mlsanityData to 7 Oct 2026

Min-Max-Plus Neural Networks

arXiv 2102.06358 ↗First posted 12 Feb 2021cs.NE cs.AI cs.CVcited by 8

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Abstract (arXiv)

We present a new model of neural networks called Min-Max-Plus Neural Networks (MMP-NNs) based on operations in tropical arithmetic. In general, an MMP-NN is composed of three types of alternately stacked layers, namely linear layers, min-plus layers and max-plus layers. Specifically, the latter two types of layers constitute the nonlinear part of the network which is trainable and more sophisticated compared to the nonlinear part of conventional neural networks. In addition, we show that with higher capability of nonlinearity expression, MMP-NNs are universal approximators of continuous functions, even when the number of multiplication operations is tremendously reduced (possibly to none in certain extreme cases). Furthermore, we formulate the backpropagation algorithm in the training process of MMP-NNs and introduce an algorithm of normalization to improve the rate of convergence in training.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 14 of its 31 references that are in the map. First posted on arXiv 12 Feb 2021.

Builds on

14 of 31 references.

References · 14

  1. 2015Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classificationcited by 3,590
  2. 2016Understanding deep learning requires rethinking generalizationcited by 1,657
  3. 2016XNOR-Net: ImageNet Classification Using Binary Convolutional Neural Networkscited by 829
  4. 2015BinaryConnect: Training Deep Neural Networks with binary weights during propagationscited by 571
  5. 2016DoReFa-Net: Training Low Bitwidth Convolutional Neural Networks with Low Bitwidth Gradientscited by 557
  6. 2014On the Number of Linear Regions of Deep Neural Networkscited by 378
  7. 2013Maxout Networkscited by 186
  8. 2015The Power of Depth for Feedforward Neural Networkscited by 181
  9. 2018Tropical Geometry of Deep Neural Networkscited by 92
  10. 2019AdderNet: Do We Really Need Multiplications in Deep Learning?cited by 82
  11. 2018A Tropical Approach to Neural Networks with Piecewise Linear Activationscited by 26
  12. 2019A Universal Approximation Result for Difference of log-sum-exp Neural Networkscited by 9
2 more
  1. 2019Tropical Polynomial Division and Neural Networkscited by 5
  2. 2019Tropical Geometry and Piecewise-Linear Approximation of Curves and Surfaces on Weighted Latticescited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 0; 2023: 1; 2024: 0; 2025: 2; 2026: 4.

8 papers.

  1. 2023Multiplication-Free Transformer Training via Piecewise Affine Operationscited by 5
  2. 2021An Alternative Practice of Tropical Convolution to Traditional Convolutional Neural Networkscited by 4
  3. 2025Training Deep Morphological Neural Networks as Universal Approximatorscited by 1
  4. 2026Exploiting Subgradient Sparsity in Max-Plus Neural Networkscited by 1
  5. 2025Compound and Parallel Modes of Tropical Convolutional Neural Networkscited by 0
  6. 2026On the explainability of max-plus neural networkscited by 0
  7. 2026Beyond Affine Transformations: A Soft Dominance Layer for Coordinate-Wise Neural Computationcited by 0
  8. 2026Correlational Training of Morphological Neural Networkscited by 0