Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificates
Smooth acyclicity constraints answer whether a weighted support is a DAG, whereas structure learning asks which support change should be made. Existing analyses establish degeneracy for particular constraint formulas but do not isolate what follows from smooth exactness itself. At a DAG boundary, we show that minimal cycle completions generate a squarefree monomial ideal containing every restricted Taylor jet of an exact representation. If the smallest completion has $q$ edges, the first possible response has order $q$ for a vector residual and $2q$ for a nonnegative scalar. Exponentially many constant-scale cyclic manifolds exhibit the same lack of ranking away from the boundary for NOTE...
| Authors | Rui Wu, Zongyuan Chen, Hong Xie et al. |
|---|---|
| Primary category | cs.LG |
| Published | 8 August 2026 |
| Last updated at source | 29 August 2026 |
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