# Hadamard Layer to Improve Semantic Segmentation

arXiv: https://arxiv.org/abs/2302.10318 · HTML: https://mlsanity.com/paper/2302.10318/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 16 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1802.02611/) (2018)
- [Pyramid Scene Parsing Network](https://mlsanity.com/paper/1612.01105/) (2016)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)
- [UNet 3+: A Full-Scale Connected UNet for Medical Image Segmentation](https://mlsanity.com/paper/2004.08790/) (2020)
- [ResUNet-a: a deep learning framework for semantic segmentation of remotely sensed data](https://mlsanity.com/paper/1904.00592/) (2019)
- [A Survey on Deep Learning-based Architectures for Semantic Segmentation on 2D images](https://mlsanity.com/paper/1912.10230/) (2019)

## Built on by (most cited first, 1 of 1)

- [Adversarial Attack and Disturbance Detection by Hadamard-Coded Output Representations for Object Detection and Semantic Segmentation](https://mlsanity.com/paper/2606.09536/) (2026)

## Abstract (arXiv)

The Hadamard Layer, a simple and computationally efficient way to improve results in semantic segmentation tasks, is presented. This layer has no free parameters that require to be trained. Therefore it does not increase the number of model parameters, and the extra computational cost is marginal. Experimental results show that the new Hadamard layer substantially improves the performance of the investigated models (variants of the Pix2Pix model). The performance's improvement can be explained by the Hadamard layer forcing the network to produce an internal encoding of the classes so that all bins are active. Therefore, the network computation is more distributed. In a sort that the Hadamard layer requires that to change the predicted class, it is necessary to modify 2k-1 bins, assuming k bins in the encoding. A specific loss function allows a stable and fast training convergence.