsanity.com/paper/2306.17486/) (2023)
- [Hierarchical Neural Operator Transformer with Learnable Frequency-aware Loss Prior for Arbitrary-scale Super-resolution](https://mlsanity.com/paper/2405.12202/) (2024)
- [Parameter-Efficient Fine-Tuning of Large Language Models via Deconvolution in Subspace](https://mlsanity.com/paper/2503.01419/) (2025)
- [Towards a Computed-Aided Diagnosis System in Colonoscopy: Automatic Polyp Segmentation Using Convolution Neural Networks](https://mlsanity.com/paper/2101.06040/) (2021)
- [Learning A 3D-CNN and Transformer Prior for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2111.13923/) (2021)

## Abstract (arXiv)

We introduce a guide to help deep learning practitioners understand and manipulate convolutional neural network architectures. The guide clarifies the relationship between various properties (input shape, kernel shape, zero padding, strides and output shape) of convolutional, pooling and transposed convolutional layers, as well as the relationship between convolutional and transposed convolutional layers. Relationships are derived for various cases, and are illustrated in order to make them intuitive.
