可约双曲正切网络的函数等价性与路径连通性
Functional Equivalence and Path Connectivity of Reducible Hyperbolic Tangent Networks
AI总结：
本文研究单隐藏层双曲正切网络的可约参数，算法化刻画单元冗余与函数等价类，并证明其为分段线性路径连通且特定情形直径至多含7条线性段。
摘要：
理解人工神经网络的学习过程，需要阐明学习发生所处的参数空间结构。神经网络参数的函数等价类是指实现相同输入—输出函数的参数集合。对于许多架构而言，几乎所有参数都具有简单且已有充分记录的函数等价类。然而，还存在极少数可约参数，由于网络单元之间的冗余，它们具有更丰富的函数等价类。在本文中，我们针对单隐藏层双曲正切架构，对单元冗余和可约函数等价类给出了算法化刻画。我们证明，此类函数等价类是分段线性路径连通集合；并且对于大多数单元均为冗余单元的参数，这些集合的直径至多由7条线性段构成。
英文摘要：
Understanding the learning process of artificial neural networks requires clarifying the structure of the parameter space within which learning takes place. A neural network parameter's functional equivalence class is the set of parameters implementing the same input--output function. For many architectures, almost all parameters have a simple and well-documented functional equivalence class. However, there is also a vanishing minority of reducible parameters, with richer functional equivalence classes caused by redundancies among the network's units. In this paper, we give an algorithmic characterisation of unit redundancies and reducible functional equivalence classes for a single-hidden-layer hyperbolic tangent architecture. We show that such functional equivalence classes are piecewise-linear path-connected sets, and that for parameters with a majority of redundant units, the sets have a diameter of at most 7 linear segments.
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。
