# An Alternative Practice of Tropical Convolution to Traditional Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2103.02096 · HTML: https://mlsanity.com/paper/2103.02096/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 3 Mar 2021.

## Builds on (most cited first, 11 of 11)

- [Cascade R-CNN: Delving into High Quality Object Detection](https://mlsanity.com/paper/1712.00726/) (2017)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [Interactive Medical Image Segmentation using Deep Learning with Image-specific Fine-tuning](https://mlsanity.com/paper/1710.04043/) (2017)
- [AdderNet: Do We Really Need Multiplications in Deep Learning?](https://mlsanity.com/paper/1912.13200/) (2019)
- [Semantic Image Segmentation with Task-Specific Edge Detection Using CNNs and a Discriminatively Trained Domain Transform](https://mlsanity.com/paper/1511.03328/) (2015)
- [Template Adaptation for Face Verification and Identification](https://mlsanity.com/paper/1603.03958/) (2016)
- [The Effects of Approximate Multiplication on Convolutional Neural Networks](https://mlsanity.com/paper/2007.10500/) (2020)
- [Min-Max-Plus Neural Networks](https://mlsanity.com/paper/2102.06358/) (2021)
- [Interleaved Weighted Round-Robin: A Network Calculus Analysis](https://mlsanity.com/paper/2003.08372/) (2020)

## Built on by (most cited first, 4 of 4)

- [Multiplication-Free Transformer Training via Piecewise Affine Operations](https://mlsanity.com/paper/2305.17190/) (2023)
- [ARC-AGI Without Pretraining](https://mlsanity.com/paper/2512.06104/) (2025)
- [Order Theory in the Context of Machine Learning](https://mlsanity.com/paper/2412.06097/) (2024)
- [Compound and Parallel Modes of Tropical Convolutional Neural Networks](https://mlsanity.com/paper/2504.06881/) (2025)

## Abstract (arXiv)

Convolutional neural networks (CNNs) have been used in many machine learning fields. In practical applications, the computational cost of convolutional neural networks is often high with the deepening of the network and the growth of data volume, mostly due to a large amount of multiplication operations of floating-point numbers in convolution operations. To reduce the amount of multiplications, we propose a new type of CNNs called Tropical Convolutional Neural Networks (TCNNs) which are built on tropical convolutions in which the multiplications and additions in conventional convolutional layers are replaced by additions and min/max operations respectively. In addition, since tropical convolution operators are essentially nonlinear operators, we expect TCNNs to have higher nonlinear fitting ability than conventional CNNs. In the experiments, we test and analyze several different architectures of TCNNs for image classification tasks in comparison with similar-sized conventional CNNs. The results show that TCNN can achieve higher expressive power than ordinary convolutional layers on the MNIST and CIFAR10 image data set. In different noise environments, there are wins and losses in the robustness of TCNN and ordinary CNNs.