# ZENITH: Automated Gradient Norm Informed Stochastic Optimization

arXiv: https://arxiv.org/abs/2601.15212 · HTML: https://mlsanity.com/paper/2601.15212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 21 Jan 2026.

## Builds on (most cited first, 22 of 22)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Deep Layer Aggregation](https://mlsanity.com/paper/1707.06484/) (2017)
- [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)
- [The Step Decay Schedule: A Near Optimal, Geometrically Decaying Learning Rate Procedure For Least Squares](https://mlsanity.com/paper/1904.12838/) (2019)
- [Training Neural Networks for and by Interpolation](https://mlsanity.com/paper/1906.05661/) (2019)
- [DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Method](https://mlsanity.com/paper/2305.16284/) (2023)
- [L4: Practical loss-based stepsize adaptation for deep learning](https://mlsanity.com/paper/1802.05074/) (2018)
- [Parabolic Approximation Line Search for DNNs](https://mlsanity.com/paper/1903.11991/) (2019)
- [Gradient descent with generalized Newton's method](https://mlsanity.com/paper/2407.02772/) (2024)
- [QLABGrad: a Hyperparameter-Free and Convergence-Guaranteed Scheme for Deep Learning](https://mlsanity.com/paper/2302.00252/) (2023)

## Abstract (arXiv)

Training deep computer vision models requires manual oversight or hyperparameter tuning of the learning rate (LR) schedule. While existing adaptive optimizers schedule the LR automatically, they suffer from computational and memory overhead, incompatibility with regularization, and suboptimal LR choices. In this work, we introduce the ZENITH (Zero-overhead Evolution using Norm-Informed Training History) optimizer, which adapts the LR using the temporal evolution of the gradient norm. Image classification experiments spanning 6 CNN architectures and 6 benchmarks demonstrate that ZENITH achieves higher test accuracy in lower wall-clock time than baselines. It also yielded superior mAP in object detection, keypoint detection, and instance segmentation on MS COCO using the R-CNN family of models. Furthermore, its compatibility with regularization enables even better generalization.