{"ID":2862311,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.01414","arxiv_id":"2510.01414","title":"Risk Phase Transitions in Spiked Regression: Alignment Driven Benign and Catastrophic Overfitting","abstract":"This paper analyzes the generalization error of minimum-norm interpolating solutions in linear regression using spiked covariance data models. The paper characterizes how varying spike strengths and target-spike alignments can affect risk, especially in overparameterized settings. The study presents an exact expression for the generalization error, leading to a comprehensive classification of benign, tempered, and catastrophic overfitting regimes based on spike strength, the aspect ratio $c=d/n$ (particularly as $c \\to \\infty$), and target alignment. Notably, in well-specified aligned problems, increasing spike strength can surprisingly induce catastrophic overfitting before achieving benign overfitting. The paper also reveals that target-spike alignment is not always advantageous, identifying specific, sometimes counterintuitive, conditions for its benefit or detriment. Alignment with the spike being detrimental is empirically demonstrated to persist in nonlinear models.","short_abstract":"This paper analyzes the generalization error of minimum-norm interpolating solutions in linear regression using spiked covariance data models. The paper characterizes how varying spike strengths and target-spike alignments can affect risk, especially in overparameterized settings. The study presents an exact expression...","url_abs":"https://arxiv.org/abs/2510.01414","url_pdf":"https://arxiv.org/pdf/2510.01414v1","authors":"[\"Jiping Li\",\"Rishi Sonthalia\"]","published":"2025-10-01T19:51:47Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.AI\",\"cs.LG\"]","methods":"[]","has_code":false}