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A Compositional Theory of Curvature in Probabilistic Circuits — arXiv:2608.12869

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.12869
License (as archived): CC0-1.0
Archived: 2026-10-19T04:18:13.067Z
SHA-256 of the archived text: bb573e155013bde8878dced63e1002aafe4cb2333130734e7cfb4c3e3f543f23
Stable URL of this page: https://metraipolis.com/documento/dc_d81f01fc2abc

How to cite

A Compositional Theory of Curvature in Probabilistic Circuits — arXiv:2608.12869 — arXiv (en), https://arxiv.org/abs/2608.12869 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_d81f01fc2abc (Metraipolis archive dc_d81f01fc2abc, sha256 bb573e155013bde8878dced63e1002aafe4cb2333130734e7cfb4c3e3f543f23)

BibTeX

@misc{dcd81f01fc2abc,
  title = {A Compositional Theory of Curvature in Probabilistic Circuits — arXiv:2608.12869},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.12869},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_d81f01fc2abc; sha256 bb573e155013bde8878dced63e1002aafe4cb2333130734e7cfb4c3e3f543f23},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.12869. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Probabilistic Circuits (PCs) are generative models that support exact inference and, unlike deep neural networks, admit an exact and tractable measure of loss-surface curvature: the trace of the Hessian of the log-likelihood. Recent work regularizes this trace globally to bias learning toward flatter, better generalizing optima. We show that treating sharpness as a global regularizer can be misspecified for PCs, whose curvature is inherently compositional. We prove that each sum node's contribution to the Hessian trace factorizes exactly into its circuit flow, which measures how heavily the node is used, and a local sharpness term determined by its output distribution. This decomposition provides insights into why global sharpness regularization is depth biased and can lead to underfitting. Building on it, we introduce an adaptive sharpness aware regularizer that penalizes nodes based on intrinsic local curvature and preserves closed form EM updates. We also show that empirically, this targeted regularization recovers the generalization that global regularization sacrifices while retaining the robustness and benefits of sharpness aware learning.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-14 in cs.AI).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2608.12869 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T04:13:06.715Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-14?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).