{"ID":3083623,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T03:54:17.966829144Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.06344","arxiv_id":"2606.06344","title":"Equivariant Neural Belief Propagation","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. We introduce Equivariant Neural Belief Propagation (ENBP), a factor-graph framework whose messages are equivariant Gaussian mixture models with sufficient statistics that transform exactly under $SE(3)$. Rank-2 precision matrices are synthesised via equivariant outer products, ingested through differentiable spectral decomposition, and kept tractable by a greedy KL-based mixture reduction that provably commutes with $SE(3)$. On GEOM-QM9 and GEOM-Drugs, ENBP achieves 98.9% conformational coverage at 0.090 $\\mathring{A}$ error with sub-second latency -- over $100\\times$ faster than diffusion baselines at higher accuracy. On multi-body robotic inference, vanilla loopy BP diverges at 15+ agents while ENBP converges with near-zero collision rates and machine-precision equivariance error (${\\sim}10^{-7}$ vs.\\ $10^{-1}$ for augmented baselines).","short_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 phy...","url_abs":"https://arxiv.org/abs/2606.06344","url_pdf":"https://arxiv.org/pdf/2606.06344v1","authors":"[\"Zehua Cheng\",\"Wei Dai\",\"Jiahao Sun\"]","published":"2026-06-04T16:16:51Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.SC\"]","methods":"[\"Diffusion Model\"]","has_code":false}