# Gradient correlation is a key ingredient to accelerate SGD with momentum

arXiv: https://arxiv.org/abs/2410.07870 · HTML: https://mlsanity.com/paper/2410.07870/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Oct 2024.

## Built on by (most cited first, 2 of 2)

- [SHANG++: Robust Stochastic Acceleration under Multiplicative Noise](https://mlsanity.com/paper/2603.09355/) (2026)
- [ANO : Faster is Better in Noisy Landscape](https://mlsanity.com/paper/2508.18258/) (2025)

## Abstract (arXiv)

Empirically, it has been observed that adding momentum to Stochastic Gradient Descent (SGD) accelerates the convergence of the algorithm. However, the literature has been rather pessimistic, even in the case of convex functions, about the possibility of theoretically proving this observation. We investigate the possibility of obtaining accelerated convergence of the Stochastic Nesterov Accelerated Gradient (SNAG), a momentum-based version of SGD, when minimizing a sum of functions in a convex setting. We demonstrate that the average correlation between gradients allows to verify the strong growth condition, which is the key ingredient to obtain acceleration with SNAG. Numerical experiments, both in linear regression and deep neural network optimization, confirm in practice our theoretical results.