# Dual Certified White-Box Inference for Input Convex Neural Networks

arXiv: https://arxiv.org/abs/2605.04722 · HTML: https://mlsanity.com/paper/2605.04722/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 30 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 16 of 16)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark](https://mlsanity.com/paper/2106.01954/) (2021)
- [Convex Potential Flows: Universal Probability Distributions with Optimal Transport and Convex Optimization](https://mlsanity.com/paper/2012.05942/) (2020)
- [A mathematical model for automatic differentiation in machine learning](https://mlsanity.com/paper/2006.02080/) (2020)
- [Nonsmooth Implicit Differentiation for Machine Learning and Optimization](https://mlsanity.com/paper/2106.04350/) (2021)
- [Input Convex Neural Networks for Building MPC](https://mlsanity.com/paper/2011.13227/) (2020)
- [A Semismooth Newton Method for Fast, Generic Convex Programming](https://mlsanity.com/paper/1705.00772/) (2017)
- [A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction](https://mlsanity.com/paper/2204.00406/) (2022)
- [On the complexity of nonsmooth automatic differentiation](https://mlsanity.com/paper/2206.01730/) (2022)
- [On the Correctness of Automatic Differentiation for Neural Networks with Machine-Representable Parameters](https://mlsanity.com/paper/2301.13370/) (2023)
- [A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport](https://mlsanity.com/paper/2310.14087/) (2023)
- [A quadratically convergent semismooth Newton method for nonlinear semidefinite programming without generalized Jacobian regularity](https://mlsanity.com/paper/2402.13814/) (2024)
- [SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions](https://mlsanity.com/paper/2604.22355/) (2026)

## Abstract (arXiv)

Input convex neural networks (ICNNs) are used to learn convex objectives whose minimizers define decisions, making efficient and reliable optimization central to inference. At nonsmooth inputs, automatic differentiation returns a single derivative rather than the full subdifferential governing optimality and descent. Second-order cone ICNNs (SOC-ICNNs) admit an exact representation as value functions of parametric second-order cone programs, providing a white-box approach to recovering their full subdifferentials from optimal dual multipliers and deriving explicit Hessians on smooth regions. Building on this representation, we develop dual-certified inference (DCI), which combines the network and feasible set geometries to obtain exact stationarity certificates and tangent common descent directions. DCI uses local curvature for Newton acceleration and an exact proximal safeguard. We establish global convergence and, under standard regularity conditions, local quadratic convergence near structurally nondegenerate interior minimizers. Numerical experiments validate the recovered geometry and demonstrate the reliability and efficiency of DCI. Code is avaliable at https://anonymous.4open.science/r/DCI-ICNN-507D/