SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions
Classical ReLU-based Input Convex Neural Networks (ICNNs) are equivalent to the optimal value functions of Linear Programming (LP). This intrinsic structural equivalence restricts their representational capacity to piecewise-linear polyhedral functions. To overcome this representational bottleneck, we propose the SOC-ICNN, an architecture that generalizes the underlying optimization class from LP to Second-Order Cone Programming (SOCP). By explicitly injecting positive semi-definite curvature and Euclidean norm-based conic primitives, our formulation introduces native smooth curvature into the representation while preserving a rigorous optimization-theoretic interpretation. We formally pr...
| Authors | Kang Liu, Jianchen Hu, Wei Peng |
|---|---|
| Primary category | cs.LG |
| Published | 24 April 2026 |
| Last updated at source | 5 May 2026 |
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