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

• URL: http://arxiv.org/abs/2603.26048v1
• Date: Fri, 27 Mar 2026 03:37:03 GMT
• Title: Asymptotic Optimism for Tensor Regression Models with Applications to Neural Network Compression
• Abstract summary: We derive population expressions for the expected training-testing discrepancy (optimism) for both CP and Tucker decompositions.<n>This yields a prediction-oriented rank-selection rule that aligns with cross-validation.<n>We showcase its practical utility on a real-world image regression task and extend its application to tensor-based compression of neural network.
• Score: 1.993243436749392
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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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