Accelerating LLM Pre-Training through Flat-Direction Dynamics Enhancement

• URL: http://arxiv.org/abs/2602.22681v1
• Date: Thu, 26 Feb 2026 06:54:57 GMT
• Title: Accelerating LLM Pre-Training through Flat-Direction Dynamics Enhancement
• Abstract summary: Pre-training Large Language Models requires immense computational resources, making efficiency essential.<n>We propose LITE, a general acceleration strategy that enhances training dynamics by applying larger Hessian damping coefficients and learning rates along flat trajectories.
• Score: 20.47449050578067
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

Related papers

• Evolution of Optimization Methods: Algorithms, Scenarios, and Evaluations [98.44542103979735]
  First-order gradient descent methods, epitomized by gradient descent (SGD) and Adam, serve as the cornerstone of modern training pipelines.<n>Large-scale model training, stringent privacy requirements, and distributed learning paradigms expose critical limitations in these conventional approaches regarding privacy protection and memory efficiency.<n>We retrospectively analyze the evolutionary trajectory of deep learning optimization algorithms and present a comprehensive empirical evaluation of mainstreams across diverse model architectures and training scenarios.<n>We distill key emerging trends and fundamental design trade-offs, pinpointing promising directions for future research.
  arXiv  Detail & Related papers  (2026-04-14T17:01:36Z)
• New Hybrid Fine-Tuning Paradigm for LLMs: Algorithm Design and Convergence Analysis Framework [52.69678300445233]
  Fine-tuning Large Language Models (LLMs) typically involves either full fine-tuning, which updates all model parameters, or.<n>Efficient Fine-Tuning (PEFT) adjusts a small subset of parameters.<n>We propose a novel hybrid fine-tuning approach that jointly updates both LLMs and PEFT modules using a combination of zeroth-order and first-order optimization methods.
  arXiv  Detail & Related papers  (2026-04-10T22:39:38Z)
• Curvature-Guided LoRA: Steering in the pretrained NTK subspace [60.35296431630704]
  We introduce the prediction alignment problem, aiming to match the predictor obtained via PEFT to that of full fine-tuning at the level of outputs.<n>We show that this objective naturally leads to a curvature-aware, second-order formulation, where optimal low-rank updates correspond to a Newton-like, curvature-whitened gradient.<n>Based on this insight, we propose Curvature-Guided LoRA (CG-LoRA), which selects and scales adaptation directions using local curvature information.
  arXiv  Detail & Related papers  (2026-03-31T14:46:39Z)
• Deriving Hyperparameter Scaling Laws via Modern Optimization Theory [55.63126290312615]
  We study modern first-order boundss for methods based on the Linear Minimization Oracle (LMO)<n>Treating bounds in recent literature as a proxy and minimizing them across different tuning regimes yields closed-form power-law schedules for learning rate, momentum, and batch size.<n>Our results draw particular attention to the interaction between momentum and batch-size scaling, suggesting that optimal performance may be achieved with several scaling strategies.
  arXiv  Detail & Related papers  (2026-03-16T22:21:27Z)
• Merging Beyond: Streaming LLM Updates via Activation-Guided Rotations [55.047454145941366]
  Streaming Merging is an innovative model updating paradigm that conceptualizes merging as an iterative optimization process.<n> ARM is a strategy designed to approximate gradient descent dynamics.<n> ARM requires only early SFT checkpoints and, through iterative merging, surpasses the fully converged SFT model.
  arXiv  Detail & Related papers  (2026-02-03T08:15:57Z)
• Mano: Restriking Manifold Optimization for LLM Training [11.778746551502593]
  Large language models (LLMs) have emerged as a significant advancement in artificial intelligence.<n>Mano is the first to bridge the performance gap between manifold optimization and moderns.
  arXiv  Detail & Related papers  (2026-01-30T14:07:03Z)
• Consolidation or Adaptation? PRISM: Disentangling SFT and RL Data via Gradient Concentration [56.074760766965085]
  PRISM achieves a dynamics-aware framework that arbitrates data based on its degree of cognitive conflict with the model's existing knowledge.<n>Our findings suggest that disentangling data based on internal optimization regimes is crucial for scalable and robust agent alignment.
  arXiv  Detail & Related papers  (2026-01-12T05:43:20Z)
• How to Set the Learning Rate for Large-Scale Pre-training? [73.03133634525635]
  We formalize this investigation into two distinct research paradigms: Fitting and Transfer.<n>Within the Fitting Paradigm, we introduce a Scaling Law for search factor, effectively reducing the search complexity from O(n3) to O(n*C_D*C_) via predictive modeling.<n>We extend the principles of $$Transfer to the Mixture of Experts (MoE) architecture, broadening its applicability to encompass model depth, weight decay, and token horizons.
  arXiv  Detail & Related papers  (2026-01-08T15:55:13Z)
• Prior-Informed Zeroth-Order Optimization with Adaptive Direction Alignment for Memory-Efficient LLM Fine-Tuning [4.278794376089146]
  We propose a plug-and-play method that incorporates prior-informed perturbations to refine gradient estimation.<n>Our method significantly accelerates convergence compared to standard ZO approaches.<n>We prove that our gradient estimator achieves stronger alignment with the true gradient direction.
  arXiv  Detail & Related papers  (2026-01-08T08:27:15Z)
• Beyond the Ideal: Analyzing the Inexact Muon Update [54.70108543057578]
  We show first analysis of the inexactized update at Muon's core.<n>We reveal a fundamental coupling between this inexactness and the optimal step size and momentum.
  arXiv  Detail & Related papers  (2025-10-22T18:01:07Z)
• ESSA: Evolutionary Strategies for Scalable Alignment [8.418036456622158]
  We present ESSA, a gradient-free framework that aligns Large Language Models (LLMs) using only forward inference and black-box optimization.<n>ESSA improves the test accuracy of Qwen2.5-Math-7B by 12.6% on GSM8K and 14.8% on PRM800K, and raises the accuracy of LLaMA3.1-8B on IFEval by 22.5%.<n>In large-scale settings ESSA shows stronger scaling than gradient-based methods.
  arXiv  Detail & Related papers  (2025-07-06T16:23:07Z)
• SUMO: Subspace-Aware Moment-Orthogonalization for Accelerating Memory-Efficient LLM Training [25.244065166421517]
  Low-rank gradient-based optimization methods have significantly improved memory efficiency during the training of large language models (LLMs)<n>These methods primarily emphasize memory savings, often overlooking potential acceleration in convergence.<n>In this paper, we propose SUMO (Subspace-Aware Moment-Orthogonalization), an norm that employs exact singular value decomposition.<n>We show that SUMO accelerates convergence, enhances stability, improves performance, and reduces memory requirements by up to 20% compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2025-05-30T16:08:40Z)
• LESA: Learnable LLM Layer Scaling-Up [57.0510934286449]
  Training Large Language Models (LLMs) from scratch requires immense computational resources, making it prohibitively expensive.<n>Model scaling-up offers a promising solution by leveraging the parameters of smaller models to create larger ones.<n>We propose textbfLESA, a novel learnable method for depth scaling-up.
  arXiv  Detail & Related papers  (2025-02-19T14:58:48Z)
• Understanding Optimization in Deep Learning with Central Flows [95.5647720254338]
  We develop theory that can describe the dynamics of optimization in a complex regime.<n>Our results suggest that central flows can be a valuable theoretical tool for reasoning about optimization in deep learning.
  arXiv  Detail & Related papers  (2024-10-31T17:58:13Z)
• Memory-Efficient Optimization with Factorized Hamiltonian Descent [11.01832755213396]
  We introduce a novel adaptive, H-Fac, which incorporates a memory-efficient factorization approach to address this challenge. By employing a rank-1 parameterization for both momentum and scaling parameter estimators, H-Fac reduces memory costs to a sublinear level. We develop our algorithms based on principles derived from Hamiltonian dynamics, providing robust theoretical underpinnings in optimization dynamics and convergence guarantees.
  arXiv  Detail & Related papers  (2024-06-14T12:05:17Z)
• Revisiting Zeroth-Order Optimization for Memory-Efficient LLM Fine-Tuning: A Benchmark [166.40879020706151]
  This paper proposes a shift towards BP-free, zeroth-order (ZO) optimization as a solution for reducing memory costs during fine-tuning. Unlike traditional ZO-SGD methods, our work expands the exploration to a wider array of ZO optimization techniques. Our study unveils previously overlooked optimization principles, highlighting the importance of task alignment, the role of the forward gradient method, and the balance between algorithm complexity and fine-tuning performance.
  arXiv  Detail & Related papers  (2024-02-18T14:08:48Z)
• Flatter, faster: scaling momentum for optimal speedup of SGD [0.0]
  We study training dynamics arising from interplay between gradient descent (SGD) and label noise and momentum in the training of neural networks. We find that scaling the momentum hyper parameter $1-NISTbeta$ with the learning rate to the power of $2/3$ maximally accelerates training, without sacrificing generalization.
  arXiv  Detail & Related papers  (2022-10-28T20:41:48Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.