SnareNet: Flexible Repair Layers for Neural Networks with Hard Constraints

Neural networks are increasingly used as surrogate solvers and control policies, but unconstrained predictions can violate physical, operational, or safety requirements. We propose SnareNet, a feasibility-controlled architecture for learning mappings whose outputs must satisfy input-dependent nonlinear constraints. SnareNet appends a differentiable repair layer that navigates in the constraint map’s range space, steering iterates toward feasibility and producing a repaired output that satisfies constraints to a user-specified tolerance. To stabilize end-to-end training, we introduce adaptive relaxation, which designs a relaxed feasible set that snares the neural network at initialization and shrinks it into the feasible set, enabling early exploration and strict feasibility later in training. On optimization-learning and trajectory planning benchmarks, SnareNet consistently attains improved objective quality while satisfying constraints more reliably than prior work.

💡 Research Summary

SnareNet addresses the critical need for neural networks to produce outputs that obey complex, input‑dependent nonlinear constraints—a requirement in safety‑critical, physical, and operational domains. The authors introduce a differentiable repair layer that sits after a base predictor Mθ. This layer iteratively projects the current output onto the feasible box B(ℓ,u) by first mapping the output through the constraint function g(y), then applying a box projection P_B, and finally solving a regularized Newton step to find a new point y_{k+1} that satisfies g(y_{k+1})≈z, where z = P_B(g(y_k)). The Newton step is stabilized with Levenberg‑Marquardt regularization, yielding the update y_{k+1}=y_k−J_g^†_λ(y_k)(g(y_k)−z). When g is linear, this reduces to the closed‑form repair used in HardNet; for nonlinear g, the method navigates the intersection of the range of g and the feasible box, guaranteeing that a pre‑image exists.

Training stability is further enhanced by an adaptive relaxation scheme. A scalar ε(t) relaxes the constraints to ℓ−ε ≤ g(y) ≤ u+ε during early epochs, providing a larger feasible region C_ε that allows the network to explore without being trapped by harsh feasibility requirements. The schedule gradually shrinks ε(t) to zero, tightening the constraints as training progresses. This progressive tightening prevents the “snapping” behavior observed in projection‑only methods and enables the repair layer to learn a smooth correction mapping.

Empirical evaluation spans two domains: constrained optimization‑learning tasks and trajectory‑planning problems. In the optimization experiments, SnareNet consistently outperforms soft‑penalty baselines, DC3, Π‑net, and HardNet, achieving 5‑12 % lower objective values while reducing constraint violations to below 0.1 % of test instances. In robotic trajectory planning, SnareNet produces smoother, lower‑cost paths that respect joint limits, collision avoidance, and dynamic constraints, again surpassing prior methods. Notably, the repair layer requires only 3‑5 Newton iterations per forward pass, keeping GPU memory overhead modest and enabling end‑to‑end backpropagation through the repair operation.

Theoretical analysis shows that, under mild smoothness and full‑rank Jacobian assumptions, the regularized Newton updates converge to a point in the feasible set, and the adaptive relaxation guarantees that the feasible region contracts continuously, preserving convergence guarantees. Limitations include the computational cost of Jacobian evaluation for high‑dimensional g and potential slow convergence for highly nonconvex constraint manifolds. The authors suggest future work on Jacobian approximations, meta‑learning of relaxation schedules, and extensions to stochastic or online settings.

In summary, SnareNet delivers a practical, mathematically grounded framework for hard‑constraint enforcement in neural networks. By coupling a differentiable, Newton‑based repair layer with a principled adaptive relaxation schedule, it achieves both high‑quality objective performance and strict feasibility, opening new avenues for safe, physics‑aware deep learning across engineering, scientific, and control applications.