Input Convex Neural Networks

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Input convex neural networks (ICNNs) constrain their layers so outputs are convex in selected inputs, making them useful for modeling costs, potentials, and optimization objectives. Common designs use nonnegative weights and convex activations; variants add maxout or conic primitives to increase expressiveness, and ICNNs also serve as learned surrogates in optimization and optimal transport. Work assesses function approximation, downstream decision quality, and solver performance in settings such as convex regression, transport, and applied planning. Convexity can enable tractable optimization and useful geometric guarantees, but expressiveness, training difficulty, and the computational cost of sensitivity analysis or exact optimization remain important tensions.

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14 papers3 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

Universal neural network approximation of symmetric polyconvex energies and envelopes
Oct 23, 2026Florian GammerNeural Network Approximation Theory Input Convex Neural Networks
Faculty of Mathematics, University of Regensburg, Universitätsstraße 31 93053 Regensburg, Germany
Convex Equilibrium Potentials for Monge--Ampère: Curvature Bounds and A Posteriori Evaluation
Oct 22, 2026Edison Vázquez, Yingdong Lu, Tomasz NowickiNeural PDE Solvers Partial Differential Equations
Departamento de Matemáticas, CINVESTAV, México · IBM Research, Thomas J. Watson Research Center, Yorktown Heights, New York, USA
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
Parameterized Complexity of $L_p$ -Lipschitz Constants for Input Convex Neural Networks and $L_p$ -Norm Maximization over Zonotopes
Aug 25, 2026Aritra Das, Vincent Froese, Moritz Grillo +6Lipschitz Neural Networks Parameterized Complexity
Ashoka University, Truth Audit Labs · Technische Universität Berlin · Max Planck Institute for Mathematics in the Sciences +3
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 PengSecond-Order Cone Programming Neural Network Optimization
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 Second-Order Cone Programming
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
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Universal neural network approximation of symmetric polyconvex energies and envelopes

Florian Gammer

Faculty of Mathematics, University of Regensburg, Universitätsstraße 31 93053 Regensburg, Germany

Neural Network Approximation Theory Input Convex Neural Networks

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Symmetric polyconvexity provides a sufficient condition for weak lower semicontinuity in small-strain elasticity and a tractable lower bound for the relaxation of non-(quasi)convex energies. Since classical algorithms for computing such functions can be computationally expensive, neural network approximations have recently emerged as an alternative. A central difficulty with establishing such neural network based approaches for symmetric polyconvexity is the additional monotonicity property. As we show, the corresponding weight restrictions on ReLU-based input-convex networks do not yield universal approximation of the lifted representers. Here, we introduce symmetric polyconvex neural networks (SPCNNs) for constitutive modeling and approximation of symmetric polyconvex envelopes. The deep architecture combines convexity with the monotonicity required of a representer in the space of minors. We prove a universal approximation theorem for symmetric polyconvex energies, without requiring isotropy, and quantify the number of affine pieces attainable by the lifted network and derive reduced architectures for isotropic energies. Numerical examples illustrate stress-based regression and approximation of the symmetric polyconvex envelope of a double-well potential. Symmetric polyconvexity is guaranteed by construction, while the accuracy of the fitted energies and envelopes is assessed numerically.