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（DNNs）缺乏概率图模型（PGMs）所具有的精确语义与确定性概率解释。本文提出了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PGMs。研究表明，在前向传播过程中，DNNs实际上执行了PGM推理的近似操作，且该近似在此替代性PGM结构中具有精确性。本研究不仅补充了将神经网络描述为核机器或无限尺度高斯过程的现有理论，还阐明了DNNs对PGM精确推理所采用的一种更直接的近似方式。其潜在价值包括改进DNNs的教学方法与解释性，以及开发融合PGMs与DNNs优势的新型算法。