mlsanityData to 7 Oct 2026

Fixed points of nonnegative neural networks

arXiv 2106.16239 ↗First posted 30 Jun 2021stat.ML cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

We use fixed point theory to analyze nonnegative neural networks, which we define as neural networks that map nonnegative vectors to nonnegative vectors. We first show that nonnegative neural networks with nonnegative weights and biases can be recognized as monotonic and (weakly) scalable mappings within the framework of nonlinear Perron-Frobenius theory. This fact enables us to provide conditions for the existence of fixed points of nonnegative neural networks having inputs and outputs of the same dimension, and these conditions are weaker than those recently obtained using arguments in convex analysis. Furthermore, we prove that the shape of the fixed point set of nonnegative neural networks with nonnegative weights and biases is an interval, which under mild conditions degenerates to a point. These results are then used to obtain the existence of fixed points of more general nonnegative neural networks. From a practical perspective, our results contribute to the understanding of the behavior of autoencoders, and we also offer valuable mathematical machinery for future developments in deep equilibrium models.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 22 of its 81 references that are in the map. First posted on arXiv 30 Jun 2021.

Builds on

22 of 81 references.

References · 22

  1. 2021Convex optimizationcited by 2,479
  2. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  3. 2019Deep Equilibrium Modelscited by 603
  4. 2020Deep Learning Techniques for Inverse Problems in Imagingcited by 290
  5. 2020Multiscale Deep Equilibrium Modelscited by 149
  6. 2017Solving ill-posed inverse problems using iterative deep neural networkscited by 145
  7. 2021Deep Equilibrium Architectures for Inverse Problems in Imagingcited by 126
  8. 2018Optimal Control Via Neural Networks: A Convex Approachcited by 82
  9. 2018Learning to Detectcited by 60
  10. 2020Training End-to-End Analog Neural Networks with Equilibrium Propagationcited by 57
  11. 2019Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operatorscited by 54
  12. 2017Recurrent Inference Machines for Solving Inverse Problemscited by 33
10 more
  1. 2019Adaptive Neural Signal Detection for Massive MIMOcited by 26
  2. 2018Deep Neural Network Structures Solving Variational Inequalitiescited by 25
  3. 2015Gamma Belief Networkscited by 19
  4. 2018Deep Learning of Nonnegativity-Constrained Autoencoders for Enhanced Understanding of Datacited by 9
  5. 2016Deep Learning of Part-based Representation of Data Using Sparse Autoencoders with Nonnegativity Constraintscited by 8
  6. 2019Connections between spectral properties of asymptotic mappings and solutions to wireless network problemscited by 6
  7. 2015Elementary Properties of Positive Concave Mappings with Applications to Network Planning and Optimizationcited by 4
  8. 2014Toward Energy-Efficient 5G Wireless Communications Technologiescited by 1
  9. 2018Spectral radii of asymptotic mappings and the convergence speed of the standard fixed point algorithmcited by 1
  10. 2019Iterative Neural Networks with Bounded Weightscited by 1

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Cited by year

Citing papers per year: 2024: 3; 2025: 2.

5 papers.

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  2. 2024Positive concave deep equilibrium modelscited by 7
  3. 2025Are We Measuring Oversmoothing in Graph Neural Networks Correctly?cited by 6
  4. 2024Subhomogeneous Deep Equilibrium Modelscited by 3
  5. 2025Random weights of DNNs and emergence of fixed pointscited by 1