# Scale-Invariant Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1411.6369 · HTML: https://mlsanity.com/paper/1411.6369/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2014.

## Built on by (most cited first, 30 of 40)

- [Chaos is a Ladder: A New Theoretical Understanding of Contrastive Learning via Augmentation Overlap](https://mlsanity.com/paper/2203.13457/) (2022)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detection](https://mlsanity.com/paper/2207.10758/) (2022)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [Text2Light: Zero-Shot Text-Driven HDR Panorama Generation](https://mlsanity.com/paper/2209.09898/) (2022)
- [Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales](https://mlsanity.com/paper/2106.06418/) (2021)
- [Scale-Equivariant UNet for Histopathology Image Segmentation](https://mlsanity.com/paper/2304.04595/) (2023)
- [Learning Online Visual Invariances for Novel Objects via Supervised and Self-Supervised Training](https://mlsanity.com/paper/2110.01476/) (2021)
- [Riesz networks: scale invariant neural networks in a single forward pass](https://mlsanity.com/paper/2305.04665/) (2023)
- [Deformation Robust Roto-Scale-Translation Equivariant CNNs](https://mlsanity.com/paper/2111.10978/) (2021)
- [Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration](https://mlsanity.com/paper/2202.03967/) (2022)
- [Scale-Equivariant Deep Learning for 3D Data](https://mlsanity.com/paper/2304.05864/) (2023)
- [Steerable Equivariant Representation Learning](https://mlsanity.com/paper/2302.11349/) (2023)
- [RSF-Conv: Rotation-and-Scale Equivariant Fourier Parameterized Convolution for Retinal Vessel Segmentation](https://mlsanity.com/paper/2309.15638/) (2023)
- [Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators](https://mlsanity.com/paper/2507.09264/) (2025)
- [Downbeat Tracking with Tempo-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/2102.02282/) (2021)
- [CNN-based Ego-Motion Estimation for Fast MAV Maneuvers](https://mlsanity.com/paper/2101.01841/) (2021)
- [Scale generalisation properties of extended scale-covariant and scale-invariant Gaussian derivative networks on image datasets with spatial scaling variations](https://mlsanity.com/paper/2409.11140/) (2024)
- [Generalized Spherical Neural Operators: Green's Function Formulation](https://mlsanity.com/paper/2512.10723/) (2025)
- [Just a Matter of Scale? Reevaluating Scale Equivariance in Convolutional Neural Networks](https://mlsanity.com/paper/2211.10288/) (2022)
- [Deep Neural Networks with Efficient Guaranteed Invariances](https://mlsanity.com/paper/2303.01567/) (2023)
- [Scale-Rotation-Equivariant Lie Group Convolution Neural Networks (Lie Group-CNNs)](https://mlsanity.com/paper/2306.06934/) (2023)
- [Scale-Preserving Automatic Concept Extraction (SPACE)](https://mlsanity.com/paper/2308.06022/) (2023)
- [Local Scale Equivariance with Latent Deep Equilibrium Canonicalizer](https://mlsanity.com/paper/2508.14187/) (2025)
- [Scalar Invariant Networks with Zero Bias](https://mlsanity.com/paper/2211.08486/) (2022)
- [Machine Learning-based Signal Quality Assessment for Cardiac Volume Monitoring in Electrical Impedance Tomography](https://mlsanity.com/paper/2301.01469/) (2023)
- [Hawk: An Industrial-strength Multi-label Document Classifier](https://mlsanity.com/paper/2301.06057/) (2023)
- [SO(2) and O(2) Equivariance in Image Recognition with Bessel-Convolutional Neural Networks](https://mlsanity.com/paper/2304.09214/) (2023)
- [Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbits](https://mlsanity.com/paper/2305.19889/) (2023)
- [Advancing Perception in Artificial Intelligence through Principles of Cognitive Science](https://mlsanity.com/paper/2310.08803/) (2023)

## Abstract (arXiv)

Even though convolutional neural networks (CNN) has achieved near-human performance in various computer vision tasks, its ability to tolerate scale variations is limited. The popular practise is making the model bigger first, and then train it with data augmentation using extensive scale-jittering. In this paper, we propose a scaleinvariant convolutional neural network (SiCNN), a modeldesigned to incorporate multi-scale feature exaction and classification into the network structure. SiCNN uses a multi-column architecture, with each column focusing on a particular scale. Unlike previous multi-column strategies, these columns share the same set of filter parameters by a scale transformation among them. This design deals with scale variation without blowing up the model size. Experimental results show that SiCNN detects features at various scales, and the classification result exhibits strong robustness against object scale variations.