# Exploring the ability of CNNs to generalise to previously unseen scales over wide scale ranges

arXiv: https://arxiv.org/abs/2004.01536 · HTML: https://mlsanity.com/paper/2004.01536/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2020.

## Built on by (most cited first, 10 of 10)

- [Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales](https://mlsanity.com/paper/2106.06418/) (2021)
- [Scale Equivariant U-Net](https://mlsanity.com/paper/2210.04508/) (2022)
- [A deep convolutional neural network that is invariant to time rescaling](https://mlsanity.com/paper/2107.04616/) (2021)
- [Unified theory for joint covariance properties under geometric image transformations for spatio-temporal receptive fields according to the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2311.10543/) (2023)
- [Riesz feature representation: scale equivariant scattering network for classification tasks](https://mlsanity.com/paper/2307.08467/) (2023)
- [Covariant spatio-temporal receptive fields for spiking neural networks](https://mlsanity.com/paper/2405.00318/) (2024)
- [Just a Matter of Scale? Reevaluating Scale Equivariance in Convolutional Neural Networks](https://mlsanity.com/paper/2211.10288/) (2022)
- [A Comprehensive Assessment Benchmark for Rigorously Evaluating Deep Learning Image Classifiers](https://mlsanity.com/paper/2308.04137/) (2023)
- [Hybrid Lie semi-group and cascade structures for the generalized Gaussian derivative model for visual receptive fields](https://mlsanity.com/paper/2509.15748/) (2025)
- [Distilling Latent Manifolds: Resolution Extrapolation by Variational Autoencoders](https://mlsanity.com/paper/2603.14536/) (2026)

## Abstract (arXiv)

The ability to handle large scale variations is crucial for many real world visual tasks. A straightforward approach for handling scale in a deep network is to process an image at several scales simultaneously in a set of scale channels. Scale invariance can then, in principle, be achieved by using weight sharing between the scale channels together with max or average pooling over the outputs from the scale channels. The ability of such scale channel networks to generalise to scales not present in the training set over significant scale ranges has, however, not previously been explored. We, therefore, present a theoretical analysis of invariance and covariance properties of scale channel networks and perform an experimental evaluation of the ability of different types of scale channel networks to generalise to previously unseen scales. We identify limitations of previous approaches and propose a new type of foveated scale channel architecture, where the scale channels process increasingly larger parts of the image with decreasing resolution. Our proposed FovMax and FovAvg networks perform almost identically over a scale range of 8, also when training on single scale training data, and do also give improvements in the small sample regime.