论文标题
复杂的振幅玻璃体机器
Complex Amplitude-Phase Boltzmann Machines
论文作者
论文摘要
我们将Boltzmann机器的框架扩展到具有可变振幅的复杂值神经元网络，称为复杂的振幅相位玻尔兹曼机器（CAP-BM）。该模型能够对复杂数据中的幅度和相对相分布进行无监督的学习。介绍了吉布斯分布的采样规则和模型的学习规则。在复杂的振幅限制的玻尔兹曼机器（CAP-RBM）中学习，在合成复合物值图像上展示了，并通过复杂的小波变换而变换的手写MNIST数字。具体而言，我们在模型中显示了新的振幅耦合项的必要性。所提出的模型对于涉及具有振幅变化的复杂值数据的机器学习任务以及为新型计算硬件的算法（例如耦合振荡器和神经形态硬件）而言，可以在其中进行Boltzmann采样。
We extend the framework of Boltzmann machines to a network of complex-valued neurons with variable amplitudes, referred to as Complex Amplitude-Phase Boltzmann machine (CAP-BM). The model is capable of performing unsupervised learning on the amplitude and relative phase distribution in complex data. The sampling rule of the Gibbs distribution and the learning rules of the model are presented. Learning in a Complex Amplitude-Phase restricted Boltzmann machine (CAP-RBM) is demonstrated on synthetic complex-valued images, and handwritten MNIST digits transformed by a complex wavelet transform. Specifically, we show the necessity of a new amplitude-amplitude coupling term in our model. The proposed model is potentially valuable for machine learning tasks involving complex-valued data with amplitude variation, and for developing algorithms for novel computation hardware, such as coupled oscillators and neuromorphic hardware, on which Boltzmann sampling can be executed in the complex domain.
