🤖 AI Summary
Deep neural networks (DNNs) suffer from probabilistic semantic ambiguity, poor interpretability, and pedagogical challenges arising from abstraction. Method: This paper introduces, for the first time, a semantically rigorous, structurally explicit infinite tree-structured probabilistic graphical model (PGM), establishing a bijective correspondence between it and any DNN. Theoretically, DNN forward propagation is proven equivalent to exact (not approximate) inference on this infinite PGM; backpropagation corresponds to gradient-driven structured parameter learning. Contribution/Results: This unified modeling framework overcomes the traditional conceptual divide between PGMs and DNNs, providing a formal foundation for interpretable AI. It enables principled PGM–DNN hybrid algorithm design and fundamentally redefines the probabilistic semantic pedagogy of deep learning.
📝 Abstract
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.