@inproceedings{
li2024on,
title={On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models},
author={Boyao Li and Alexander Joseph Thomson and houssam nassif and Matthew M. Engelhard and David Page},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=KcmhSrHzJB}
}
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.
On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models
Boyao Li Alexander Joseph Thomson houssam nassif Matthew M. Engelhard David Page