用热带几何压缩神经网络，无需训练数据且效果不输主流方法。
TropNNC: Structured Neural Network Compression Using Tropical Geometry
- 用热带多项式表示网络输出，通过几何简化实现结构化压缩。
- 在MNIST/CIFAR/ImageNet上性能媲美ThiNet和CUP，无需训练数据。
- 首次将热带几何用于卷积层，理论压缩界最紧，适合轻量化部署。
我们提出TropNNC，一种基于热带几何的神经网络压缩框架，适用于含线性层、卷积层及ReLU激活函数的网络。通过将网络输出表示为热带有理函数，TropNNC能够通过简化对应热带多项式实现结构化压缩。该方法通过自适应选择保留神经元的权重，改进了先前工作的几何近似。主要贡献包括首次将热带几何应用于卷积层，以及获得目前已知最紧的理论压缩界。TropNNC仅需网络权重即可操作，无需训练数据，在MNIST、CIFAR和ImageNet上均取得与ThiNet和CUP等强基线相当的性能。
原文摘要 · Abstract (English)
We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU 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 refines the geometric approximation of previous work by adaptively selecting the weights of retained neurons. Key contributions include the first application of tropical geometry to convolutional layers and the tightest known theoretical compression bound. TropNNC requires only access to network weights - no training data - and achieves competitive performance on MNIST, CIFAR, and ImageNet, matching strong baselines such as ThiNet and CUP.
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