# Rethinking Gauss-Newton for learning over-parameterized models

arXiv: https://arxiv.org/abs/2302.02904 · HTML: https://mlsanity.com/paper/2302.02904/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 56 references that are in the map.
- First posted on arXiv 6 Feb 2023.

## Builds on (most cited first, 30 of 36)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [New insights and perspectives on the natural gradient method](https://mlsanity.com/paper/1412.1193/) (2014)
- [On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transport](https://mlsanity.com/paper/1805.09545/) (2018)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [Kernel and Rich Regimes in Overparametrized Models](https://mlsanity.com/paper/2002.09277/) (2020)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Practical Gauss-Newton Optimisation for Deep Learning](https://mlsanity.com/paper/1706.03662/) (2017)
- [A Kronecker-factored approximate Fisher matrix for convolution layers](https://mlsanity.com/paper/1602.01407/) (2016)
- [Implicit regularization for deep neural networks driven by an Ornstein-Uhlenbeck like process](https://mlsanity.com/paper/1904.09080/) (2019)
- [Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity](https://mlsanity.com/paper/2106.09524/) (2021)
- [Does data interpolation contradict statistical optimality?](https://mlsanity.com/paper/1806.09471/) (2018)
- [Fast Convergence of Natural Gradient Descent for Overparameterized Neural Networks](https://mlsanity.com/paper/1905.10961/) (2019)
- [Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs](https://mlsanity.com/paper/2206.00939/) (2022)
- [A Unifying View on Implicit Bias in Training Linear Neural Networks](https://mlsanity.com/paper/2010.02501/) (2020)
- [SGD with Large Step Sizes Learns Sparse Features](https://mlsanity.com/paper/2210.05337/) (2022)
- [Sparse Optimization on Measures with Over-parameterized Gradient Descent](https://mlsanity.com/paper/1907.10300/) (2019)
- [Gram-Gauss-Newton Method: Learning Overparameterized Neural Networks for Regression Problems](https://mlsanity.com/paper/1905.11675/) (2019)
- [On the Convergence of Gradient Descent Training for Two-layer ReLU-networks in the Mean Field Regime](https://mlsanity.com/paper/2005.13530/) (2020)
- [Efficient Subsampled Gauss-Newton and Natural Gradient Methods for Training Neural Networks](https://mlsanity.com/paper/1906.02353/) (2019)
- [Non-Convex Bilevel Games with Critical Point Selection Maps](https://mlsanity.com/paper/2207.04888/) (2022)
- [Understanding Approximate Fisher Information for Fast Convergence of Natural Gradient Descent in Wide Neural Networks](https://mlsanity.com/paper/2010.00879/) (2020)
- [Regularized Newton Method with Global O(1/k2) Convergence](https://mlsanity.com/paper/2112.02089/) (2021)

## Built on by (most cited first, 6 of 6)

- [Exact Gauss-Newton Optimization for Training Deep Neural Networks](https://mlsanity.com/paper/2405.14402/) (2024)
- [Regularized Gauss-Newton for Optimizing Overparameterized Neural Networks](https://mlsanity.com/paper/2404.14875/) (2024)
- [A Riemannian Optimization Perspective of the Gauss-Newton Method for Feedforward Neural Networks](https://mlsanity.com/paper/2412.14031/) (2024)
- [Gradient-Normalized Smoothness for Optimization with Approximate Hessians](https://mlsanity.com/paper/2506.13710/) (2025)
- [Non-Asymptotic Optimization and Generalization Bounds for Stochastic Gauss-Newton in Overparameterized Models](https://mlsanity.com/paper/2511.03972/) (2025)
- [Convergence Analysis of Newton's Method for Neural Networks in the Overparameterized Limit](https://mlsanity.com/paper/2605.08352/) (2026)

## Abstract (arXiv)

This work studies the global convergence and implicit bias of Gauss Newton's (GN) when optimizing over-parameterized one-hidden layer networks in the mean-field regime. We first establish a global convergence result for GN in the continuous-time limit exhibiting a faster convergence rate compared to GD due to improved conditioning. We then perform an empirical study on a synthetic regression task to investigate the implicit bias of GN's method. While GN is consistently faster than GD in finding a global optimum, the learned model generalizes well on test data when starting from random initial weights with a small variance and using a small step size to slow down convergence. Specifically, our study shows that such a setting results in a hidden learning phenomenon, where the dynamics are able to recover features with good generalization properties despite the model having sub-optimal training and test performances due to an under-optimized linear layer. This study exhibits a trade-off between the convergence speed of GN and the generalization ability of the learned solution.