Towards establishing a meaningful and practical dynamics results for the unified RNN model
Towards establishing a meaningful and practical dynamics results for the unified RNN model
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DOI：
10.1016/j.neucom.2014.12.007
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发表时间：
2015-06
期刊：
影响因子：
6
通讯作者：
C. Qiao;H. Chen;Wenfeng Jing;Ke-Feng Sun
中科院分区：
文献类型：
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作者：
C. Qiao;H. Chen;Wenfeng Jing;Ke-Feng Sun
由于连续时间递归神经网络的统一模型，即连续时间一致伪投影反单调网络，可以共同覆盖几乎所有已知的连续时间递归神经网络个体，并且临界条件可以表征递归神经网络稳定性和不稳定的内在有界线，因此，深入研究统一模型的临界动力学行为是非常有意义的。本文获得了连续时间均匀伪投影反单调网络的临界全局收敛性和稳定性，这里的临界分析不需要任何额外的要求，即只需要统一模型满足给定判别矩阵非负定的临界条件。结果可以共同覆盖、简化和扩展大多数已知的、针对每个循环神经网络个体验证的多样化动力学结果，包括那些关键分析，更不用说那些非关键分析，从而可以直接消除这些已知结果之间的冗余。这里采用的方法为连续时间 RNN 建立有意义且实用的统一理论迈出了明显的一步。
Since the unified model of continuous-time recurrent neural networks, i.e., continuous-time uniformly pseudo-projection-anti-monotone net, can jointly cover almost all of the known continuous-time recurrent neural network individuals, and the critical condition can characterize the intrinsic bounded line of stability and un-stability of a recurrent neural network, thus, it is quite meaningful to study thoroughly the critical dynamics behaviors of the unified model. In the present paper, the critical global convergence and stability are obtained for the continuous-time uniformly pseudo-projection-anti-monotone net, and the critical analysis here does not need any extra requirements, namely, only require the unified model to satisfy the critical condition that one given discriminant matrix is nonnegative definite. The results can jointly cover, simplify and extend most of those known diverse dynamics results validated for each recurrent neural network individual, including those critical analysis and let alone those non-critical analysis, thus can eliminate the redundant among those known results directly. The approach adopted here launches a visible step towards establishing a meaningful and practical unified theory for the continuous-time RNNs.