论文标题
近似Lipschitz连续函数与组神经网络
Approximating Lipschitz continuous functions with GroupSort neural networks
论文作者
论文摘要
对抗性攻击和瓦斯坦斯坦甘斯（Wasserstein Gans）的最新进展已主张使用具有限制性Lipschitz常数的神经网络。在这些观察结果的推动下，我们研究了最近引入的群体神经网络，对权重的限制，并迈出了更好地理解其表现力的理论步骤。我们特别展示了这些网络如何表示Lipschitz连续的分段线性函数。我们还证明它们非常适合近似Lipschitz的连续功能，并且在深度和大小上都表现出上限。总而言之，在一组合成实验中说明了Groupsort网络与更标准的Relu网络相比的效率。
Recent advances in adversarial attacks and Wasserstein GANs have advocated for use of neural networks with restricted Lipschitz constants. Motivated by these observations, we study the recently introduced GroupSort neural networks, with constraints on the weights, and make a theoretical step towards a better understanding of their expressive power. We show in particular how these networks can represent any Lipschitz continuous piecewise linear functions. We also prove that they are well-suited for approximating Lipschitz continuous functions and exhibit upper bounds on both the depth and size. To conclude, the efficiency of GroupSort networks compared with more standard ReLU networks is illustrated in a set of synthetic experiments.
