In sampling-based Bayesian models of brain function, neural activities are assumed to be samples from probability distributions that the brain uses for probabilistic computation. However, a comprehensive understanding of how mechanistic models of neural dynamics can sample from arbitrary distributions is still lacking. We use tools from functional analysis and stochastic differential equations to explore the minimum architectural requirements for $\textit{recurrent}$ neural circuits to sample from complex distributions. We first consider the traditional sampling model consisting of a network of neurons whose outputs directly represent the samples (sampler-only network). We argue that synaptic current and firing-rate dynamics in the traditional model have limited capacity to sample from a complex probability distribution. We show that the firing rate dynamics of a recurrent neural circuit with a separate set of output units can sample from an arbitrary probability distribution. We call such circuits reservoir-sampler networks (RSNs). We propose an efficient training procedure based on denoising score matching that finds recurrent and output weights such that the RSN implements Langevin sampling. We empirically demonstrate our model's ability to sample from several complex data distributions using the proposed neural dynamics and discuss its applicability to developing the next generation of sampling-based brain models.

使用功能分析和随机微分方程的工具，探索基于采样的脑功能贝叶斯模型中神经动力学机制在复杂分布中的采样能力的最小体系结构要求，并提出了能够从任意概率分布中进行采样的储液器-采样网络（RSN）以及基于去噪评分匹配的有效训练过程，从而实现 Langevin 采样，并在实验中展示了该模型从多个复杂数据分布中进行采样的能力，探讨了其在开发基于采样的大脑模型的潜力。

递归神经网络中的表达性概率抽样