Accelerating LLM Pre-Training through Flat-Direction Dynamics Enhancement

TL;DR

This paper introduces LITE, a novel acceleration method for large language model pre-training that leverages flat-direction dynamics and Riemannian geometry to improve optimizer efficiency and convergence speed.

Contribution

The paper develops a Riemannian ODE framework for optimizer analysis and proposes LITE, a generalized acceleration strategy that enhances training dynamics along flat directions.

Findings

LITE significantly accelerates training of Muon and SOAP optimizers.

LITE improves convergence across diverse architectures and datasets.

Theoretical analysis confirms faster convergence along flat directions.

Abstract

Pre-training Large Language Models requires immense computational resources, making optimizer efficiency essential. The optimization landscape is highly anisotropic, with loss reduction driven predominantly by progress along flat directions. While matrix-based optimizers such as Muon and SOAP leverage fine-grained curvature information to outperform AdamW, their updates tend toward isotropy -- relatively conservative along flat directions yet potentially aggressive along sharp ones. To address this limitation, we first establish a unified Riemannian Ordinary Differential Equation (ODE) framework that elucidates how common adaptive algorithms operate synergistically: the preconditioner induces a Riemannian geometry that mitigates ill-conditioning, while momentum serves as a Riemannian damping term that promotes convergence. Guided by these insights, we propose LITE, a generalized acceleration strategy that enhances training dynamics by applying larger Hessian damping coefficients and learning rates along flat trajectories. Extensive experiments demonstrate that LITE significantly accelerates both Muon and SOAP across diverse architectures (Dense, MoE), parameter scales (130M--1.3B), datasets (C4, Pile), and learning-rate schedules (cosine, warmup-stable-decay). Theoretical analysis confirms that LITE facilitates faster convergence along flat directions in anisotropic landscapes, providing a principled approach to efficient LLM pre-training. The code is available at https://github.com/SHUCHENZHU/LITE.