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Paper · 2305.17583 · NeurIPS · 2024

On Neural Networks as Infinite Tree-Structured Probabilistic Graphical Models

Boyao Li, Alexander Thomson, Houssam Nassif, Matthew Engelhard, David Page

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 7 functions out of this paper's own repositories and ran 0 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
engelhard-lab/dnn_treepgm canonical 0 of 7
FunctionStatusWhere it lives
cont_bern_log_norm Not yet run engelhard-lab/dnn_treepgm/model.py
code served (permissive licence) · get_code("d34f7dd289b54567")
covertype Not yet run engelhard-lab/dnn_treepgm/datagen.py
code served (permissive licence) · get_code("9fe2624d6c30505c")
get_pdf_dataset Not yet run engelhard-lab/dnn_treepgm/synthetic.py
code served (permissive licence) · get_code("c9160cab40cffc68")
make_digit Not yet run engelhard-lab/dnn_treepgm/datagen.py
code served (permissive licence) · get_code("cecdb4590b47072c")
make_moon Not yet run engelhard-lab/dnn_treepgm/datagen.py
code served (permissive licence) · get_code("8182061f5e947d2b")
normal_logpdf Not yet run engelhard-lab/dnn_treepgm/model.py
code served (permissive licence) · get_code("8f3c00e6c1d9e951")
sampling Not yet run engelhard-lab/dnn_treepgm/synthetic.py
code served (permissive licence) · get_code("3599f178c703e331")

Repositories linked to this paper

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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.

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