Equivariant Neural Belief Propagation
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 trac...
| Authors | Zehua Cheng, Wei Dai, Jiahao Sun |
|---|---|
| Primary category | cs.LG |
| Published | 4 June 2026 |
| Last updated at source | 4 June 2026 |
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