# Compound and Parallel Modes of Tropical Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2504.06881 · HTML: https://mlsanity.com/paper/2504.06881/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 49 of its 82 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design](https://mlsanity.com/paper/1807.11164/) (2018)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [SqueezeNet: AlexNet-level accuracy with 50x fewer parameters and <0.5MB model size](https://mlsanity.com/paper/1602.07360/) (2016)
- [YOLOv7: Trainable bag-of-freebies sets new state-of-the-art for real-time object detectors](https://mlsanity.com/paper/2207.02696/) (2022)
- [XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networks](https://mlsanity.com/paper/1603.05279/) (2016)
- [RWKV: Reinventing RNNs for the Transformer Era](https://mlsanity.com/paper/2305.13048/) (2023)
- [A Survey of Quantization Methods for Efficient Neural Network Inference](https://mlsanity.com/paper/2103.13630/) (2021)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Retentive Network: A Successor to Transformer for Large Language Models](https://mlsanity.com/paper/2307.08621/) (2023)
- [BinaryConnect: Training Deep Neural Networks with binary weights during propagations](https://mlsanity.com/paper/1511.00363/) (2015)
- [Hyena Hierarchy: Towards Larger Convolutional Language Models](https://mlsanity.com/paper/2302.10866/) (2023)
- [YOLOv6: A Single-Stage Object Detection Framework for Industrial Applications](https://mlsanity.com/paper/2209.02976/) (2022)
- [Towards Accurate Binary Convolutional Neural Network](https://mlsanity.com/paper/1711.11294/) (2017)

## Abstract (arXiv)

Convolutional neural networks (CNNs) are foundational to many state-of-the-art computer vision systems, yet their reliance on multiplication-intensive computations poses challenges for deployment on resource-constrained devices. While tropical convolutional neural networks (TCNNs) reduce this computational burden by replacing multiplications with cheaper min/maxplus operations, they often do so at the cost of reduced model accuracy. To address this tradeoff, we introduce two novel extensions of tropical convolution: compound tropical convolution (cTCNN) and parallel tropical convolution (pTCNN). These operators combine minplus and maxplus algebraic operations within a single layer to enhance representational capacity while maintaining low computational cost. We provide an open-source implementation of these operators in a PyTorch-compatible framework, featuring optimized GPU kernels developed with TileLang. Through extensive experiments on image classification and semantic segmentation benchmarks, we demonstrate that our proposed cTCNN and pTCNN layers achieve competitive performance against standard CNNs while significantly reducing the number of multiplications. Moreover, we show that hybrid models, which integrate both tropical and conventional convolutions, can further improve the accuracy-efficiency balance. Our findings suggest that these tropical convolution variants are viable and effective components for building efficient deep learning models