New Method Improves Hard Constraint Handling in LTN-GANs.

Logic Tensor Network-Enhanced Generative Adversarial Networks (LTN-GANs) incorporate background knowledge by grounding logical axioms as predicates, training the generator to increase their satisfaction. Previous LTN-GAN methods applied this predicate-level grounding to all constraints, improving satisfaction but failing to embed hard structural constraints—rules like orderings or positivity that must always hold. These methods often clamped violating samples onto the feasible boundary, ensuring validity but sacrificing realism. This new work investigates grounding each axiom as a function symbol within the LTN framework. This approach allows the constrained variable to be computed directly, rather than merely scored. By forming a "chart" or coordinate system within the feasible region, every generated sample is valid by construction, and the crucial margin distribution—how far a sample is from a boundary—is learned and preserved. The research demonstrates that while boundary clamping produces valid outputs, it often loses the realistic distribution of the margin. A diagnostic resolution ratio (R) is introduced, which can predict before training whether a chosen grounding method will succeed. Function symbols avoid the failures of predicate grounding and clamping, ensuring both validity and realism in generated data, especially when R is large.