We propose an alternating minimization heuristic for regression over the space of tropical rational functions with fixed exponents. The method alternates between fitting the numerator and denominator terms via tropical polynomial regression, which is known to admit a closed form solution. We demonstrate the behavior of the alternating minimization method experimentally. Experiments demonstrate that the heuristic provides a reasonable approximation of the input data. Our work is motivated by applications to ReLU neural networks, a popular class of network architectures in the machine learning community which are closely related to tropical rational functions.

翻译：我们提出了一种针对固定指数热带有理函数空间的交替极小化启发式回归方法。该方法通过热带多项式回归交替拟合分子项与分母项——该回归过程已知具有闭合形式解。我们通过实验展示了交替极小化方法的表现特性。实验结果表明，该启发式方法能够对输入数据提供合理的近似。本研究源于对ReLU神经网络的潜在应用，这类在机器学习领域广泛使用的网络架构与热带有理函数具有密切联系。