Yupeng Su

Yupeng Su, Ziyi Guan, Xiaoqun Liu et al.

Large language models (LLMs) have seen substantial growth, necessitating efficient model pruning techniques. Existing post-training pruning methods primarily measure weight importance in converged dense models, often overlooking changes in weight significance during the pruning process, leading to performance degradation. To address this issue, we present LLM-Barber (Block-Aware Rebuilder for Sparsity Mask in One-Shot), a novel one-shot pruning framework that rebuilds the sparsity mask of pruned models without any retraining or weight reconstruction. LLM-Barber incorporates block-aware error optimization across Self-Attention and MLP blocks, facilitating global performance optimization. We are the first to employ the product of weights and gradients as a pruning metric in the context of LLM post-training pruning. This enables accurate identification of weight importance in massive models and significantly reduces computational complexity compared to methods using secondorder information. Our experiments show that LLM-Barber efficiently prunes models from LLaMA and OPT families (7B to 13B) on a single A100 GPU in just 30 minutes, achieving state-of-the-art results in both perplexity and zero-shot performance across various language benchmarks. Code is available at https://github.com/YupengSu/LLM-Barber.

Yupeng Su, Ruijie Zhang, Ziyue Liu et al.

The Muon optimizer has emerged as a compelling alternative to Adam for training large language models, achieving remarkable computational savings through gradient orthogonalization. However, Muon's optimizer state is more sensitive to quantization errors: because the orthogonalization discards the magnitudes of singular values and retains only directional information, even small quantization errors in singular vector directions are amplified in the update. In this work, we propose MuonQ, a low-bit Muon training framework built on the principle of directional fidelity optimization. First, we apply a pre-quantization normalization so that each step introduces quantization errors of the same magnitude, preventing the accumulated error from developing a preferred direction. Second, we introduce a structural decomposition that separately quantizes the dominant singular components via power iteration, ensuring that quantization errors perturb only singular value magnitudes rather than rotating singular vector directions. Third, we adopt $μ$-law companding quantization to allocate higher resolution to densely packed momentum values, shifting the quantization objective from outlier preservation to dense-region distinguishability. Together, these techniques enable stable 4-bit quantization of Muon's optimizer states. Pre-training experiments on GPT-style and LLaMA-style models demonstrate that MuonQ at 4-bit precision closely matches full-precision Muon in both training loss and downstream task accuracy, while reducing optimizer state memory by up to 7.3 $\times$. Our code is available at https://github.com/YupengSu/MuonQ.

Ziyue Liu, Ruijie Zhang, Zhengyang Wang et al.

Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization. However, its practical efficiency is limited by the need for multiple Newton--Schulz (NS) iterations per optimization step, which introduces non-trivial computation and communication overhead. We propose Muon$^2$, an extension of Muon that applies Adam-style adaptive second-moment preconditioning before orthogonalization. Our key insight is that the core challenge of polar approximation in Muon lies in the ill-conditioned momentum matrix, of which the spectrum is substantially improved by Muon$^2$, leading to faster convergence toward a practically sufficient orthogonalization. We further characterize the practical orthogonalization quality via directional alignment, under which Muon$^2$ demonstrates dramatic improvement over Muon at each polar step. Across GPT and LLaMA pre-training experiments from 60M to 1.3B parameters, Muon$^2$ consistently outperforms Muon and recent Muon variants while reducing NS iterations by 40\%. We further introduce Muon$^2$-F, a memory-efficient factorized variant that preserves most of the gains of Muon$^2$ with negligible memory overhead.

Jiayi Tian, Yupeng Su, Ryan Solgi et al.

Large reasoning models (LRMs) enhance problem-solving capabilities by generating explicit multi-step chains of thought (CoT) reasoning; however, they incur substantial inference latency and computational overhead. To mitigate this issue, recent works have explored model collaboration paradigms, where small reasoning models (SRMs) generate intermediate reasoning steps to achieve a better accuracy--latency trade-off. Despite recent progress, effectively and efficiently detecting and mitigating SRM failures in collaborative systems remains a key challenge. To address this issue, we analyze SRM inference in both the generated text and hidden-state spaces, and identify three types of failure modes: \textit{overconfidence}, \textit{uncertainty}, and \textit{heavy revalidation}. Building on these insights, we propose \textbf{RankGuide}, a framework that improves the efficiency and effectiveness of SRM--LRM collaboration through tensor-rank-guided routing and steering. Specifically, RankGuide leverages a routing signal that incorporates tensor-rank signals derived from consecutive hidden states to detect when SRMs are likely to fail and selectively invoke LRMs. In addition, we introduce a tensor-rank-filtered steering vector extraction method to modulate the reasoning trajectory of SRMs, thereby improving their generation quality. By improving both routing and steering through tensor-rank signals, RankGuide enables SRM--LRM collaborative systems to achieve more efficient reasoning with fewer steps and improved accuracy. Experiments on multiple reasoning benchmarks demonstrate the efficacy of RankGuide in reducing latency by up to $1.75\times$ compared to LRM, while maintaining competitive accuracy relative to prior methods.

Ruijie Zhang, Yequan Zhao, Ziyue Liu et al.

The Muon optimizer has demonstrated strong empirical performance in pre-training large language models by performing matrix-level gradient (or momentum) orthogonalization in each layer independently. In this work, we propose TEON, a principled generalization of Muon that extends orthogonalization beyond individual layers by modeling the gradients of a neural network as a structured higher-order tensor. We present TEON's improved convergence guarantee over layer-wise Muon, and further develop a practical instantiation of TEON based on the theoretical analysis with corresponding ablation. We evaluate our approach on two widely adopted architectures: GPT-style models, ranging from 130M to 774M parameters, and LLaMA-style models, ranging from 60M to 1B parameters. Experimental results show that TEON consistently improves training and validation perplexity across model scales and exhibits strong robustness under various approximate SVD schemes.

He Xiao, Runming Yang, Qingyao Yang et al.

Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and model expressiveness. While existing ultra-low-bit PTQ methods rely on binary approximations or complex compensation mechanisms, they suffer from either limited representational capacity or computational overhead that undermines their efficiency gains. We introduce PTQ to Trit-Planes (PTQTP), the first ternary-weight PTQ framework that decomposes weight matrices into structured ternary {-1, 0, 1} trit-planes using 2x1.58-bit representation. PTQTP achieves multiplication-free inference, identical to 1-bit quantization, while maintaining superior expressiveness through its novel structured decomposition. Our approach provides: (1) a theoretically grounded progressive approximation algorithm ensuring global weight consistency; (2) model-agnostic deployment across diverse modern LLMs without architectural modifications; and (3) uniform ternary operations that eliminate the need for mixed-precision or compensation schemes. Comprehensive experiments across LLaMA3.x and Qwen3 model families (0.6B-70B parameters) demonstrate that PTQTP significantly outperforms existing low-bit PTQ methods, achieving 82.4% mathematical reasoning retention versus 0% for competing approaches. PTQTP approaches and sometimes surpasses 1.58-bit quantization-aware training performance while requiring only single-hour quantization compared to 10-14 GPU days for training-based methods. These results establish PTQTP as a practical solution for efficient LLM deployment in resource-constrained environments. The code will be available at https://github.com/HeXiao-55/PTQTP.

Ziyi Guan, Hantao Huang, Yupeng Su et al.

Large Language Models (LLMs) have greatly advanced the natural language processing paradigm. However, the high computational load and huge model sizes pose a grand challenge for deployment on edge devices. To this end, we propose APTQ (Attention-aware Post-Training Mixed-Precision Quantization) for LLMs, which considers not only the second-order information of each layer's weights, but also, for the first time, the nonlinear effect of attention outputs on the entire model. We leverage the Hessian trace as a sensitivity metric for mixed-precision quantization, ensuring an informed precision reduction that retains model performance. Experiments show APTQ surpasses previous quantization methods, achieving an average of 4 bit width a 5.22 perplexity nearly equivalent to full precision in the C4 dataset. In addition, APTQ attains state-of-the-art zero-shot accuracy of 68.24\% and 70.48\% at an average bitwidth of 3.8 in LLaMa-7B and LLaMa-13B, respectively, demonstrating its effectiveness to produce high-quality quantized LLMs.

Zhen Li, Yupeng Su, Runming Yang et al.

Large language models have achieved significant advancements in complex mathematical reasoning benchmarks, such as MATH. However, their substantial computational requirements present challenges for practical deployment. Model quantization has emerged as an effective strategy to reduce memory usage and computational costs by employing lower precision and bit-width representations. In this study, we systematically evaluate the impact of quantization on mathematical reasoning tasks. Our results demonstrate that aggressive quantization methods like AWQ and GPTQ introduce up to 32.39% accuracy degradation (average 11.31%) on Llama-3 models, particularly in numerical computation and reasoning planning. To address this, we introduce a multidimensional evaluation framework combining qualitative capability analysis and quantitative error assessment. We further develop targeted recovery strategies, showing that fine-tuning quantized models on only 545 task-specific examples for 3 minutes on 4 GPUs effectively restores reasoning capabilities to near full-precision levels. Additionally, our error assessment pipeline achieves 98.9% accuracy in diagnosing and localizing errors across 3,366 failure cases, providing actionable insights for mitigating quantization-induced degradation.