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

arXiv: https://arxiv.org/abs/2405.07098 · HTML: https://mlsanity.com/paper/2405.07098/

## Key facts

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

## Builds on (most cited first, 14 of 14)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [The Loss Surfaces of Multilayer Networks](https://mlsanity.com/paper/1412.0233/) (2014)
- [Deep Learning without Poor Local Minima](https://mlsanity.com/paper/1605.07110/) (2016)
- [Neural Collapse Under MSE Loss: Proximity to and Dynamics on the Central Path](https://mlsanity.com/paper/2106.02073/) (2021)
- [Neural collapse with unconstrained features](https://mlsanity.com/paper/2011.11619/) (2020)
- [An Analytical Formula of Population Gradient for two-layered ReLU network and its Applications in Convergence and Critical Point Analysis](https://mlsanity.com/paper/1703.00560/) (2017)
- [Hidden symmetries of ReLU networks](https://mlsanity.com/paper/2306.06179/) (2023)
- [The loss landscape of deep linear neural networks: a second-order analysis](https://mlsanity.com/paper/2107.13289/) (2021)
- [Functional dimension of feedforward ReLU neural networks](https://mlsanity.com/paper/2209.04036/) (2022)
- [Geometric structure of Deep Learning networks and construction of global mathcal L2 minimizers](https://mlsanity.com/paper/2309.10639/) (2023)
- [Geometric structure of shallow neural networks and constructive mathcal L2 cost minimization](https://mlsanity.com/paper/2309.10370/) (2023)

## Built on by (most cited first, 4 of 4)

- [Air-Know: Arbiter-Calibrated Knowledge-Internalizing Robust Network for Composed Image Retrieval](https://mlsanity.com/paper/2604.19386/) (2026)
- [Derivation of effective gradient flow equations and dynamical truncation of training data in Deep Learning](https://mlsanity.com/paper/2501.07400/) (2025)
- [Architecture independent generalization bounds for overparametrized deep ReLU networks](https://mlsanity.com/paper/2504.05695/) (2025)
- [Explicit neural network classifiers for non-separable data](https://mlsanity.com/paper/2504.18710/) (2025)

## 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.