Asymptotic Optimism for Tensor Regression Models with Applications to Neural Network Compression

Haoming Shi; Eric C. Chi; Hengrui Luo

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arXiv · 2603.26048

Asymptotic Optimism for Tensor Regression Models with Applications to Neural Network Compression

Haoming Shi·Eric C. Chi·Hengrui Luo

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Abstract

We study rank selection for low-rank tensor regression under random covariates design. Under a Gaussian random-design model and some mild conditions, we derive population expressions for the expected training-testing discrepancy (optimism) for both CP and Tucker decomposition. We further demonstrate that the optimism is minimized at the true tensor rank for both CP and Tucker regression. This yields a prediction-oriented rank-selection rule that aligns with cross-validation and extends naturally to tensor-model averaging. We also discuss conditions under which under- or over-ranked models may appear preferable, thereby clarifying the scope of the method. Finally, we showcase its practical utility on a real-world image regression task and extend its application to tensor-based compression of neural network, highlighting its potential for model selection in deep learning.

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BibTeX RIS

Haoming Shi, Eric C. Chi, Hengrui Luo. 2026-03-27. Asymptotic Optimism for Tensor Regression Models with Applications to Neural Network Compression. https://arxiv.org/abs/2603.26048

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