# Fully complex-valued deep learning model for visual perception

arXiv: https://arxiv.org/abs/2212.07146 · HTML: https://mlsanity.com/paper/2212.07146/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 14 Dec 2022.

## Builds on (most cited first, 10 of 10)

- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups](https://mlsanity.com/paper/1802.03690/) (2018)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [Superposition of many models into one](https://mlsanity.com/paper/1902.05522/) (2019)
- [A Survey of Complex-Valued Neural Networks](https://mlsanity.com/paper/2101.12249/) (2021)
- [Complex Gated Recurrent Neural Networks](https://mlsanity.com/paper/1806.08267/) (2018)
- [Affinity CNN: Learning Pixel-Centric Pairwise Relations for Figure/Ground Embedding](https://mlsanity.com/paper/1512.02767/) (2015)
- [Neural network is heterogeneous: Phase matters more](https://mlsanity.com/paper/2111.02014/) (2021)
- [Co-domain Symmetry for Complex-Valued Deep Learning](https://mlsanity.com/paper/2112.01525/) (2021)

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

- [OV-COAST: Cost Aggregation with Optimal Transport for Open-Vocabulary Semantic Segmentation](https://mlsanity.com/paper/2506.03706/) (2025)

## Abstract (arXiv)

Deep learning models operating in the complex domain are used due to their rich representation capacity. However, most of these models are either restricted to the first quadrant of the complex plane or project the complex-valued data into the real domain, causing a loss of information. This paper proposes that operating entirely in the complex domain increases the overall performance of complex-valued models. A novel, fully complex-valued learning scheme is proposed to train a Fully Complex-valued Convolutional Neural Network (FC-CNN) using a newly proposed complex-valued loss function and training strategy. Benchmarked on CIFAR-10, SVHN, and CIFAR-100, FC-CNN has a 4-10% gain compared to its real-valued counterpart, maintaining the model complexity. With fewer parameters, it achieves comparable performance to state-of-the-art complex-valued models on CIFAR-10 and SVHN. For the CIFAR-100 dataset, it achieves state-of-the-art performance with 25% fewer parameters. FC-CNN shows better training efficiency and much faster convergence than all the other models.