Saddle Networks: Structure-Preserving Architectures for Convex-Concave Functions

• URL: http://arxiv.org/abs/2605.28894v1
• Date: Wed, 27 May 2026 08:25:24 GMT
• Title: Saddle Networks: Structure-Preserving Architectures for Convex-Concave Functions
• Abstract summary: In many applications, the relevant function f(x,y) is convex in x and concave in y, and preserving this geometry is essential.<n>We introduce a structured separable decomposition that preserves the convex-concave geometry.<n>We then describe practical saddle network architectures that preserve convexity in x and concavity in y by construction.
• Score: 4.56877715768796
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Saddle-point models arise throughout optimization, optimal transport, robust learning, and control. In many applications, the relevant function f(x,y) is convex in x and concave in y, and preserving this geometry is essential for obtaining tractable min--max formulations and reliable certificates. We introduce a structured separable decomposition that preserves the convex-concave geometry and prove a complete one-dimensional approximation theorem under a mixed Monge-type convexity condition. We then describe practical saddle network architectures that preserve convexity in x and concavity in y by construction. The proposed architectures require only convexity-preserving neural networks, together with simple output transformations enforcing sign and concavity constraints. Finally, we report numerical benchmarks in dimension 1 and 5, showing that the proposed saddle networks achieve high accuracy on smooth, nonsmooth, and high-rank convex--concave test functions.

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