Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914331273199616 |
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| author | Wu, Mingqi Yang, Archer Y. Sun, Qiang |
| author_facet | Wu, Mingqi Yang, Archer Y. Sun, Qiang |
| contents | Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these limits. The recursion separates two competing forces: a systematic component that grows with iteration due to progressive signal forgetting, and a stochastic component that decays due to denoising via repeated data-dependent projections. Their interaction yields a $U$-shaped test-risk curve and an optimal early-stopping time. In spiked covariance models, iteration further acts as an iteration-dependent spectral filter that preserves strong eigendirections while suppressing weaker ones, inducing an implicit form of soft feature selection distinct from ridge regression. Finally, we propose an iterated generalized cross-validation criterion and prove its uniform consistency for estimating the risk along the self-training trajectory, enabling fully data-driven selection of the stopping time and regularization. Experiments on synthetic covariances validate the theory and illustrate the predicted denoising-forgetting trade-off. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14029 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting Wu, Mingqi Yang, Archer Y. Sun, Qiang Machine Learning Statistics Theory Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these limits. The recursion separates two competing forces: a systematic component that grows with iteration due to progressive signal forgetting, and a stochastic component that decays due to denoising via repeated data-dependent projections. Their interaction yields a $U$-shaped test-risk curve and an optimal early-stopping time. In spiked covariance models, iteration further acts as an iteration-dependent spectral filter that preserves strong eigendirections while suppressing weaker ones, inducing an implicit form of soft feature selection distinct from ridge regression. Finally, we propose an iterated generalized cross-validation criterion and prove its uniform consistency for estimating the risk along the self-training trajectory, enabling fully data-driven selection of the stopping time and regularization. Experiments on synthetic covariances validate the theory and illustrate the predicted denoising-forgetting trade-off. |
| title | Why Self-Training Helps and Hurts: Denoising vs. Signal Forgetting |
| topic | Machine Learning Statistics Theory |
| url | https://arxiv.org/abs/2602.14029 |