🤖 AI Summary
This work addresses the high computational cost and inefficiency of existing methods in low-Tucker-rank tensor sensing, particularly when handling high-dimensional multimodal data. To overcome these limitations, we propose a stochastic alternating minimization algorithm that directly optimizes over the core tensor and factor matrices in the Tucker decomposition. By avoiding expensive full-tensor projection operations and enabling mini-batch gradient updates on low-dimensional factor matrices, our approach significantly reduces computational overhead. As the first to introduce stochastic alternating minimization into Tucker-structured tensor sensing, this method breaks the reliance of prior approaches on full gradients or full-tensor operations, achieving provable convergence while markedly improving efficiency. Experimental results on synthetic data demonstrate that our algorithm attains substantially faster convergence than state-of-the-art stochastic tensor recovery baselines under identical runtime constraints.
📝 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.