# Stochastic Gradient Variance Reduction by Solving a Filtering Problem

arXiv: https://arxiv.org/abs/2012.12418 · HTML: https://mlsanity.com/paper/2012.12418/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2020.

## Built on by (most cited first, 4 of 4)

- [Subspace Networks: Scaling Decentralized Training with Communication-Efficient Model Parallelism](https://mlsanity.com/paper/2506.01260/) (2025)
- [A Method for Enhancing Generalization of Adam by Multiple Integrations](https://mlsanity.com/paper/2412.12473/) (2024)
- [Unified High-Probability Analysis of Stochastic Variance-Reduced Estimation](https://mlsanity.com/paper/2605.15388/) (2026)
- [Understanding weight-magnitude hyperparameters in training binary networks](https://mlsanity.com/paper/2303.02452/) (2023)

## Abstract (arXiv)

Deep neural networks (DNN) are typically optimized using stochastic gradient descent (SGD). However, the estimation of the gradient using stochastic samples tends to be noisy and unreliable, resulting in large gradient variance and bad convergence. In this paper, we propose Filter Gradient Decent~(FGD), an efficient stochastic optimization algorithm that makes the consistent estimation of the local gradient by solving an adaptive filtering problem with different design of filters. Our method reduces variance in stochastic gradient descent by incorporating the historical states to enhance the current estimation. It is able to correct noisy gradient direction as well as to accelerate the convergence of learning. We demonstrate the effectiveness of the proposed Filter Gradient Descent on numerical optimization and training neural networks, where it achieves superior and robust performance compared with traditional momentum-based methods. To the best of our knowledge, we are the first to provide a practical solution that integrates filtering into gradient estimation by making the analogy between gradient estimation and filtering problems in signal processing. (The code is provided in https://github.com/Adamdad/Filter-Gradient-Decent)