mlsanityData to 7 Oct 2026

Interpretable global minima of deep ReLU neural networks on sequentially separable data

arXiv 2405.07098 ↗First posted 11 May 2024cs.LG cs.AI math-phcited by 4

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Abstract (arXiv)

We explicitly construct zero loss neural network classifiers. We write the weight matrices and bias vectors in terms of cumulative parameters, which determine truncation maps acting recursively on input space. The configurations for the training data considered are (i) sufficiently small, well separated clusters corresponding to each class, and (ii) equivalence classes which are sequentially linearly separable. In the best case, for Q classes of data in ℝM, global minimizers can be described with Q(M+2) parameters.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 14 of its 26 references that are in the map. First posted on arXiv 11 May 2024.

Builds on

14 of 26 references.

References · 14

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,597
  2. 2020Prevalence of Neural Collapse during the terminal phase of deep learning trainingcited by 713
  3. 2017Deep Neural Networks as Gaussian Processescited by 617
  4. 2017Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networkscited by 304
  5. 2014The Loss Surfaces of Multilayer Networkscited by 278
  6. 2016Deep Learning without Poor Local Minimacited by 233
  7. 2021Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Pathcited by 156
  8. 2020Neural collapse with unconstrained featurescited by 140
  9. 2017An Analytical Formula of Population Gradient for two-layered ReLU network and its Applications in Convergence and Critical Point Analysiscited by 52
  10. 2023Hidden symmetries of ReLU networkscited by 38
  11. 2021The loss landscape of deep linear neural networks: a second-order analysiscited by 24
  12. 2022Functional dimension of feedforward ReLU neural networkscited by 20
2 more
  1. 2023Geometric structure of Deep Learning networks and construction of global mathcal L2 minimizerscited by 6
  2. 2023Geometric structure of shallow neural networks and constructive mathcal L2 cost minimizationcited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 1.

4 papers.

  1. 2026Air-Know: Arbiter-Calibrated Knowledge-Internalizing Robust Network for Composed Image Retrievalcited by 17
  2. 2025Derivation of effective gradient flow equations and dynamical truncation of training data in Deep Learningcited by 0
  3. 2025Architecture independent generalization bounds for overparametrized deep ReLU networkscited by 0
  4. 2025Explicit neural network classifiers for non-separable datacited by 0