Yupeng Su
Publications
RankGuide: Tensor-Rank-Guided Routing and Steering for Efficient Reasoning
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 across three reasoning domains -- mathematics, code generation, and scientific QA -- 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. The code is available at \href{https://github.com/TTTTTTris/RankGuide}{https://github.com/TTTTTTris/RankGuide}.
Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning
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.
TEON: Tensorized Orthonormalization Beyond Layer-Wise Muon for Large Language Model Pre-Training
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.