mlsanityData to 14 Oct 2026

Neural network training under semidefinite constraints

arXiv 2201.00632 ↗First posted 3 Jan 2022cs.LG cs.SY eess.SYcited by 11

Not on the map. Why?

Abstract (arXiv)

This paper is concerned with the training of neural networks (NNs) under semidefinite constraints, which allows for NN training with robustness and stability guarantees. In particular, we focus on Lipschitz bounds for NNs. Exploiting the banded structure of the underlying matrix constraint, we set up an efficient and scalable training scheme for NN training problems of this kind based on interior point methods. Our implementation allows to enforce Lipschitz constraints in the training of large-scale deep NNs such as Wasserstein generative adversarial networks (WGANs) via semidefinite constraints. In numerical examples, we show the superiority of our method and its applicability to WGAN training.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 15 of its 27 references that are in the map. First posted on arXiv 3 Jan 2022.

Builds on

15 of 27 references.

References · 15

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2021Convex optimizationcited by 2,515
  4. 2017Improved Training of Wasserstein GANscited by 2,235
  5. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  6. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 101
  7. 2020Training robust neural networks using Lipschitz boundscited by 99
  8. 2018The Singular Values of Convolutional Layerscited by 95
  9. 2016Label-Free Supervision of Neural Networks with Physics and Domain Knowledgecited by 74
  10. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 44
  11. 2017Imposing Hard Constraints on Deep Networks: Promises and Limitationscited by 43
  12. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
3 more
  1. 2020Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimizationcited by 18
  2. 2020Offset-free setpoint tracking using neural network controllerscited by 10
  3. 2021Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multiplierscited by 6

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 2; 2023: 2; 2024: 4; 2025: 1; 2026: 2.

11 papers.

  1. 2023RAYEN: Imposition of Hard Convex Constraints on Neural Networkscited by 30
  2. 2022Lipschitz constant estimation for 1D convolutional neural networkscited by 13
  3. 2023Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramiancited by 9
  4. 2022Synthesis of Stabilizing Recurrent Equilibrium Network Controllerscited by 8
  5. 2024Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guaranteescited by 4
  6. 2024State space representations of the Roesser type for convolutional layerscited by 3
  7. 2024LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layerscited by 2
  8. 2024Identification For Control Based on Neural Networks: Approximately Linearizable Modelscited by 1
  9. 2025A Scalable Approach for Safe and Robust Learning via Lipschitz-Constrained Networkscited by 0
  10. 2026Scalable Incremental Robustness Analysis of Neural Network Feedback Systemscited by 0
  11. 2026Learning Provable Neural Network Observer for Uncertain Dynamical Systemscited by 0