# Quasi-Quadratic Gradient: A New Direction for Accelerating the BFGS Method in Quasi-Newton Optimization

arXiv: https://arxiv.org/abs/2604.23922 · HTML: https://mlsanity.com/paper/2604.23922/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 5 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Privacy-Preserving Logistic Regression Training with A Faster Gradient Variant](https://mlsanity.com/paper/2201.10838/) (2022)
- [Simplified Quadratic Gradient: A Unified Framework Bridging Gradient Descent and Newton-Type Methods by Synthesizing Hessians and Gradients](https://mlsanity.com/paper/2209.03282/) (2022)

## Built on by (most cited first, 1 of 1)

- [Generalized Quadratic Gradient: A New Direction in Optimization via the Fusion of Positive-Definite Curvature Matrices and Gradients into A Unified Framework](https://mlsanity.com/paper/2608.01552/) (2026)

## Abstract (arXiv)

In this paper, we introduce the Quasi-Quadratic Gradient (QQG), a novel search direction designed to accelerate the BFGS method within the quasi-Newton framework. By defining the QQG as the product of the inverse Hessian approximation and the current gradient, we explicitly leverage local second-order curvature to rectify the search path. Theoretical analysis and empirical results demonstrate that our approach significantly outperforms vanilla BFGS in convergence speed while maintaining computational efficiency.