Tropical Geometrical Zonotope Reduction as Applied to Neural Network Compression.
Recently, tropical geometry had a significant impact on the study of deep neural networks. Motivated by this progress, we provide a novel framework for tropical polynomial approximation based on geometrical zonotope reduction. In particular, we show that the bounded error of two tropical polynomials depends on the Hausdorff distance of their respective Extended Newton Polytopes. Based on this result, we propose geometrical neural network compression methods that employ the K-means algorithm. Our methods apply to the fully connected layers of a network. We analyze the error bounds of our algorithms theoretically based on the Hausdorff approximation and evaluate them experimentally on the task of neural network compression. We deduce that our methods show an improvement over relevant tropical geometry techniques, advance baseline pruning methods, and have competitive performance against a modern pruning technique.
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