基于复杂增长变换动力系统的共振机器学习
Resonant Machine Learning Based on Complex Growth Transform Dynamical Systems
摘要：
传统的基于能量的学习模型将单个能量度量与底层优化过程中涉及的每个变量配置相关联。这种模型将最低能量状态与所考虑的变量的最佳配置相关联，因此本质上是耗散的。在本文中，我们提出了一个节能的学习框架，利用机器学习网络和满足特勒根定理的一般电气网络之间的结构和功能的相似性。与标准的基于能量的模型相比，所提出的公式将两个能量分量，即有功和无功能量与网络相关联。这确保了网络的有功功率仅在学习过程中耗散，而无功功率始终保持为零。因此，在稳态下，学习的参数被存储并通过由网络的节点电感和电容确定的电谐振自我维持。在此基础上，本文提出了三个新的概念：（a）以网络的有功功率耗散作为学习目标函数的正则化，并使学习目标函数满足总无功功率为零的约束;（b）基于复域的动力系统，连续时间增长变换优化了学习目标函数，并在稳态下驱动网络向电谐振方向发展。状态操作;以及（c）控制有功功率耗散和收敛速度之间的折衷的退火过程。作为一个有代表性的例子，我们展示了如何建议的框架可以用于设计谐振支持向量机（SVM），在那里我们表明，支持向量对应于一个LC网络与自维持振荡。
英文摘要：
Traditional energy-based learning models associate a single energy metric to each configuration of variables involved in the underlying optimization process. Such models associate the lowest energy state to the optimal configuration of variables under consideration, and are thus inherently dissipative. In this paper we propose an energy-efficient learning framework that exploits structural and functional similarities between a machine learning network and a general electrical network satisfying the Tellegen's theorem. In contrast to the standard energy-based models, the proposed formulation associates two energy components, namely, active and reactive energy to the network. This ensures that the network's active-power is dissipated only during the process of learning, whereas the reactive-power is maintained to be zero at all times. As a result, in steady-state, the learned parameters are stored and self-sustained by electrical resonance determined by the network's nodal inductances and capacitances. Based on this approach, this paper introduces three novel concepts: (a) A learning framework where the network's active-power dissipation is used as a regularization for a learning objective function that is subjected to zero total reactive-power constraint; (b) A dynamical system based on complex-domain, continuous-time growth transforms which optimizes the learning objective function and drives the network towards electrical resonance under steady-state operation; and (c) An annealing procedure that controls the trade-off between active-power dissipation and the speed of convergence. As a representative example, we show how the proposed framework can be used for designing resonant support vector machines (SVMs), where we show that the support-vectors correspond to an LC network with self-sustained oscillations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
