Tensor-valued data arise naturally in multidimensional signal and imaging problems, such as biomedical imaging. When incorporated into generalized linear models (GLMs), naive vectorization can destroy their multi-way structure and lead to high-dimensional, ill-posed estimation. To address this challenge, Low Separation Rank (LSR) decompositions reduce model complexity by imposing low-rank multilinear structure on the coefficient tensor. A representative approach for estimating LSR-based tensor GLMs (LSR-TGLMs) is the Low Separation Rank Tensor Regression (LSRTR) algorithm, which adopts block coordinate descent and enforces orthogonality of the factor matrices through repeated QR-based projections. However, the repeated projection steps can be computationally demanding and slow convergence. Motivated by the need for scalable estimation and classification from such data, we propose LSRTR-M, which incorporates Muon (MomentUm Orthogonalized by Newton-Schulz) updates into the LSRTR framework. Specifically, LSRTR-M preserves the original block coordinate scheme while replacing the projection-based factor updates with Muon steps. Across synthetic linear, logistic, and Poisson LSR-TGLMs, LSRTR-M converges faster in both iteration count and wall-clock time, while achieving lower normalized estimation and prediction errors. On the Vessel MNIST 3D task, it further improves computational efficiency while maintaining competitive classification performance.

翻译：张量值数据在生物医学成像等多维信号与成像问题中自然产生。当将其纳入广义线性模型（GLMs）时，朴素向量化会破坏其多路结构，导致高维病态估计。为解决这一挑战，低分离秩（LSR）分解通过给系数张量施加低秩多线性结构来降低模型复杂度。一种代表性的基于LSR的张量GLMs（LSR-TGLMs）估计方法是低分离秩张量回归（LSRTR）算法，该算法采用块坐标下降法，并通过基于QR的重复投影强制因子矩阵正交。然而，重复投影步骤计算量大且收敛缓慢。受此类数据可扩展估计与分类需求的驱动，我们提出LSRTR-M，该方法将Muon（通过牛顿-舒尔茨正交化的动量）更新融入LSRTR框架。具体而言，LSRTR-M保留原始块坐标方案，同时用Muon步骤替代基于投影的因子更新。在合成线性、逻辑斯蒂和泊松LSR-TGLMs上，LSRTR-M在迭代次数和墙上时间两方面均收敛更快，同时实现更低的归一化估计与预测误差。在Vessel MNIST 3D任务上，它进一步提高了计算效率，同时保持具有竞争力的分类性能。