mlsanityData to 7 Oct 2026

Input Convex Neural Networks

arXiv 1609.07152 ↗First posted 22 Sep 2016cs.LG math.OCcited by 407

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Abstract (arXiv)

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with a minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.

Key facts. Cited by 407 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Sep 2016.

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Citing papers per year: 2020: 1; 2021: 50; 2022: 58; 2023: 64; 2024: 76; 2025: 82; 2026: 76.

407 papers.

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38 more
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  3. 2021Polyconvex anisotropic hyperelasticity with neural networkscited by 54
  4. 2021Optimizing Functionals on the Space of Probabilities with Input Convex Neural Networkscited by 53
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  6. 2021Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimizationcited by 50
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  11. 2021Neural Monge Map estimation and its applicationscited by 40
  12. 2021Greedification Operators for Policy Optimization: Investigating Forward and Reverse KL Divergencescited by 40
  13. 2022A Neural-Network-Based Convex Regularizer for Inverse Problemscited by 40
  14. 2022Normalizing flow neural networks by JKO schemecited by 39
  15. 2023Generative Modeling through the Semi-dual Formulation of Unbalanced Optimal Transportcited by 39
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  21. 2023Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translationcited by 32
  22. 2022Fast Convex Optimization for Two-Layer ReLU Networks: Equivalent Model Classes and Cone Decompositionscited by 31
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  26. 2022On amortizing convex conjugates for optimal transportcited by 30
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  28. 2021Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equationscited by 28
  29. 2021Offline Reinforcement Learning for Autonomous Driving with Safety and Exploration Enhancementcited by 28
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  31. 2022Transformers from an Optimization Perspectivecited by 27
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  34. 2023What's in a Prior? Learned Proximal Networks for Inverse Problemscited by 24
  35. 2024Scaling physics-informed hard constraints with mixture-of-expertscited by 24
  36. 2024Dynamic Conditional Optimal Transport through Simulation-Free Flowscited by 24
  37. 2022Wasserstein Iterative Networks for Barycenter Estimationcited by 23
  38. 2022Alternating Differentiation for Optimization Layerscited by 22

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