Dual Certified White-Box Inference for Input Convex Neural Networks
Abstract
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/
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BibTeX
@misc{liu2026dual,
title = {{Dual Certified White-Box Inference for Input Convex Neural Networks}},
author = {Kang Liu and Jianchen Hu and Wei Peng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.04722},
eprint = {2605.04722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04722},
}
RIS
TY - UNPB
TI - Dual Certified White-Box Inference for Input Convex Neural Networks
AU - Kang Liu
AU - Jianchen Hu
AU - Wei Peng
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2605.04722
UR - https://arxiv.org/abs/2605.04722
AB - 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/
ER -