FENCE: Enforcing Mixed Functional Constraints in Neural Fields

Enforcing constraints at sampled points does not guarantee that a neural field remains admissible throughout the domain. We introduce Functional Equality– iNequality Constraint Enforcement (FENCE), which assembles linear field functionals, basis envelopes, and cover-dependent variation margins into a finite convex feasible set enforced by a standard differentiable QP layer. For representations with valid enclosure or variation bounds, this jointly enforces equalities and continuous-domain inequalities without a nonlinear inner solve. On heat design, sufficient constraints pass all independent dense and finite-difference checks across held-out tasks and seeds. Constraint exchange preserves full-system objectives while cutting final QP size by over two orders of magnitude on a development cover sweep. On motion retargeting, derivative envelopes meet continuous rate limits on every held-out clip where sampling misses inter-sample violations, with < 0.1% mean objective overhead relative to analytic exchange. Matched QP implementations confirm that coverage follows from the constraint construction