A Unified Neural Architecture for Variable-Wise Shape Constraints

We introduce COMONet (Convex-Concave and Monotonicity-Constrained Neural Networks), a unified architecture for enforcing variable-wise shape constraints in neural networks. COMONet addresses the limitations of prior methods that either support only a restricted subset of monotonicity and curvature constraints or enforce them through penalties without strict architectural guarantees. Our framework assigns each input variable to one of eight shape regimes, covering monotonicity, convexity, concavity, and their combinations. This is achieved through a partially connected architecture that routes each variable to specialized units equipped with sign-constrained weights and constraint-preserving activation functions. We also provide theoretical guarantees showing that COMONet satisfies the prescribed variable-wise shape constraints by construction. Experiments on synthetic and real-world datasets demonstrate that COMONet achieves competitive performance and remains robust to noise while preserving its architectural guarantees. COMONet thus offers a practical and principled framework for incorporating domain knowledge as shape constraints into neural network training.