非约束自动编码器的保守性
Conservativeness of untied auto-encoders
摘要：
我们讨论了一个自动编码器定义一个保守的向量场，在这种情况下，它是与一个能量函数类似的数据的非归一化对数概率的必要条件和充分条件。我们证明了保守性的条件比编码器和解码器权重相同（“捆绑权重”）更一般，并且它们还取决于隐藏单元激活函数的形式，但是收缩训练标准（如去噪）将局部执行这些条件。基于这些观察，我们展示了如何使用自动编码器来提取向量场的保守分量。
英文摘要：
We discuss necessary and sufficient conditions for an auto-encoder to define a conservative vector field, in which case it is associated with an energy function akin to the unnormalized log-probability of the data. We show that the conditions for conservativeness are more general than for encoder and decoder weights to be the same ("tied weights"), and that they also depend on the form of the hidden unit activation function, but that contractive training criteria, such as denoising, will enforce these conditions locally. Based on these observations, we show how we can use auto-encoders to extract the conservative component of a vector field.
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