arXiv:2607. 28706v1 Announce Type: cross Abstract: We study the convergence properties of the random-sweep Gibbs sampler for Gaussian graphical models with a thin-membrane prior.
arXiv:2607. 08303v1 Announce Type: new Abstract: The problem of learning constant-depth circuits holds profound implications for computational learning theory.
arXiv:2607. 07232v1 Announce Type: cross Abstract: Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.
Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem.
arXiv:2607. 18559v1 Announce Type: cross Abstract: Gaussian graphical model selection is usually studied under independent sampling, but in many applications the data arise as a single trajectory of a dependent stochastic process.
arXiv:2503. 14549v3 Announce Type: replace-cross Abstract: How can a cheap but biased sequential, finite-horizon sampler over a discrete space be corrected so that its terminal output follows a prescribed Gibbs distribution?
arXiv:2404.17763v3 Announce Type: replace-cross Abstract: Probabilistic graphical models that encode an underlying Markov random field are fundamental building blocks of generative modeling to learn...
The paper presents a computational framework for determining the maximum likelihood threshold (MLT) in colored Gaussian graphical models (CGGMs). It focuses on a geometric approach that seeks the minimal rank of a sample covariance matrix whose projection lies within the interior of the cone of sufficient statistics. The authors extend theoretical results from uncolored to colored models, introduce new symbolic algorithms, and demonstrate how topological data analysis (TDA) can alleviate computational challenges associated with traditional symbolic algebraic methods.
Transport-Coupled Bayesian Flows for Molecular Graph Generation (TopBF) addresses a key mismatch in existing diffusion models for molecular graph generation by eliminating the need for hard discretization during sampling. The framework generates graphs directly in continuous parameter distributions, learns graph topology via a Quasi-Wasserstein optimal‑transport coupling with geodesic costs, and enables property‑conditioned generation without retraining. Experiments on QM9 and ZINC250k show that TopBF achieves higher structural fidelity and more efficient generation compared to prior methods.
The paper introduces the Generalized Graph Variational Autoencoder (GGVA), which replaces the Kullback–Leibler divergence in the standard variational graph autoencoder with any member of the Rényi–Tsallis family of order $q$. The authors show that for $q<1$ the Tsallis divergence is bounded, whereas the KL and Rényi divergences are unbounded, and that this boundedness can significantly increase the amount of posterior information retained—up to 49× more than the VGAE on several benchmark graphs. Experiments demonstrate that the GGVA’s retained information improves node classification performance, though it does not improve link‑prediction accuracy and only delays, rather than prevents, posterior collapse.
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
arXiv:2606. 05042v1 Announce Type: new Abstract: Marginal inference in discrete graphical models forces a choice between exactness and scalability: exact algorithms are intractable for high-treewidth graphs, while iterative approximations (Belief Propagation, variational methods) sacrifice convergence guarantees on frustrated topologies.
arXiv:2607. 14304v1 Announce Type: cross Abstract: We study sparse random geometric graphs generated by connecting pairs of high-dimensional vectors whose inner product exceeds a threshold.