Scalable Levenberg-Marquardt Training Framework for Deep Learning

Xianghao Wang, Johan Barthélemy, John Taylor

The Levenberg-Marquardt (LMA) algorithm is a widely used nonlinear least-squares solver known for its rapid convergence. For small-scale neural networks, LMA provides better convergence and architectural robustness than first-order optimizers like Adam. However, LMA imposes prohibitive memory and computational costs. These costs are primarily from the Jacobian matrix, whose dimensions scale with both the number of samples and parameters. This bottleneck prevents its use in large-scale neural networks. Recent efforts scale LMA using preconditioned conjugate gradient (PCG) solvers to avoid materializing the Jacobian. However, PCG only approximates the solution, requiring many network propagations and a task-specific preconditioner. Other studies optimize LMA to reduce costs, but they restrict their methods to specific tasks or network architectures. As a result, LMA remains impractical for training general large-scale neural networks. In this paper, we propose LeMA, a distributed LMA algorithm for large-scale neural network training on multi-GPU platforms. Our contributions are twofold: First, an exact dual formulation of LMA removes the memory dependence on the parameter…