The Muon optimizer has recently offered a promising alternative to AdamW for large language model training, leveraging matrix orthogonalization to produce geometry-aware updates. However, like all first-order methods, Muon can become trapped in sharp local minima. In this work, we present **MONA**, an optimizer that bridges Muon’s orthogonalization framework with curvature-aware acceleration. MONA adds an acceleration term directly into Muon’s gradient processing pipeline. This term is calculated from the exponential moving average of gradient differences. We provide a detailed convergence analysis for MONA, showing that the acceleration term enables escape from sharp minima while preserving Muon’s spectral-norm regularization. Empirically, MONA achieves better convergence and downstream task performance compared to both Muon and AdamW across three scales of Mixture-of-Experts pretraining, spanning from 1B to 68B parameters, with the largest model trained on 1 trillion tokens. Furthermore, we conduct supervised fine-tuning on the MOE-68B-A3B model and evaluate it on general capability, mathematical reasoning, and code generation benchmarks, where MONA achieves **SOTA** performance.

Transformer architecture gradually dominates the LLM field. Recent advances in training optimization for Transformer-based large language models (LLMs) primarily focus on architectural modifications or optimizer adjustments. However, these approaches lack systematic optimization of weight patterns during training. Weight pattern refers to the distribution and relative magnitudes of weight parameters in a neural network. To address this issue, we propose a Weight Scaling method called WISCA to enhance training efficiency and model quality by strategically improving neural network weight patterns—without changing network structures. By rescaling weights while preserving model outputs, WISCA indirectly optimizes the model’s training trajectory. Experiments demonstrate that WISCA significantly improves convergence quality (measured by generalization capability and loss reduction), particularly in LLMs with Grouped Query Attention (GQA) architectures and LoRA fine-tuning tasks. Empirical results show 5.6% average improvement on zero-shot validation tasks and 2.12% average reduction in training perplexity across multiple architectures.