# TropNNC: Structured Neural Network Compression Using Tropical Geometry

arXiv: https://arxiv.org/abs/2409.03945 · HTML: https://mlsanity.com/paper/2409.03945/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 79 references that are in the map.
- First posted on arXiv 5 Sep 2024.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Object Detection in 20 Years: A Survey](https://mlsanity.com/paper/1905.05055/) (2019)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [On the Number of Linear Regions of Deep Neural Networks](https://mlsanity.com/paper/1402.1869/) (2014)
- [Filter Pruning via Geometric Median for Deep Convolutional Neural Networks Acceleration](https://mlsanity.com/paper/1811.00250/) (2018)
- [Learning Deconvolution Network for Semantic Segmentation](https://mlsanity.com/paper/1505.04366/) (2015)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [HRank: Filter Pruning using High-Rank Feature Map](https://mlsanity.com/paper/2002.10179/) (2020)
- [Model compression via distillation and quantization](https://mlsanity.com/paper/1802.05668/) (2018)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [NISP: Pruning Networks using Neuron Importance Score Propagation](https://mlsanity.com/paper/1711.05908/) (2017)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Quantized Convolutional Neural Networks for Mobile Devices](https://mlsanity.com/paper/1512.06473/) (2015)
- [A Comprehensive Survey of Deep Learning for Image Captioning](https://mlsanity.com/paper/1810.04020/) (2018)
- [Compressing Deep Convolutional Networks using Vector Quantization](https://mlsanity.com/paper/1412.6115/) (2014)
- [From Words to Watts: Benchmarking the Energy Costs of Large Language Model Inference](https://mlsanity.com/paper/2310.03003/) (2023)
- [Compressing Neural Networks with the Hashing Trick](https://mlsanity.com/paper/1504.04788/) (2015)
- [Structured Pruning for Deep Convolutional Neural Networks: A survey](https://mlsanity.com/paper/2303.00566/) (2023)
- [Convolutional neural networks with low-rank regularization](https://mlsanity.com/paper/1511.06067/) (2015)
- [Tropical Geometry of Deep Neural Networks](https://mlsanity.com/paper/1805.07091/) (2018)
- [CHIP: CHannel Independence-based Pruning for Compact Neural Networks](https://mlsanity.com/paper/2110.13981/) (2021)
- [Convolutional Neural Network Pruning with Structural Redundancy Reduction](https://mlsanity.com/paper/2104.03438/) (2021)

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

- [Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry](https://mlsanity.com/paper/2602.03204/) (2026)
- [Geometric Capacity of Transformers: A Tropical Geometry Perspective](https://mlsanity.com/paper/2604.14727/) (2026)
- [UltraLIF: Fully Differentiable Spiking Neural Networks via Ultradiscretization and Max-Plus Algebra](https://mlsanity.com/paper/2602.11206/) (2026)

## Abstract (arXiv)

We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU-type activations using tropical geometry. By representing a network's output as a tropical rational function, TropNNC enables structured compression via reduction of the corresponding tropical polynomials. Our method identifies redundancy via similarity and improves upon the geometric approximation of previous work by adaptively selecting the weights of retained neurons. We relate it to SVD and spectral clustering, and provide insights into network compression beyond the specific setting considered. We provide the tightest known theoretical compression bound, and the first successful application of tropical geometry to convolutional layers. TropNNC requires access only to network weights - no training data - and achieves competitive performance on MNIST, CIFAR, and ImageNet, matching strong baselines such as ThiNet and CUP.