TROPICS: Tropical Geometry for Structured Neural Network Compression through Zonotope Approximation

Structured compression of neural networks remains challenging when high accuracy must be preserved under severe parameter reduction. We introduce Tropical Representation for Optimized Pruning, Informed Clustering, and Scaling (TROPICS), a data-free, non-uniform, and single-pass framework based on the tropical geometry of ReLU neural networks. We compress layers in two phases. First, neurons are mapped to zonotope generators and clustered using K-means, merging inputs by mean and outputs by sum, while scale factors recover the signal energy lost during clustering. Second, to avoid forcing dissimilar generators to merge, we magnitude-prune the weakest remaining units. TROPICS requires neither training data nor fine-tuning, and it substantially outperforms existing baselines on VGG16-BN (CIFAR-10): our scaled Mixed strategy achieves an 84.7% parameter reduction with only a 0.44% accuracy drop, while at 92.5% parameter reduction the scale factors preserve up to 29% more accuracy than unscaled variants. On ResNet18 (ImageNet), TROPICS surpasses strong methods such as TropNNC, CUP, and Model Folding at comparable compression.