Input Convex Neural Networks

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Beyond Overparameterization: Provable Learning of Input-Convex Multi-Layer Polynomial Networks with Active Queries
Oct 4, 2026Jinqi Tang, Qian Chen, Shihong Ding +1Polynomial Neural Networks Input Convex Neural Networks
Peking University
Input convex neural networks as surrogates in mathematical optimisation
Aug 10, 2026Yu Liu, Jan Kronqvist, Fabricio OliveiraSurrogate-Assisted Optimization Mixed-Integer Linear Programming
Department of Mathematics and Systems Analysis, School of Science, Aalto University, Espoo, Finland · Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden · DTU Management, Technical University of Denmark, Lyngby, Denmark
Role-Aware Neural Convex Divergence Heads for Asymmetric Representation Learning
Jul 2, 2026He Huang, Lu Shen, Yunfeng Huang +1Representation Learning Functional Bregman Divergences
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, China · School of Food Science, Chongqing Technology and Business University, Chongqing,2026 400067, China · Faculty of Electrical EngineeringUniversity, andDortmund,InformationGermanyTechnology, TU Dortmund +1
LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization
Jun 8, 2026Binh Nguyen, Trinh Tran, Truong X. NghiemLearning to Optimize Alternating Direction Method of Multipliers
Department of Electrical and Computer Engineering, College of Engineering and Computer Science, University of Central Florida, Orlando, FL 32816, USA
A lift for input-convex neural net training
May 22, 2026Ali SiahkoohiNeural Network Optimization Input Convex Neural Networks
Department of Computer Science University of Central Florida
Convex Compositional Reasoning Models
May 22, 2026Meir Roketlishvili, Semyon Semenov, Maksim Bobrin +7Compositional Reasoning Energy-Based Models
Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE · Applied AI Institute, Computational Imaging Lab · AXXX
Structure-Preserving Reconstruction of Convex Lipschitz Functionals on Hilbert Spaces from Finite Samples
May 8, 2026Anastasis KratsiosInput Convex Neural Networks Neural Network Approximation Theory
Exact Dual Geometry of SOC-ICNN Value Functions
May 6, 2026Kang Liu, Jianchen Hu, Wei PengNeural Network Optimization Input Convex Neural Networks
School of Future Technology Xi’an Jiaotong University Xi’an, China · School of Future Technology School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China · School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China
Hyper Input Convex Neural Networks for Shape Constrained Learning and Optimal Transport
Apr 29, 2026Shayan Hundrieser, Insung Kong, Johannes Schmidt-HieberInput Convex Neural Networks Neural Network Approximation Theory
*Department of Applied Mathematics, University of Twente, Enschede, The Netherlands
SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions
Apr 24, 2026Kang Liu, Jianchen Hu, Wei PengNeural Surrogate Modeling Input Convex Neural Networks
School of Future Technology Xi’an Jiaotong University Xi’an, China · School of Future Technology School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China · School of Automation Science and Engineering Xi’an Jiaotong University Xi’an, China
Amortized Maximum Inner Product Search with Learned Support Functions
Mar 9, 2026Theo X. Olausson, João Monteiro, Michal Klein +1Amortized Inference Information Retrieval
Apple

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Beyond Overparameterization: Provable Learning of Input-Convex Multi-Layer Polynomial Networks with Active Queries

Jinqi Tang, Qian Chen, Shihong Ding, Cong Fang

Peking University

Polynomial Neural Networks Input Convex Neural Networks Neural Network Approximation Theory

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The theoretical understanding of multi-layer neural networks is largely confined to overparameterized settings, which obscure parameter identifiability and incur high sample complexity. Neural tangent kernel (NTK) provides a general theory for wide networks, but does not offer efficient sample-complexity guarantees. Recent feature-learning results go beyond kernel methods for single-neuron, multi-index, and hierarchical targets. However, the analysis is often restricted to shallow or specific architectures and to the overparameterized regime. We break this paradigm to achieve parameter-level recovery of deep target networks, albeit by using active data queries. Specifically, we study

L

-layer polynomial networks with even degree-

k

monomial activations and nonnegative higher-layer weights. This structure makes the target network input-convex, while the optimization landscape remains highly nonconvex with respect to the parameters. Leveraging input convexity and active queries, we propose \textbf{ASPIRE} (\textbf{A}ctive \textbf{S}am\textbf{P}ling for \textbf{I}terative \textbf{R}ecovery via \textbf{E}igendirections), a layerwise sampling-based diagonalization algorithm that recovers all network parameters to

δ

-accuracy with sample complexity

\widetilde O_{k,L}\left(d^{L^2+O(L)}δ^{-2e}\right)

in polynomial time. To our knowledge, this is the \emph{first} parameter-recovery guarantee for deep target networks whose exponent grows only polynomially with depth, as well as the \emph{first} justification for the effectiveness of using high-quality data in neural network training, with a remarkably \emph{exponential} separation.

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