# Efficient and Invariant Convolutional Neural Networks for Dense Prediction

arXiv: https://arxiv.org/abs/1711.09064 · HTML: https://mlsanity.com/paper/1711.09064/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Nov 2017.

## Built on by (most cited first, 3 of 3)

- [Modularity in Deep Learning: A Survey](https://mlsanity.com/paper/2310.01154/) (2023)
- [Data-aware customization of activation functions reduces neural network error](https://mlsanity.com/paper/2301.06635/) (2023)
- [Rotaflip: A New CNN Layer for Regularization and Rotational Invariance in Medical Images](https://mlsanity.com/paper/2108.02704/) (2021)

## Abstract (arXiv)

Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other transformations, including rotation and flip. Recent attempts have been made to incorporate more invariance in image recognition applications, but they are not applicable to dense prediction tasks, such as image segmentation. In this paper, we propose a set of methods based on kernel rotation and flip to enable rotation and flip invariance in convolutional neural networks. The kernel rotation can be achieved on kernels of 3 × 3, while kernel flip can be applied on kernels of any size. By rotating in eight or four angles, the convolutional layers could produce the corresponding number of feature maps based on eight or four different kernels. By using flip, the convolution layer can produce three feature maps. By combining produced feature maps using maxout, the resource requirement could be significantly reduced while still retain the invariance properties. Experimental results demonstrate that the proposed methods can achieve various invariance at reasonable resource requirements in terms of both memory and time.