Canonical Polyadic (CP) tensor decomposition is a fundamental technique for analyzing high-dimensional tensor data. While the Alternating Least Squares (ALS) algorithm is widely used for computing CP decomposition due to its simplicity and empirical success, its theoretical foundation, particularly regarding statistical optimality and convergence behavior, remain underdeveloped, especially in noisy, non-orthogonal, and higher-rank settings. In this work, we revisit CP tensor decomposition from a statistical perspective and provide a comprehensive theoretical analysis of ALS under a signal-plus-noise model. We establish non-asymptotic, minimax-optimal error bounds for tensors of general order, dimensions, and rank, assuming suitable initialization. To enable such initialization, we propose Tucker-based Approximation with Simultaneous Diagonalization (TASD), a robust method that improves stability and accuracy in noisy regimes. Combined with ALS, TASD yields a statistically consistent estimator. We further analyze the convergence dynamics of ALS, identifying a two-phase pattern-initial quadratic convergence followed by linear refinement. We further show that in the rank-one setting, ALS with an appropriately chosen initialization attains optimal error within just one or two iterations.

Exploiting sparsity in deep neural networks (DNNs) has been a promising area to meet the growing computation need of modern DNNs. However, in practice, sparse DNN acceleration still faces a key challenge. To minimize the overhead of sparse acceleration, hardware designers have proposed structured sparse hardware support recently, which provides limited flexibility and requires extra model fine-tuning. Moreover, any sparse model fine-tuned for certain structured sparse hardware cannot be accelerated by other structured hardware. To bridge the gap between sparse DNN models and hardware, this paper proposes tensor approximation via structured decomposition (TASD), which leverages the distributive property in linear algebra to turn any sparse tensor into a series of structured sparse tensors. Next, we develop a software framework, TASDER, to accelerate DNNs by searching layer-wise, high-quality structured decomposition for both weight and activation tensors so that they can be accelerated by any systems with structured sparse hardware support. Evaluation results show that, by exploiting prior structured sparse hardware baselines, our method can accelerate off-the-shelf dense and sparse DNNs without fine-tuning and improves energy-delay-product by up to 83% and 74% on average.