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.

中文翻译：

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均值场逼近在尖峰神经网络中二进制马尔可夫随机场的概率推断。

最近的研究表明，人脑的认知过程是通过概率推断实现的，并且可以通过诸如Markov随机场之类的概率图形模型进一步建模。尽管如此，目前尚不清楚如何通过大脑中尖刺神经元网络实现概率推断。先前的研究试图通过置信度传播算法和重新参数化将二值马尔可夫随机场的推理方程与尖峰神经网络的动力学方程联系起来，但它们仅对网络结构有限的马尔可夫随机场有效。在本文中，我们提出了一个尖峰神经网络模型，该模型可以实现任意二进制马尔可夫随机场的推断。特别，我们设计了一个尖峰递归神经网络，并通过采用均值场理论证明了其神经元动力学在数学上等同于马尔可夫随机场的推理过程。此外，我们的均值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表明，我们提出的尖峰神经网络可以获得与均值场推理相当的结果。