# Invariant Integration in Deep Convolutional Feature Space

arXiv: https://arxiv.org/abs/2004.09166 · HTML: https://mlsanity.com/paper/2004.09166/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

## Built on by (most cited first, 6 of 6)

- [LaneCPP: Continuous 3D Lane Detection using Physical Priors](https://mlsanity.com/paper/2406.08381/) (2024)
- [Interspace Pruning: Using Adaptive Filter Representations to Improve Training of Sparse CNNs](https://mlsanity.com/paper/2203.07808/) (2022)
- [Dimensionality Reduced Training by Pruning and Freezing Parts of a Deep Neural Network, a Survey](https://mlsanity.com/paper/2205.08099/) (2022)
- [Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration](https://mlsanity.com/paper/2202.03967/) (2022)
- [Deep Neural Networks with Efficient Guaranteed Invariances](https://mlsanity.com/paper/2303.01567/) (2023)
- [Collaborative Learning for Semi-Supervised LiDAR Semantic Segmentation](https://mlsanity.com/paper/2605.17135/) (2026)

## Abstract (arXiv)

In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to construct a complete feature space invariant to finite transformation groups. We apply our proposed layer to explicitly insert invariance properties for vision-related classification tasks, demonstrate our approach for the case of rotation invariance and report state-of-the-art performance on the Rotated-MNIST dataset. Our method is especially beneficial when training with limited data.