StoTAM: Stochastic Alternating Minimization for Tucker-Structured Tensor Sensing

TL;DR

This paper introduces StoTAM, a stochastic alternating minimization algorithm for low-Tucker-rank tensor sensing that improves efficiency by avoiding tensor projections and enabling mini-batch updates, with promising experimental results.

Contribution

The paper presents a novel stochastic alternating minimization method operating directly on Tucker-structured tensors, reducing computational costs compared to existing approaches.

Findings

Favorable convergence behavior demonstrated in synthetic experiments.

Efficient mini-batch updates enable faster tensor recovery.

Outperforms baseline methods in wall-clock time.

Abstract

Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace structures in high-dimensional data. Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations, while most stochastic factorized approaches are restricted to tensor decomposition settings. In this work, we propose a stochastic alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization. The proposed method avoids repeated tensor projections and enables efficient mini-batch updates on low-dimensional tensor factors. Numerical experiments on synthetic tensor sensing demonstrate that the proposed algorithm exhibits favorable convergence behavior in wall-clock time compared with representative stochastic tensor recovery baselines.