Portrait of Xiao Liang

Ph.D. Student · Iowa State University

Xiao Liang

梁笑

Mapping nonconvex landscapes, one saddle point at a time.

Department of Electrical and Computer Engineering
Iowa State University, Ames, Iowa

About

Hi, I'm Xiao! I'm a Ph.D. student in Electrical and Computer Engineering at Iowa State University, working with Prof. Shuang Li.

I'm fascinated by a question that sounds almost too simple: why does plain gradient descent work so well on certain problems that look hopelessly nonconvex on paper? To find out, I map optimization landscapes. I look for the valleys, ridges, and saddle points of structured low-rank problems, such as recovering a signal and its blur kernel from magnitude-only measurements, or sensing tensors through their Fourier slices. Once I understand the geometry, I like to turn those insights into faster algorithms. More recently, I've been exploring how Muon-style orthogonalized updates can accelerate tensor regression.

My path here has a few turns in it. I studied data science in Beijing at North China University of Technology (2018–2022), then computer science at Washington University in St. Louis (2022–2024), and spent some time as an intern at Huawei before starting my Ph.D. in Ames. Iowa is famously flat, so these days the interesting terrain lives in my loss functions.

Try it Click anywhere to drop a ball and watch gradient descent roll downhill. The landscape has a saddle in the middle, but no spurious minima, so every ball ends at one of the two global solutions, ±x★. That sign ambiguity is exactly what phase retrieval has to live with.

Research

  1. r₁=2 r₂=2 r₃=1 r₄=3 strict saddle Preprint

    Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing

    Eugene Agyei-Kodie*, Longxiu Huang*, Shuang Li†, Xiao Liang†

    arXiv preprint, 2026 (*, † equal contribution)

    Under a tubal restricted isometry condition, the balanced factorized objective has no spurious local minima and a quantitative strict-saddle structure. Its local geometry is governed by the ranks of the Fourier slices, not by the tubal rank alone.

    arXiv PDF
    BibTeX 
    @article{agyeikodie2026strict,
  title   = {Strict-Saddle Landscapes and Multi-Rank Geometry in Low-Tubal-Rank Tensor Sensing},
  author  = {Agyei-Kodie, Eugene and Huang, Longxiu and Li, Shuang and Liang, Xiao},
  journal = {arXiv preprint arXiv:2609.37865},
  year    = {2026}
}
  2. U ← NS(momentum) Preprint

    A Muon-Accelerated Algorithm for Low Separation Rank Tensor Generalized Linear Models

    Xiao Liang, Shuang Li

    arXiv preprint, 2026

    LSRTR-M replaces the QR-based projection steps of LSRTR with Muon (momentum orthogonalized by Newton–Schulz) updates. On linear, logistic, and Poisson tensor GLMs it converges faster in both iterations and wall-clock time, and it stays competitive on Vessel MNIST 3D classification.

    arXiv PDF Code
    BibTeX 
    @article{liang2026muon,
  title   = {A Muon-Accelerated Algorithm for Low Separation Rank Tensor Generalized Linear Models},
  author  = {Liang, Xiao and Li, Shuang},
  journal = {arXiv preprint arXiv:2604.04726},
  year    = {2026}
}
  3. −x★ +x★ ICASSP 2026

    Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval

    Xiao Liang, Zhen Qin, Zhihui Zhu, Shuang Li

    IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, 2026

    Blind deconvolution and phase retrieval, solved at the same time, become a structured low-rank tensor recovery problem. For a tractable surrogate, the paper characterizes the global landscape of the population risk on the sphere and shows that Riemannian gradient descent converges linearly.

    Paper DOI
    BibTeX 
    @inproceedings{liang2026landscape,
  title     = {Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval},
  author    = {Liang, Xiao and Qin, Zhen and Zhu, Zhihui and Li, Shuang},
  booktitle = {IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages     = {511--515},
  year      = {2026},
  doi       = {10.1109/ICASSP55912.2026.11461778}
}
  4. x★ noise robust Preprint

    Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval via Structured Low-Rank Tensor Recovery

    Xiao Liang*, Zhen Qin*, Zhihui Zhu, Shuang Li

    arXiv preprint, 2025 (* equal contribution)

    The full story behind the ICASSP paper. Beyond the global landscape of the population surrogate, it establishes local geometry, convergence guarantees, and robustness to measurement noise for the full tensor sensing problem, with experiments that point the way back to the original problem.

    arXiv PDF
    BibTeX 
    @article{liang2025landscape,
  title   = {Landscape Analysis of Simultaneous Blind Deconvolution and Phase Retrieval via Structured Low-Rank Tensor Recovery},
  author  = {Liang, Xiao and Qin, Zhen and Zhu, Zhihui and Li, Shuang},
  journal = {arXiv preprint arXiv:2509.10834},
  year    = {2025}
}

Other Publications

Education