Dense Neuro-Symbolic Reasoning in a Unified Geometry State
Geometry reasoning is naturally stateful: solving a problem repeatedly alternates between structural proposals and exact deductions. We formulate this process as dense neural-symbolic coupling, in which neural guidance and symbolic execution share a typed state and communicate through executable actions at every search step. Neural proposals contribute theorem instances, constructions, and algebraic bridges; the symbolic runtime applies registered rules, propagates exact constraints, and records provenance. A nested controller allocates computation first between neural and symbolic proposal sources and then among admitted actions. We instantiate the framework in OmniGeo, a single solver f...
| Authors | Ruoran Xu, Wending Gao, Haoyu Cheng et al. |
|---|---|
| Primary category | cs.AI |
| Published | 3 October 2026 |
| Last updated at source | 3 October 2026 |
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