Mano: Restriking Manifold Optimization for LLM Training

• URL: http://arxiv.org/abs/2601.23000v1
• Date: Fri, 30 Jan 2026 14:07:03 GMT
• Title: Mano: Restriking Manifold Optimization for LLM Training
• Authors: Yufei Gu, Zeke Xie,
• Abstract summary: 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.
• Score: 11.778746551502593
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: While large language models (LLMs) have emerged as a significant advancement in artificial intelligence, the hardware and computational costs for training LLMs are also significantly burdensome. Among the state-of-the-art optimizers, AdamW relies on diagonal curvature estimates and ignores structural properties, while Muon applies global spectral normalization at the expense of losing curvature information. In this study, we restriked manifold optimization methods for training LLMs, which may address both optimizers' limitations, while conventional manifold optimization methods have been largely overlooked due to the poor performance in large-scale model optimization. By innovatively projecting the momentum onto the tangent space of model parameters and constraining it on a rotational Oblique manifold, we propose a novel, powerful, and efficient optimizer **Mano** that is the first to bridge the performance gap between manifold optimization and modern optimizers. Extensive experiments on the LLaMA and Qwen3 models demonstrate that Mano consistently and significantly outperforms AdamW and Muon even with less memory consumption and computational complexity, respectively, suggesting an expanded Pareto frontier in terms of space and time efficiency.

Related papers

• Accelerating LLM Pre-Training through Flat-Direction Dynamics Enhancement [20.47449050578067]
  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.
  arXiv  Detail & Related papers  (2026-02-26T06:54:57Z)
• Divergence Minimization Preference Optimization for Diffusion Model Alignment [66.31417479052774]
  Divergence Minimization Preference Optimization (DMPO) is a principled method for aligning diffusion models by minimizing reverse KL divergence.<n>DMPO can consistently outperform or match existing techniques across different base models and test sets.
  arXiv  Detail & Related papers  (2025-07-10T07:57:30Z)
• Optimization-Inspired Few-Shot Adaptation for Large Language Models [25.439708260502556]
  Large Language Models (LLMs) have demonstrated remarkable performance in real-world applications.<n>Adapting LLMs to novel tasks via fine-tuning often requires substantial training data and computational resources that are impractical in few-shot scenarios.<n>Existing approaches, such as in-context learning and.<n>Efficient Fine-Tuning (PEFT), face key limitations.
  arXiv  Detail & Related papers  (2025-05-25T11:54:23Z)
• Modality-Balancing Preference Optimization of Large Multimodal Models by Adversarial Negative Mining [75.14823970163685]
  We propose a novel preference learning framework, Modality-Balancing Preference Optimization (MBPO), to address the modality imbalance in LMMs.<n>MBPO constructs a more effective offline preference dataset by generating hard negatives, i.e., rejected responses misled by LLM biases.<n>It can enhance LMM performance on challenging vision-language tasks and effectively reduce hallucinations.
  arXiv  Detail & Related papers  (2025-05-20T03:59:05Z)
• COSMOS: A Hybrid Adaptive Optimizer for Memory-Efficient Training of LLMs [77.79640601822341]
  Large Language Models (LLMs) have demonstrated remarkable success across various domains.<n>Their optimization remains a significant challenge due to the complex and high-dimensional loss landscapes they inhabit.
  arXiv  Detail & Related papers  (2025-02-24T18:42:19Z)
• A Convex-optimization-based Layer-wise Post-training Pruner for Large Language Models [24.185245582500876]
  We introduce FISTAPruner, the first post-training pruner based on convex optimization models and algorithms. FISTAPruner incorporates an intra-layer cumulative error correction mechanism and supports parallel pruning. We evaluate FISTAPruner on models such as OPT, LLaMA, LLaMA-2, and LLaMA-3 with 125M to 70B parameters under unstructured and 2:4 semi-structured sparsity.
  arXiv  Detail & Related papers  (2024-08-07T12:33:46Z)
• 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)
• Multi-Reference Preference Optimization for Large Language Models [56.84730239046117]
  We introduce a novel closed-form formulation for direct preference optimization using multiple reference models. The resulting algorithm, Multi-Reference Preference Optimization (MRPO), leverages broader prior knowledge from diverse reference models. Our experiments demonstrate that LLMs finetuned with MRPO generalize better in various preference data, regardless of data scarcity or abundance.
  arXiv  Detail & Related papers  (2024-05-26T00:29:04Z)
• Model Extrapolation Expedites Alignment [135.12769233630362]
  We propose a method called ExPO to expedite alignment training with human preferences.<n>We demonstrate that ExPO boosts a DPO model trained with only 20% steps to outperform the fully-trained one.<n>We show that ExPO notably improves existing open-source LLMs on the leading AlpacaEval 2.0 and MT-Bench benchmarks.
  arXiv  Detail & Related papers  (2024-04-25T17:39:50Z)
• 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)
• AdaLomo: Low-memory Optimization with Adaptive Learning Rate [59.64965955386855]
  We introduce low-memory optimization with adaptive learning rate (AdaLomo) for large language models. AdaLomo results on par with AdamW, while significantly reducing memory requirements, thereby lowering the hardware barrier to training large language models.
  arXiv  Detail & Related papers  (2023-10-16T09:04:28Z)

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.