Mild Over-Parameterization Benefits Asymmetric Tensor PCA
Asymmetric Tensor PCA (ATPCA) is a prototypical model for studying the trade-offs between sample complexity, computation, and memory. Existing algorithms for this problem typically require at least $d^{\left\lceil\overline{k}/2\right\rceil}$ state memory cost to recover the signal, where $d$ is the vector dimension and $\overline{k}$ is the tensor order. We focus on the setting where $\overline{k} \geq 4$ is even and consider (stochastic) gradient descent-based algorithms under a limited memory budget, which permits only mild over-parameterization of the model. We propose a matrix-parameterized method (in $d^{2}$ state memory cost) using a novel three-phase alternating-update algorithm to...
| Authors | Shihong Ding, Weicheng Lin, Cong Fang |
|---|---|
| Primary category | cs.LG |
| Published | 11 April 2026 |
| Last updated at source | 11 April 2026 |
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