{"ID":2871054,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.12165","arxiv_id":"2509.12165","title":"Reachability of gradient descent","abstract":"We show that gradient descent can converge to any local minimum of a smooth semi-algebraic function. This holds if the step sizes are nonsummable and sufficiently small. The same results hold for the subgradient method on locally Lipschitz semi-algebraic functions if the step size is constant.","short_abstract":"We show that gradient descent can converge to any local minimum of a smooth semi-algebraic function. This holds if the step sizes are nonsummable and sufficiently small. The same results hold for the subgradient method on locally Lipschitz semi-algebraic functions if the step size is constant.","url_abs":"https://arxiv.org/abs/2509.12165","url_pdf":"https://arxiv.org/pdf/2509.12165v2","authors":"[\"Cédric Josz\",\"Wenqing Ouyang\"]","published":"2025-09-15T17:27:00Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}