异或问题的Copula表示与误差曲面投影
Copula Representations and Error Surface Projections for the Exclusive Or Problem
AI总结：
本文以异或问题为例，通过概率逻辑和Copula函数探讨非线性前馈网络优于线性回归的原因，并利用三维误差曲面图展示不同激活函数的动态，旨在作为机器学习的教学导论。
摘要：
异或（xor）函数是最简单的例子之一，说明了为何非线性前馈网络在机器学习应用中优于线性回归。我们回顾了xor表示与逼近问题，并从概率逻辑和关联copula函数的角度讨论了其解。在简要回顾前馈网络的规格后，我们通过一组彩色三维图表比较了使用RELU和tanh等不同激活函数时学习到的误差曲面的动态。Copula表示将xor从布尔值扩展到实数值，从而提供了一种便捷方式来演示在样本内和样本外数据集上进行交叉验证的概念。我们的方法是教学性的，旨在作为机器学习的导论。
英文摘要：
The exclusive or (xor) function is one of the simplest examples that illustrate why nonlinear feedforward networks are superior to linear regression for machine learning applications. We review the xor representation and approximation problems and discuss their solutions in terms of probabilistic logic and associative copula functions. After briefly reviewing the specification of feedforward networks, we compare the dynamics of learned error surfaces with different activation functions such as RELU and tanh through a set of colorful three-dimensional charts. The copula representations extend xor from Boolean to real values, thereby providing a convenient way to demonstrate the concept of cross-validation on in-sample and out-sample data sets. Our approach is pedagogical and is meant to be a machine learning prolegomenon.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
