论文标题
非欧几里得单调操作员理论，其应用于复发性神经网络
Non-Euclidean Monotone Operator Theory with Applications to Recurrent Neural Networks
论文作者
论文摘要
我们将单调操作员理论的新颖转录转录到非欧盟有限二维空间$ \ ell_1 $和$ \ ell _ {\ infty} $。我们首先建立映射的属性，这些属性相对于非Euclidean Narms $ \ ELL_1 $或$ \ ell _ {\ infty} $。与他们的欧几里得对应物类似，相对于非欧几里得规范是单调的映射与许多用于计算其零的算法的算法。我们证明，用于计算单调操作员的零的几种经典迭代方法直接适用于非欧几里得框架。我们在复发性神经网络的均衡计算中提出了一个案例研究，并证明将计算作为合适的操作员分裂问题提高了收敛率。
We provide a novel transcription of monotone operator theory to the non-Euclidean finite-dimensional spaces $\ell_1$ and $\ell_{\infty}$. We first establish properties of mappings which are monotone with respect to the non-Euclidean norms $\ell_1$ or $\ell_{\infty}$. In analogy with their Euclidean counterparts, mappings which are monotone with respect to a non-Euclidean norm are amenable to numerous algorithms for computing their zeros. We demonstrate that several classic iterative methods for computing zeros of monotone operators are directly applicable in the non-Euclidean framework. We present a case-study in the equilibrium computation of recurrent neural networks and demonstrate that casting the computation as a suitable operator splitting problem improves convergence rates.
