Context-Conditioned Monotonic Response Surface Networks

In a partially monotonic setting, unconstrained features may not only affect the output nonmonotonically but also change the shape of the monotonic response. Additive branches and scalar calibration can limit context-dependent variation in the constrained response, while lattice architectures support richer interactions. To model this variation explicitly, Context-Conditioned Monotonic Response Surface Networks (CMRSN) use unconstrained context features to modulate only monotonicity-safe quantities, including positive basis scales, basis shifts, expert gates, and normalized nonnegative score directions. Each expert combines a context-modulated smooth shape block with an ordered Bernstein block to model multivariate monotonic response surfaces whose shapes vary across contexts. Theoretical analysis establishes exact partial monotonicity and, with sufficient model capacity, universal approximation of continuous partially monotonic score functions. Experiments on regression, binary classification, and ordinal classification show competitive predictive performance while maintaining zero sampled monotonicity violations. A controlled multivariate synthetic task further demonstrates recovery of context-dependent response geometry by comparing results with known conditional probabilities and expected-response surfaces.