The article surveys recent progress in tractable probabilistic generative modeling, with a focus on Probabilistic Circuits (PCs). It offers a unified view of the trade‑offs between expressivity and tractability, outlining design principles, algorithmic extensions, and a taxonomy of the field. The review also covers deep and hybrid PCs that integrate ideas from deep neural models, and highlights challenges and open questions for future research.
arXiv:2605.29713v2 Announce Type: replace-cross Abstract: This book provides a compact, derivation-oriented introduction to the mathematical foundations of modern generative artificial intelligence....
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.
arXiv:2603. 11946v2 Announce Type: replace-cross Abstract: Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold.
arXiv:2610. 12520v1 Announce Type: cross Abstract: The goal of circuit discovery is to decompose a monolithic neural network into tiny modular subnetworks which are interpretable in the sense that each does an identifiable subtask.
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.
The paper introduces Particle GFlowNets, showing that Generative Marginalization Models (MaMs) are equivalent to Generative Flow Networks. It extends MaMs to non‑autoregressive sampling and proposes an automatic full‑state rejuvenation criterion based on the Gelman‑Rubin statistic to accelerate learning. Experiments demonstrate significant training speedups in large combinatorial spaces.
The paper introduces JSP-GFN, a Generative Flow Network that jointly infers the structure and parameters of a Bayesian Network. It sequentially generates a directed acyclic graph edge by edge and then samples the corresponding conditional probability parameters once the full structure is known. Experiments on simulated and real data show that JSP‑GFN accurately approximates the joint posterior and outperforms existing methods.
arXiv:2607. 19126v1 Announce Type: cross Abstract: Neural Markov Logic Networks (NMLNs) are a flexible neurosymbolic relational model.
arXiv:2608. 16565v1 Announce Type: new Abstract: This cumulative habilitation thesis studies probabilistic circuits (PCs) as a powerful and tractable framework for reasoning and learning under uncertainty in artificial intelligence (AI).
arXiv:2603. 14161v2 Announce Type: replace Abstract: Many disciplines need quantitative models that synthesize experimental data across multiple instances of the same general system.
arXiv:2210.00580v4 Announce Type: replace Abstract: This paper builds bridges between two families of probabilistic algorithms: (hierarchical) variational inference (VI), which is typically used to m...
The article explores how biological learning and decision-making, often modeled as Bayesian processes, can be replicated in computing systems by leveraging noisy neural and synaptic dynamics for stochastic sampling. It proposes a biologically grounded framework where internal energy functions capture uncertainty over latent states and model parameters, enabling predictive coding networks to perform Markov chain Monte Carlo sampling. By drawing parallels between intrinsic biological noise and electrical noise in emerging probabilistic analogue memory technologies, the authors argue that analogue in‑memory computing hardware offers a massively scalable and energy‑efficient solution for probabilistic inference.