We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and marginal volatilities and how to regularise the eigenvalues of large equity covariance matrices. This explicit mathematical mapping offers clear interpretability of each module's role, so the model cannot be regarded as a pure black box. The architecture mirrors the analytical form of the global minimum-variance solution yet remains agnostic to dimension, so a single model can be calibrated on panels of a few hundred stocks and applied, without retraining, to one thousand US equities, a cross-sectional jump that indicates robust generalization capability. The loss function is the future short-term realized minimum variance and is optimized end-to-end on real returns. In out-of-sample tests from January 2000 to December 2024, the estimator delivers systematically lower realized volatility, smaller maximum drawdowns, and higher Sharpe ratios than the best competitors, including state-of-the-art non-linear shrinkage, and these advantages persist across both short and long evaluation horizons despite the model's training focus is short-term. Furthermore, although the model is trained end-to-end to produce an unconstrained minimum-variance portfolio, we show that its learned covariance representation can be used in general optimizers under long-only constraints with virtually no loss in its performance advantage over competing estimators. These advantages persist when the strategy is executed under a highly realistic implementation framework that models market orders at the auctions, empirical slippage, exchange fees, and financing charges for leverage, and they remain stable during episodes of acute market stress.

翻译：本文提出一种旋转不变神经网络，通过联合学习历史收益与边际波动率的滞后变换以及大型权益协方差矩阵特征值的正则化方法，实现全局最小方差投资组合的求解。该显式数学映射清晰阐明了每个模块的功能，使得模型并非纯粹的黑箱。其架构呼应全局最小方差解的解析形式，同时保持维度无关性，因此单个模型可在数百只股票的面板数据上完成校准，并直接应用于1000只美国股票而无需重新训练——这一跨截面跳跃表明其具备稳健的泛化能力。损失函数为未来短期已实现最小方差，并在实际收益数据上实现端到端优化。在2000年1月至2024年12月的样本外测试中，该估计器相较于包括最先进非线性压缩方法在内的最佳竞争者，系统性地实现了更低的已实现波动率、更小的最大回撤和更高的夏普比率，且这些优势在短期与长期评估窗口内持续存在——尽管模型训练聚焦于短期。此外，尽管该模型以端到端方式训练以生成无约束最小方差投资组合，但研究表明其习得的协方差表征可用于仅做多约束条件下的通用优化器，且相对于竞争估计器的性能优势几乎没有损失。当策略在高度现实的执行框架（模拟集合竞价市价单、经验滑点、交易所费用及杠杆融资成本）中实施时，这些优势依然保持，并在市场剧烈压力时期保持稳定。