# Interpreting Adaptive Gradient Methods by Parameter Scaling for Learning-Rate-Free Optimization

arXiv: https://arxiv.org/abs/2401.03240 · HTML: https://mlsanity.com/paper/2401.03240/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 30 references that are in the map.
- First posted on arXiv 6 Jan 2024.

## Builds on (most cited first, 20 of 20)

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- [SegNeXt: Rethinking Convolutional Attention Design for Semantic Segmentation](https://mlsanity.com/paper/2209.08575/) (2022)
- [Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks](https://mlsanity.com/paper/1907.04595/) (2019)
- [Stochastic Polyak Step-size for SGD: An Adaptive Learning Rate for Fast Convergence](https://mlsanity.com/paper/2002.10542/) (2020)
- [Prodigy: An Expeditiously Adaptive Parameter-Free Learner](https://mlsanity.com/paper/2306.06101/) (2023)
- [Learning-Rate-Free Learning by D-Adaptation](https://mlsanity.com/paper/2301.07733/) (2023)
- [DoG is SGD's Best Friend: A Parameter-Free Dynamic Step Size Schedule](https://mlsanity.com/paper/2302.12022/) (2023)

## Abstract (arXiv)

We address the challenge of estimating the learning rate for adaptive gradient methods used in training deep neural networks. While several learning-rate-free approaches have been proposed, they are typically tailored for steepest descent. However, although steepest descent methods offer an intuitive approach to finding minima, many deep learning applications require adaptive gradient methods to achieve faster convergence. In this paper, we interpret adaptive gradient methods as steepest descent applied on parameter-scaled networks, proposing learning-rate-free adaptive gradient methods. Experimental results verify the effectiveness of this approach, demonstrating comparable performance to hand-tuned learning rates across various scenarios. This work extends the applicability of learning-rate-free methods, enhancing training with adaptive gradient methods.