# Painless step size adaptation for SGD

arXiv: https://arxiv.org/abs/2102.00853 · HTML: https://mlsanity.com/paper/2102.00853/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 111 references that are in the map.
- First posted on arXiv 1 Feb 2021.

## Builds on (most cited first, 30 of 40)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [A Survey on Explainable Artificial Intelligence (XAI): Towards Medical XAI](https://mlsanity.com/paper/1907.07374/) (2019)
- [In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning](https://mlsanity.com/paper/1412.6614/) (2014)
- [On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization](https://mlsanity.com/paper/1802.06509/) (2018)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss](https://mlsanity.com/paper/2002.04486/) (2020)
- [Characterizing Implicit Bias in Terms of Optimization Geometry](https://mlsanity.com/paper/1802.08246/) (2018)
- [Learning Overparameterized Neural Networks via Stochastic Gradient Descent on Structured Data](https://mlsanity.com/paper/1808.01204/) (2018)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [Deep Information Propagation](https://mlsanity.com/paper/1611.01232/) (2016)
- [A Convergence Analysis of Gradient Descent for Deep Linear Neural Networks](https://mlsanity.com/paper/1810.02281/) (2018)
- [On the Origin of Implicit Regularization in Stochastic Gradient Descent](https://mlsanity.com/paper/2101.12176/) (2021)
- [Adaptive Gradient Methods with Dynamic Bound of Learning Rate](https://mlsanity.com/paper/1902.09843/) (2019)
- [Towards moderate overparameterization: global convergence guarantees for training shallow neural networks](https://mlsanity.com/paper/1902.04674/) (2019)
- [An Exponential Learning Rate Schedule for Deep Learning](https://mlsanity.com/paper/1910.07454/) (2019)
- [Painless Stochastic Gradient: Interpolation, Line-Search, and Convergence Rates](https://mlsanity.com/paper/1905.09997/) (2019)
- [On the Impact of the Activation Function on Deep Neural Networks Training](https://mlsanity.com/paper/1902.06853/) (2019)
- [Overparameterized Nonlinear Learning: Gradient Descent Takes the Shortest Path?](https://mlsanity.com/paper/1812.10004/) (2018)
- [How Much Over-parameterization Is Sufficient to Learn Deep ReLU Networks?](https://mlsanity.com/paper/1911.12360/) (2019)
- [A Unifying View on Implicit Bias in Training Linear Neural Networks](https://mlsanity.com/paper/2010.02501/) (2020)
- [Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression](https://mlsanity.com/paper/1602.05419/) (2016)
- [Stochastic Gradient Descent on Separable Data: Exact Convergence with a Fixed Learning Rate](https://mlsanity.com/paper/1806.01796/) (2018)
- [Learning a Single Neuron with Gradient Methods](https://mlsanity.com/paper/2001.05205/) (2020)
- [Agnostic Learning of a Single Neuron with Gradient Descent](https://mlsanity.com/paper/2005.14426/) (2020)

## Abstract (arXiv)

Convergence and generalization are two crucial aspects of performance in neural networks. When analyzed separately, these properties may lead to contradictory results. Optimizing a convergence rate yields fast training, but does not guarantee the best generalization error. To avoid the conflict, recent studies suggest adopting a moderately large step size for optimizers, but the added value on the performance remains unclear. We propose the LIGHT function with the four configurations which regulate explicitly an improvement in convergence and generalization on testing. This contribution allows to: 1) improve both convergence and generalization of neural networks with no need to guarantee their stability; 2) build more reliable and explainable network architectures with no need for overparameterization. We refer to it as "painless" step size adaptation.