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:2606. 11831v1 Announce Type: cross Abstract: Neural relational inference (NRI) methods discover interaction graphs from trajectories through variational reasoning on discrete potential edges.
arXiv:2609.23774v1 Announce Type: new Abstract: Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings....
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
arXiv:2607. 08303v1 Announce Type: new Abstract: The problem of learning constant-depth circuits holds profound implications for computational learning theory.
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.
arXiv:2606. 06344v1 Announce Type: new Abstract: Probabilistic inference over spatially embedded variables requires beliefs that respect $SE(3)$ symmetry, yet existing equivariant networks produce only scalars and vectors -- not the rank-2 precision tensors needed for anisotropic uncertainty, and single-component messages collapse multi-modal energy landscapes to physically meaningless averages.
arXiv:2609. 29466v1 Announce Type: cross Abstract: Approximate message passing on factor graphs underlies two dominant families of probabilistic inference algorithms: expectation propagation (EP) and variational message passing (VMP).
arXiv:2310.02423v3 Announce Type: replace Abstract: We present a new algorithm for amortized inference in sparse probabilistic graphical models (PGMs), which we call $\Delta$-amortized inference ($\D...
arXiv:2609.40024v1 Announce Type: new Abstract: We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a direc...
The paper applies parameterised graph theory to tensor networks, showing that cutwidth and tree‑cutwidth bound the bond‑dimension overhead needed to represent a tensor‑network state as a matrix product state or tree tensor network. It derives graph‑dependent upper bounds on the sample and computational complexity of tensor‑network tomography, introducing a new graph parameter called learning complexity. Finally, it extends the framework to an agnostic learner that approximates any state with a tensor‑network state of given bond dimension, providing explicit graph‑dependent complexity bounds.
We develop a general method for amortized Bayesian inference on multilevel models of arbitrary structure. Given a generative model specified as a directed acyclic graph, our method automatically deriv...
arXiv:2607. 03329v1 Announce Type: new Abstract: Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks.