We define and establish the conditions for `equivalent neural networks' - neural networks with different weights, biases, and threshold functions that result in the same associated function. We prove that given a neural network $\mathcal{N}$ with piece-wise linear activation, the space of coefficients describing all equivalent neural networks is given by a semialgebraic set. This result is obtained by studying different representations of a given piece-wise linear function using the Tarski-Seidenberg theorem.
翻译:我们定义并确定了“等效神经网络”的条件,即具有不同重量、偏差和阈值功能从而产生相同相关功能的神经网络。我们证明,鉴于神经网络$\mathcal{N}$具有片度线性激活,描述所有等效神经网络的系数空间由一组半代数表示。通过使用Tarski-Seidenberg定理来研究对特定片度线性函数的不同表达方式,得出了这一结果。