{"ID":2852007,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.18242","arxiv_id":"2510.18242","title":"Fast and Efficient Parallel Sampling Using Higher Order Langevin Dynamics","abstract":"We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps in the dimension $d$, the target accuracy $\\varepsilon^{-1}$, or both. Picard-based parallel sampling methods reduce this sequential depth to polylogarithmic scale by solving for many time-discretization points in parallel; however, existing guarantees often require a polynomial number of processors, leading to substantial memory and gradient-evaluation costs in high dimensions. We show that higher-order Langevin structure can reduce this parallel resource burden while preserving polylogarithmic sequential depth. Our method combines arbitrary-order Langevin dynamics with blockwise Lagrange polynomial interpolation. This sharper discretization reduces the number of parallel points required to achieve a target accuracy. Our results cover both higher-order smooth potentials and ridge-separable potentials, including models such as Bayesian logistic regression and two-layer neural networks, and improve upon the space complexity of the current literature on parallel log-concave sampling.","short_abstract":"We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps in the dimension $d$, the target accuracy $\\varepsilon^{-1}$, or both. Picard-bas...","url_abs":"https://arxiv.org/abs/2510.18242","url_pdf":"https://arxiv.org/pdf/2510.18242v2","authors":"[\"Jaideep Mahajan\",\"Kaihong Zhang\",\"Feng Liang\",\"Jingbo Liu\"]","published":"2025-10-21T03:04:58Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.ME\",\"stat.ML\"]","methods":"[]","has_code":false}