递归网络的规范化降维
Dimension reduction in recurrent networks by canonicalization
摘要：
许多递归神经网络机器学习范例可以使用状态空间表示来制定。经典的概念规范的状态空间实现适应本文半无限的输入，使它可以作为一个降维工具，在经常性的网络设置。所谓的输入遗忘属性被确定为关键假设，保证存在性和唯一性（系统同构）的因果和时不变的输入/输出系统的规范实现与半无限输入。此外，来自对称哈密顿系统理论的最优约简的概念在我们的设置中实现，以构造出输入遗忘的正则实现，但不一定是正则实现。这两个过程中的线性衰落记忆输入/输出系统的框架进行了详细研究。最后，使用再生核希尔伯特空间（RKHS）的隐式减少的概念被引入，它允许，对于具有线性读出的系统，实现维数减少，而不需要实际计算的减少空间中介绍的第一部分的文件。
英文摘要：
Many recurrent neural network machine learning paradigms can be formulated using state-space representations. The classical notion of canonical state-space realization is adapted in this paper to accommodate semi-infinite inputs so that it can be used as a dimension reduction tool in the recurrent networks setup. The so-called input forgetting property is identified as the key hypothesis that guarantees the existence and uniqueness (up to system isomorphisms) of canonical realizations for causal and time-invariant input/output systems with semi-infinite inputs. Additionally, the notion of optimal reduction coming from the theory of symmetric Hamiltonian systems is implemented in our setup to construct canonical realizations out of input forgetting but not necessarily canonical ones. These two procedures are studied in detail in the framework of linear fading memory input/output systems. Finally, the notion of implicit reduction using reproducing kernel Hilbert spaces (RKHS) is introduced which allows, for systems with linear readouts, to achieve dimension reduction without the need to actually compute the reduced spaces introduced in the first part of the paper.
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