Accelerating LLM Pre-Training through Flat-Direction Dynamics Enhancement

2026-02-26

AI Summary

This work addresses the inefficiency of large language model pretraining caused by the highly anisotropic loss landscape, where conventional optimizers struggle to make progress along flat directions. The authors propose LITE, an acceleration strategy that, for the first time, unifies adaptive optimization algorithms within a Riemannian ordinary differential equation framework. By dynamically applying larger Hessian damping coefficients and learning rates along flat directions, LITE achieves principle-driven optimization enhancement. Integrating Riemannian geometry, Hessian damping, and adaptive methods such as Muon or SOAP, LITE consistently accelerates pretraining across diverse model architectures, scales, datasets, and learning rate schedules. Both theoretical analysis and empirical experiments confirm its superior convergence speed in flat regions of the loss landscape.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Optimization
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Web Mining and Content Analysis: Large pretrained models with web data

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.

Problem

• LLM pre-training
• optimization landscape
• flat directions
• optimizer efficiency
• anisotropy

Innovation

• LITE
• Riemannian ODE
• flat-direction dynamics
• Hessian damping
• LLM pre-training acceleration