mlsanityData to 7 Oct 2026

Quiver neural networks

arXiv 2207.12773 ↗First posted 26 Jul 2022cs.LG math.RTcited by 4

Not on the map. Why?

Abstract (arXiv)

We develop a uniform theoretical approach towards the analysis of various neural network connectivity architectures by introducing the notion of a quiver neural network. Inspired by quiver representation theory in mathematics, this approach gives a compact way to capture elaborate data flows in complex network architectures. As an application, we use parameter space symmetries to prove a lossless model compression algorithm for quiver neural networks with certain non-pointwise activations known as rescaling activations. In the case of radial rescaling activations, we prove that training the compressed model with gradient descent is equivalent to training the original model with projected gradient descent.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 47 of its 72 references that are in the map. First posted on arXiv 26 Jul 2022.

Builds on

47 of 72 references.

References · 47

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  2. 2016Densely Connected Convolutional Networkscited by 6,691
  3. 2014Fully Convolutional Networks for Semantic Segmentationcited by 4,845
  4. 2017MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applicationscited by 3,827
  5. 2015Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Codingcited by 2,291
  6. 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,250
  7. 2016Group Equivariant Convolutional Networkscited by 1,154
  8. 2017Dynamic Routing Between Capsulescited by 689
  9. 2020What is the State of Neural Network Pruning?cited by 578
  10. 2020Picking Winning Tickets Before Training by Preserving Gradient Flowcited by 467
  11. 2013Do Deep Nets Really Need to be Deep?cited by 466
  12. 2017Sharp Minima Can Generalize For Deep Netscited by 462
35 more
  1. 2019General E(2)-Equivariant Steerable CNNscited by 441
  2. 20183D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Datacited by 348
  3. 2021Vector Neurons: A General Framework for SO(3)-Equivariant Networkscited by 304
  4. 2016Steerable CNNscited by 298
  5. 2017A Survey of Model Compression and Acceleration for Deep Neural Networkscited by 298
  6. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  7. 2016Harmonic Networks: Deep Translation and Rotation Equivariancecited by 293
  8. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 262
  9. 2020Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Datacited by 248
  10. 2017Learning to Prune Deep Neural Networks via Layer-wise Optimal Brain Surgeoncited by 219
  11. 2015Quantized Convolutional Neural Networks for Mobile Devicescited by 212
  12. 2014Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decompositioncited by 199
  13. 2017Learning Steerable Filters for Rotation Equivariant CNNscited by 193
  14. 2014Compressing Deep Convolutional Networks using Vector Quantizationcited by 189
  15. 2017Equivariance Through Parameter-Sharingcited by 139
  16. 2015Path-SGD: Path-Normalized Optimization in Deep Neural Networkscited by 117
  17. 2015Convolutional neural networks with low-rank regularizationcited by 102
  18. 2019A Signal Propagation Perspective for Pruning Neural Networks at Initializationcited by 96
  19. 2016Fully-adaptive Feature Sharing in Multi-Task Networks with Applications in Person Attribute Classificationcited by 93
  20. 2016Exploiting Cyclic Symmetry in Convolutional Neural Networkscited by 91
  21. 2020A Wigner-Eckart Theorem for Group Equivariant Convolution Kernelscited by 46
  22. 2016Recurrent Highway Networkscited by 36
  23. 2020Lossless Compression of Deep Neural Networkscited by 34
  24. 2018G-SGD: Optimizing ReLU Neural Networks in its Positively Scale-Invariant Spacecited by 26
  25. 2020Algebraic Neural Networks: Stability to Deformationscited by 22
  26. 2021Scaling Up Exact Neural Network Compression by ReLU Stabilitycited by 19
  27. 2020The Representation Theory of Neural Networkscited by 18
  28. 2018Rotation Equivariance and Invariance in Convolutional Neural Networkscited by 12
  29. 2020Lossless Compression of Structured Convolutional Models via Liftingcited by 11
  30. 2018Y-Net: A deep Convolutional Neural Network for Polyp Detectioncited by 10
  31. 2021Universal approximation and model compression for radial neural networkscited by 7
  32. 2020Homotopy Theoretic and Categorical Models of Neural Information Networkscited by 4
  33. 2015An exploration of parameter redundancy in deep networks with circulant projectionscited by 3
  34. 2021K"ahler Geometry of Quiver Varieties and Machine Learningcited by 3
  35. 2021Double framed moduli spaces of quiver representationscited by 2

Built on by

Cited by year (2026 to 7 Oct)

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

4 papers.

  1. 2023Hidden symmetries of ReLU networkscited by 38
  2. 2023Improving Convergence and Generalization Using Parameter Symmetriescited by 23
  3. 2024Advancing Neural Network Performance through Emergence-Promoting Initialization Schemecited by 0
  4. 2026PAGR: Proof-Carrying Algebraic-Geometric Retrieval: A Quiver-, Provenance-, and Sheaf-Theoretic Framework for Grounded LLM Retrievalcited by 0