Typed signed-monotone dual Choquet-Stieltjes networks for semantically constrained grouped prediction.

Abstract

Grouped prediction over semantically labeled criteria may require signed directional constraints and non-additive interaction modeling. We study these requirements jointly through typed signed-monotone dual Choquet-Stieltjes networks (TSM-DCSNs), a constrained family for grouped inputs with adverse, benefit, and neutral score semantics. For a fixed typed score map, a shared threshold law drives trigger and veto Choquet-Stieltjes branches. Anchored additivity characterizes conditions that force affine collapse. Every normalized piecewise-linear threshold law on a fixed knot grid, including the affine law, is finitely identifiable on a nondegenerate criterion ray. Designated probes permit exact local recovery of branch weights and supported dual-capacity values, with stable recovery under bounded perturbations. For fixed k, block-k-additive instances admit polynomial-time forward evaluation and supported Möbius inversion from a polynomial number of designated probes. Synthetic probe experiments confirm machine-precision recovery in the matched noiseless regime and monotone error growth under bounded noise. On five grouped tabular benchmarks, all structured configurations attain zero signed-direction violations; validation-based rankings favor the full member on some tasks and reduced members on others. Because within-group score constructions differ, these comparisons are not single-component ablations. An outer-test-isolated nested pilot gate matches the descriptive full-versus-additive decision on only two of five datasets and makes three false skips relative to the stated descriptive reference, so it is not validated for pre-full-model screening. The contribution is a validation-selectable constrained family for semantically specified grouped prediction with analyzable threshold geometry and probe-based recovery of interaction structure, not a claim of uniform predictive superiority.