On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models
This work provides a theoretical foundation for interpreting neural networks, potentially improving pedagogy and enabling hybrid algorithms, though it is incremental in linking DNNs to existing probabilistic frameworks.
The paper tackles the lack of precise semantics and probabilistic interpretation in deep neural networks by constructing infinite tree-structured probabilistic graphical models that correspond exactly to neural networks, revealing that DNNs perform approximations of PGM inference in this structure.
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.