National Engineering Laboratory for Video Technology, Department of Computer Science and Technology, Peking University, Beijing 100871, China; Peng Cheng Laboratory, Shenzhen 518055, China.
National Engineering Laboratory for Video Technology, Department of Computer Science and Technology, Peking University, Beijing 100871, China; Peng Cheng Laboratory, Shenzhen 518055, China.
Neural Netw. 2020 Jun;126:42-51. doi: 10.1016/j.neunet.2020.03.003. Epub 2020 Mar 9.
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how probabilistic inference can be implemented by a network of spiking neurons in the brain. Previous studies have tried to relate the inference equation of binary Markov random fields to the dynamic equation of spiking neural networks through belief propagation algorithm and reparameterization, but they are valid only for Markov random fields with limited network structure. In this paper, we propose a spiking neural network model that can implement inference of arbitrary binary Markov random fields. Specifically, we design a spiking recurrent neural network and prove that its neuronal dynamics are mathematically equivalent to the inference process of Markov random fields by adopting mean-field theory. Furthermore, our mean-field approach unifies previous works. Theoretical analysis and experimental results, together with the application to image denoising, demonstrate that our proposed spiking neural network can get comparable results to that of mean-field inference.
最近的研究表明，人类大脑的认知过程是通过概率推理实现的，可以进一步通过马尔可夫随机场等概率图模型进行建模。然而，目前尚不清楚概率推理如何通过大脑中的脉冲神经元网络来实现。先前的研究试图通过置信传播算法和重新参数化将二进制马尔可夫随机场的推理方程与脉冲神经网络的动态方程联系起来，但它们仅适用于具有有限网络结构的马尔可夫随机场。在本文中，我们提出了一种可以实现任意二进制马尔可夫随机场推理的脉冲神经网络模型。具体来说，我们设计了一个脉冲递归神经网络，并通过平均场理论证明了其神经元动力学与马尔可夫随机场的推理过程在数学上是等价的。此外，我们的平均场方法统一了以前的工作。理论分析和实验结果，以及在图像去噪中的应用，都表明我们提出的脉冲神经网络可以得到与平均场推理相当的结果。
