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Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Probabilistic Modeling

Background:

  • Deep neural networks (DNNs) offer powerful predictive capabilities but lack the clear probabilistic interpretation and semantic precision of probabilistic graphical models (PGMs).
  • Existing research has drawn parallels between neural networks and kernel machines or Gaussian processes, but a direct link to PGM inference has remained less explored.

Purpose of the Study:

  • To bridge the interpretability gap between DNNs and PGMs by establishing an exact correspondence.
  • To demonstrate that DNNs perform precise approximations of PGM inference within a novel PGM structure.

Main Methods:

  • Construction of infinite tree-structured probabilistic graphical models (PGMs) that are isomorphic to deep neural networks (DNNs).
  • Analysis of the forward propagation process in DNNs to identify the underlying inference mechanisms in the corresponding PGM structure.

Main Results:

  • DNNs, through their forward propagation, execute precise approximations of exact inference in the newly constructed tree-structured PGMs.
  • This work provides a more direct interpretation of DNNs as performing approximate PGM inference compared to existing analogies.

Conclusions:

  • The proposed framework offers a more direct and precise probabilistic interpretation of DNNs by linking them to exact inference in corresponding infinite PGMs.
  • This research facilitates improved understanding and pedagogy of DNNs and opens avenues for hybrid algorithms combining the strengths of DNNs and PGMs.