发表机构
The University of Hong Kong（香港大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对训练样本估计非凸梯度流的条件总体风险曲线，提出Flow-ALO方法，通过误差分解与相关条件推导得到误差界，可完成条件总体风险曲线的恢复，且对特定两层平均场网络得分误差界在宽度上均匀。
AI 中文摘要
我们从训练样本估计已实现的光滑非凸梯度流的条件总体风险曲线。Flow-ALO（流近似留一法）传播删除响应，并在近似删除路径上评估遗漏观测值。风险曲线误差可分解为响应近似、精确留一法波动和删除到完整风险的传递。在每个固定有限时间范围内，有界中心化训练损失梯度、单侧海森矩阵下界、局部利普希茨海森矩阵以及严格管闭合条件，可得到删除响应误差的显式(n-1)⁻²界。有界评估损失梯度将删除响应界传递到得分，无需海森矩阵可逆。直接一阶刀切法抵消和精确留一法分别控制删除到完整风险的传递与波动，完成条件总体风险曲线的恢复。对于训练两层的有界光滑两层平均场网络，得分误差界在宽度上是均匀的。
英文摘要
We estimate the conditional population-risk curve of a realized smooth nonconvex gradient flow from the training sample. Flow approximate leave-one-out (Flow-ALO) propagates a deletion response and evaluates omitted observations at approximate deleted paths. The risk-curve error decomposes into response approximation, exact-LOO fluctuation, and deletion-to-full risk transfer. On each fixed finite horizon, bounded centered training-loss gradients, a one-sided Hessian lower bound, locally Lipschitz Hessians, and a strict tube-closure condition yield an explicit $(n-1)^{-2}$ bound for the deletion-response error. Bounded evaluation-loss gradients transfer the deletion-response bound to the score without requiring the Hessian to be invertible. Direct first-order jackknife cancellation and exact-LOO concentration control deletion-to-full risk transfer and fluctuation, respectively, completing recovery of the conditional population-risk curve. For bounded smooth two-layer mean-field networks training both layers, the score-error bound is uniform in width.
Comments63 pages
