{"ID":3053244,"CreatedAt":"2026-06-04T04:41:36.695875263Z","UpdatedAt":"2026-06-05T20:57:27.554373511Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04212","arxiv_id":"2606.04212","title":"Edge of Stability Selectively Shapes Learning Across the Data Distribution","abstract":"Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching intervention that enters or exits the EoS regime from the same training state, we causally demonstrate this trade-off and identify two necessary conditions for a group to benefit. First, its aggregate gradient must align with the top Hessian eigenvector. We isolate this mechanism with a controlled perturbation that preserves distance but randomizes direction, destroying alignment and eliminating the advantage. Second, the group must sustain non-vanishing gradient magnitude over time. Under cross-entropy loss, gradient saturation decouples confidently classified groups, shifting the advantage to output-outliers, whose gradients persist. Together, these results show that EoS functions not only as a stability boundary, but as a mechanism governing the allocation of learning across the data distribution.","short_abstract":"Existing analyses of the edge of stability (EoS) treat it as a global property of optimization. We show that it is also selective: the stability constraint redistributes learning across subsets of the training distribution, amplifying progress on some groups while suppressing progress on others. Using a branching inter...","url_abs":"https://arxiv.org/abs/2606.04212","url_pdf":"https://arxiv.org/pdf/2606.04212v1","authors":"[\"Shauna Kwag\",\"Anakha Ganesh\",\"Tomaso Poggio\",\"Pierfrancesco Beneventano\"]","published":"2026-06-02T20:58:40Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ML\"]","methods":"[]","has_code":false}