# Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods

arXiv: https://arxiv.org/abs/1710.07462 · HTML: https://mlsanity.com/paper/1710.07462/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2017.

## Built on by (most cited first, 5 of 5)

- [Recent and Upcoming Developments in Randomized Numerical Linear Algebra for Machine Learning](https://mlsanity.com/paper/2406.11151/) (2024)
- [Stochastic Variance-Reduced Newton: Accelerating Finite-Sum Minimization with Large Batches](https://mlsanity.com/paper/2206.02702/) (2022)
- [On the SAGA algorithm with decreasing step](https://mlsanity.com/paper/2410.03760/) (2024)
- [A Stochastic Variance Reduced Gradient using Barzilai-Borwein Techniques as Second Order Information](https://mlsanity.com/paper/2208.11075/) (2022)
- [SVRG and Beyond via Posterior Correction](https://mlsanity.com/paper/2512.01930/) (2025)

## Abstract (arXiv)

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.