Deep neural networks (DNNs) lack the precise semantics and definitive probabilistic interpretation of probabilistic graphical models (PGMs). In this paper, we propose an innovative solution by constructing infinite tree-structured PGMs that correspond exactly to neural networks. Our research reveals that DNNs, during forward propagation, indeed perform approximations of PGM inference that are precise in this alternative PGM structure. Not only does our research complement existing studies that describe neural networks as kernel machines or infinite-sized Gaussian processes, it also elucidates a more direct approximation that DNNs make to exact inference in PGMs. Potential benefits include improved pedagogy and interpretation of DNNs, and algorithms that can merge the strengths of PGMs and DNNs.

翻译：深度神经网络（DNN）缺乏概率图模型（PGM）所具有的精确语义与确定的概率解释。本文提出一种创新性解决方案，通过构建与神经网络精确对应的无限树结构概率图模型。研究表明，前向传播过程中的深度神经网络确实在对这种替代性PGM结构进行精确的概率推理近似。本研究不仅补充了将神经网络描述为核机器或无限高斯过程的现有研究，还阐明了DNN对PGM精确推理所采用的更直接近似方法。潜在价值包括改进DNN的教学方法与解释机制，以及开发融合PGM与DNN优势的算法。