arXiv：cs.LG· Kang Liu, Jianchen Hu, Wei Peng·· 5 小时前AI 评分35
面向输入凸神经网络的双认证白盒推理
Dual Certified White-Box Inference for Input Convex Neural Networks
AI 导读
研究提出双认证推理（DCI），针对二阶锥输入凸神经网络（SOC-ICNNs），利用其作为参数化二阶锥规划值函数的精确表示，从最优对偶乘子恢复完整次微分，并在光滑区域推导显式 Hessian。DCI 结合网络与可行集几何获得精确驻点证书和切向共同下降方向，用局部曲率做 Newton 加速并配精确近端保护，具备全局收敛性，在标准正则条件下于结构非退化内点极小值附近实现局部二次收敛。
正文
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 this https URL
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Optimization and Control (math.OC) |
| Cite as: | arXiv:2605.04722 [cs.LG] |
| (or arXiv:2605.04722v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.04722 arXiv-issued DOI via DataCite |
Submission history
From: Kang Liu [view email]
[v1]
Wed, 6 May 2026 10:14:36 UTC (27 KB)
[v2]
Fri, 2 Oct 2026 16:00:10 UTC (114 KB)
来源：arXiv：cs.LG · arxiv.org