# Locally Scale-Invariant Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1412.5104 · HTML: https://mlsanity.com/paper/1412.5104/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2014.

## Built on by (most cited first, 30 of 34)

- [Estimating Body and Hand Motion in an Ego-sensed World](https://mlsanity.com/paper/2410.03665/) (2024)
- [DEVIANT: Depth EquiVarIAnt NeTwork for Monocular 3D Object Detection](https://mlsanity.com/paper/2207.10758/) (2022)
- [Expansion and Shrinkage of Localization for Weakly-Supervised Semantic Segmentation](https://mlsanity.com/paper/2209.07761/) (2022)
- [DISCO: accurate Discrete Scale Convolutions](https://mlsanity.com/paper/2106.02733/) (2021)
- [Resolution learning in deep convolutional networks using scale-space theory](https://mlsanity.com/paper/2106.03412/) (2021)
- [Scale-invariant scale-channel networks: Deep networks that generalise to previously unseen scales](https://mlsanity.com/paper/2106.06418/) (2021)
- [Truly Scale-Equivariant Deep Nets with Fourier Layers](https://mlsanity.com/paper/2311.02922/) (2023)
- [Group Equivariant Subsampling](https://mlsanity.com/paper/2106.05886/) (2021)
- [Scale-Equivariant UNet for Histopathology Image Segmentation](https://mlsanity.com/paper/2304.04595/) (2023)
- [Riesz networks: scale invariant neural networks in a single forward pass](https://mlsanity.com/paper/2305.04665/) (2023)
- [Canonical Factors for Hybrid Neural Fields](https://mlsanity.com/paper/2308.15461/) (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)
- [Sampling Equivariant Self-attention Networks for Object Detection in Aerial Images](https://mlsanity.com/paper/2111.03420/) (2021)
- [Scale-Equivariant Deep Learning for 3D Data](https://mlsanity.com/paper/2304.05864/) (2023)
- [Downbeat Tracking with Tempo-Invariant Convolutional Neural Networks](https://mlsanity.com/paper/2102.02282/) (2021)
- [Empowering Networks With Scale and Rotation Equivariance Using A Similarity Convolution](https://mlsanity.com/paper/2303.00326/) (2023)
- [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)
- [Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization](https://mlsanity.com/paper/2203.05006/) (2022)
- [Just a Matter of Scale? Reevaluating Scale Equivariance in Convolutional Neural Networks](https://mlsanity.com/paper/2211.10288/) (2022)
- [Equivariant and Steerable Neural Networks: A review with special emphasis on the symmetric group](https://mlsanity.com/paper/2301.03019/) (2023)
- [Deep Neural Networks with Efficient Guaranteed Invariances](https://mlsanity.com/paper/2303.01567/) (2023)
- [TpopT: Efficient Trainable Template Optimization on Low-Dimensional Manifolds](https://mlsanity.com/paper/2310.10039/) (2023)
- [Local Scale Equivariance with Latent Deep Equilibrium Canonicalizer](https://mlsanity.com/paper/2508.14187/) (2025)
- [Quantised Transforming Auto-Encoders: Achieving Equivariance to Arbitrary Transformations in Deep Networks](https://mlsanity.com/paper/2111.12873/) (2021)
- [Evaluating Machine Learning Models with NERO: Non-Equivariance Revealed on Orbits](https://mlsanity.com/paper/2305.19889/) (2023)
- [Learning and extrapolating scale-invariant processes](https://mlsanity.com/paper/2601.14810/) (2026)
- [Characterizing and Taming Resolution in Convolutional Neural Networks](https://mlsanity.com/paper/2110.14819/) (2021)
- [Wiggling Weights to Improve the Robustness of Classifiers](https://mlsanity.com/paper/2111.09779/) (2021)
- [Euclidean Invariant Recognition of 2D Shapes Using Histograms of Magnitudes of Local Fourier-Mellin Descriptors](https://mlsanity.com/paper/2203.06787/) (2022)

## Abstract (arXiv)

Convolutional Neural Networks (ConvNets) have shown excellent results on many visual classification tasks. With the exception of ImageNet, these datasets are carefully crafted such that objects are well-aligned at similar scales. Naturally, the feature learning problem gets more challenging as the amount of variation in the data increases, as the models have to learn to be invariant to certain changes in appearance. Recent results on the ImageNet dataset show that given enough data, ConvNets can learn such invariances producing very discriminative features [1]. But could we do more: use less parameters, less data, learn more discriminative features, if certain invariances were built into the learning process? In this paper we present a simple model that allows ConvNets to learn features in a locally scale-invariant manner without increasing the number of model parameters. We show on a modified MNIST dataset that when faced with scale variation, building in scale-invariance allows ConvNets to learn more discriminative features with reduced chances of over-fitting.