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TropNNC: Structured Neural Network Compression Using Tropical Geometry

We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU activations. TropNNC is a structured compression framework based on a geometrical approach to machine/deep learning, using tropical geometry and extending the work of Misiakos et al. (2022). We use the Hausdorff distance of zonotopes in its standard continuous form to achieve a tighter approximation bound for tropical polynomials compared to previous work. This enhancement leads to the development of an effective compression algorithm that achieves superior functional approximations of neural networks. Our method is significantly easier to implement compared to other frameworks, and does not depend on the availability of training data samples. We validate our framework through extensive empirical evaluations on the MNIST, CIFAR, and ImageNet datasets. Our results demonstrate that TropNNC achieves performance on par with state-of-the-art methods like ThiNet (even surpassing it in compressing linear layers) and CUP. To the best of our knowledge, it is the first method that achieves this using tropical geometry.

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