A Compositional Theory of Curvature in Probabilistic Circuits
Quick summary
arXiv:2608.12869v1 Announce Type: cross Abstract: 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 i
Key takeaways
- arXiv:2608.12869v1 Announce Type: cross Abstract: 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.
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