Belief Propagation (BP) is a simple probabilistic inference algorithm,
consisting of passing messages between nodes of a graph representing a
probability distribution. Its analogy with a neural network suggests that it
could have far-ranging applications for neuroscience and artificial
intelligence. Unfortunately, it is only exact when applied to cycle-free
graphs, which restricts the potential of the algorithm. In this paper, we
propose Circular Belief Propagation (CBP), an extension of BP which limits the
detrimental effects of message reverberation caused by cycles by learning to
detect and cancel spurious correlations and belief amplifications. We show in
numerical experiments involving binary probabilistic graphs that CBP far
outperforms BP and reaches good performance compared to that of previously
proposed algorithms.

Circular Belief Propagation (CBP) 是 Belief Propagation (BP) 的扩展，通过学习检测和取消虚假相关性和置信度放大来限制循环引起的消息回声的负面影响，实验结果表明 CBP 在二进制概率图的数值实验中远远超过了 BP，并且与先前提出的算法相比表现良好。

循环置信传播用于近似概率推断

Circular Belief Propagation for Approximate Probabilistic Inference

Many complex systems are composed of interacting parts, and the underlying
laws are usually simple and universal. While graph neural networks provide a
useful relational inductive bias for modeling such systems, generalization to
new system instances of the same type is less studied. In this work we trained
graph neural networks to fit time series from an example nonlinear dynamical
system, the belief propagation algorithm. We found simple interpretations of
the learned representation and model components, and they are consistent with
core properties of the probabilistic inference algorithm. We successfully
identified a 'graph translator' between the statistical interactions in belief
propagation and parameters of the corresponding trained network, and showed
that it enables two types of novel generalization: to recover the underlying
structure of a new system instance based solely on time series observations, or
to construct a new network from this structure directly. Our results
demonstrated a path towards understanding both dynamics and structure of a
complex system and how such understanding can be used for generalization.

本研究训练了图神经网络以适应来自非线性动力系统的时间序列，发现了学习表示和模型组件的简单解释，并成功地确定了 ' 图翻译器 '，使两种新类型广义：仅基于时间序列观测来恢复新系统实例的潜在结构，或者直接从该结构构造新网络。结果表明，理解复杂系统的动态和结构及其如何用于泛化的途径。