arXiv subjects

Xianliang Li

Publications and source records attributed to Xianliang Li.

3 recordsLinked to original sources

arXiv2026

Denoise First, Orthogonalize Later: Understanding Momentum in Muon via Spectral Filtering

Muon has recently demonstrated strong empirical performance in large language model training, but the theoretical role of momentum in Muon remains unclear. Existing analyses of Muon either remove momentum to study spectral updates in isolation, or retain momentum without explaining why it improves empirical performance. Our work bridges this gap by showing momentum in Muon acts as a spectral filter. Under a structured signal-plus-perturbation gradient model, we prove that momentum suppresses perturbations while preserving the dominant signal, thereby enlarging the spectral gap between them. This enlarged gap stabilizes the singular subspaces of the matrix passed to Muon's orthogonalization step, making the resulting update more reliable. We further show that applying momentum before orthogonalization achieves provably stronger alignment with the signal component of the gradient than either reversing this order or simply removing momentum. Experiments across diverse tasks, including LLM pretraining, support our theoretical analysis. More broadly, our theory offers a starting point for understanding the benefits of momentum in other matrix-based optimizers.

cs.LG↗

arXiv2025

On the Performance Analysis of Momentum Method: A Frequency Domain Perspective

Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic gradient methods. In this paper, we present a frequency domain analysis framework that interprets the momentum method as a time-variant filter for gradients, where adjustments to momentum coefficients modify the filter characteristics. Our experiments support this perspective and provide a deeper understanding of the mechanism involved. Moreover, our analysis reveals the following significant findings: high-frequency gradient components are undesired in the late stages of training; preserving the original gradient in the early stages, and gradually amplifying low-frequency gradient components during training both enhance performance. Based on these insights, we propose Frequency Stochastic Gradient Descent with Momentum (FSGDM), a heuristic optimizer that dynamically adjusts the momentum filtering characteristic with an empirically effective dynamic magnitude response. Experimental results demonstrate the superiority of FSGDM over conventional momentum optimizers.

cs.LG↗

arXiv2018

Scaling Up Large-Scale Graph Processing for GPU-Accelerated Heterogeneous Systems

Not only with the large host memory for supporting large scale graph processing, GPU-accelerated heterogeneous architecture can also provide a great potential for high-performance computing. However, few existing heterogeneous systems can exploit both hardware advantages to enable the scale-up performance for graph processing due to the limited CPU-GPU transmission efficiency. In this paper, we investigate the transmission inefficiency problem of heterogeneous graph systems. Our key insight is that the transmission efficiency for heterogeneous graph processing can be greatly improved by simply iterating each subgraph multiple times (rather than only once in prior work) in the GPU, further enabling to obtain the improvable efficiency of heterogeneous graph systems by enhancing GPU processing capability. We therefore present Seraph, with the highlights of {\em pipelined} subgraph iterations and {\em predictive} vertex updating, to cooperatively maximize the effective computations of GPU on graph processing. Our evaluation on a wide variety of large graph datasets shows that Seraph outperforms state-of-the-art heterogeneous graph systems by 5.42x (vs. Graphie) and 3.05x (vs. Garaph). Further, Seraph can be significantly scaled up over Graphie as fed with more computing power for large-scale graph processing.

cs.DC↗