# NysAct: A Scalable Preconditioned Gradient Descent using Nystrom Approximation

arXiv: https://arxiv.org/abs/2506.08360 · HTML: https://mlsanity.com/paper/2506.08360/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 42 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 27 of 27)

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- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
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- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
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- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
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- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
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- [TrivialAugment: Tuning-free Yet State-of-the-Art Data Augmentation](https://mlsanity.com/paper/2103.10158/) (2021)
- [ADAHESSIAN: An Adaptive Second Order Optimizer for Machine Learning](https://mlsanity.com/paper/2006.00719/) (2020)
- [Practical Quasi-Newton Methods for Training Deep Neural Networks](https://mlsanity.com/paper/2006.08877/) (2020)
- [M-FAC: Efficient Matrix-Free Approximations of Second-Order Information](https://mlsanity.com/paper/2107.03356/) (2021)
- [Augment your batch: better training with larger batches](https://mlsanity.com/paper/1901.09335/) (2019)
- [Gradient Descent on Neurons and its Link to Approximate Second-Order Optimization](https://mlsanity.com/paper/2201.12250/) (2022)
- [Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data](https://mlsanity.com/paper/1706.05736/) (2017)
- [Better SGD using Second-order Momentum](https://mlsanity.com/paper/2103.03265/) (2021)
- [SketchySGD: Reliable Stochastic Optimization via Randomized Curvature Estimates](https://mlsanity.com/paper/2211.08597/) (2022)
- [Sublinear Time Approximation of Text Similarity Matrices](https://mlsanity.com/paper/2112.09631/) (2021)

## Abstract (arXiv)

Adaptive gradient methods are computationally efficient and converge quickly, but they often suffer from poor generalization. In contrast, second-order methods enhance convergence and generalization but typically incur high computational and memory costs. In this work, we introduce NysAct, a scalable first-order gradient preconditioning method that strikes a balance between state-of-the-art first-order and second-order optimization methods. NysAct leverages an eigenvalue-shifted Nystrom method to approximate the activation covariance matrix, which is used as a preconditioning matrix, significantly reducing time and memory complexities with minimal impact on test accuracy. Our experiments show that NysAct not only achieves improved test accuracy compared to both first-order and second-order methods but also demands considerably less computational resources than existing second-order methods. Code is available at https://github.com/hseung88/nysact.