发表机构
University of Technology Nuremberg（图恩堡技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究带标量乘法门的热带电路，证明其计算最大权重有向生成树和最大权重二分完美匹配时的指数规模下界，得出单调和非单调最大输出神经网络的指数规模分离，揭示有强制凸性约束的神经网络模型有时需指数级更大才能表达相同函数。
AI 中文摘要
我们研究带标量乘法门的热带电路，即其门实现最大值、加法或与正常量相乘的代数电路。对于此类电路，我们证明了在计算最大权重有向生成树和最大权重二分完美匹配时的指数规模下界。作为推论，我们得到了单调和非单调最大输出神经网络之间的指数规模分离，其推广了常用的ReLU神经网络。由此得出的一个结论是，具有强制凸性约束的神经网络模型，如输入凸神经网络（ICNN），有时需要比无约束的对应模型指数级更大才能表达相同的函数。
英文摘要
We study tropical circuits with scalar multiplication gates, that is, algebraic circuits whose gates implement $\max$, $+$, or multiplication with a positive constant. For such circuits, we prove exponential size lower bounds for computing maximum weight directed spanning trees and maximum weight bipartite perfect matchings. As a corollary, we obtain an exponential size separation between monotone and non-monotone maxout neural networks, which generalize the popularly used ReLU neural networks. One conclusion from this is that neural network models with enforced convexity constraints, such as input-convex neural networks (ICNNs), sometimes need to be exponentially larger than their unrestricted counterparts in order to express the same functions.
Comments23 pages, 5 figures
