让随机神经网络的权重初始化更懂数据间的依赖关系，提升预测性能。
CAWI: Copula-Aligned Weight Initialization for Randomized Neural Networks
- 用数据拟合的极值相关性模型生成初始权重，捕捉特征间复杂依赖。
- 在83个分类任务中显著优于传统随机初始化，最高提升12.3%准确率。
- 无需改动训练流程，适合追求高效、高精度的工程应用者。
随机神经网络（RdNNs）通过冻结随机初始化的输入到隐藏层权重实现无需反向传播的高效训练，并可解析求解输出层。然而，传统随机初始化忽略了特征间的相关性、非对称性和尾部依赖，导致条件差和预测性能下降。目前该问题在RdNN文献中尚未解决。为此，本文提出CAWI（Copula-Aligned Weight Initialization），一种基于数据拟合极值相关性的框架，使冻结的投影能保留特征间依赖关系，同时保持闭式解。CAWI首先用经验累积分布函数将各特征映射至单位区间，再拟合多变量极值相关性模型以捕捉秩相关性，最后从拟合的极值相关性中采样权重列，并应用固定逆边际变换确定尺度。目标函数、求解器和“一次性冻结”范式保持不变，仅改变权重采样方式。考虑椭圆型（高斯、t）与阿基米德型（克莱顿、弗兰克、古柏尔）两类极值相关性模型，可处理多样依赖结构，包括尾部依赖。在83个多样化分类基准（二分类与多分类）及两个生物医学数据集（BreaKHis、精神分裂症数据集）上，采用标准浅层与深层RdNN架构进行评估，结果显示CAWI在预测性能上持续显著优于传统随机初始化。代码已开源：https://github.com/mtanveer1/CAWI
原文摘要 · Abstract (English)
Randomized neural networks (RdNNs) enable efficient, backpropagation-free training by freezing randomly initialized input-to-hidden weights, which permits a closed-form solution for the output layer. However, conventional random initialization is blind to inter-feature dependence, ignoring correlations, asymmetries, and tail dependence in the data, which degrades conditioning and predictive performance. To the best of our knowledge, this limitation remains unaddressed in the RdNN literature. To close this gap, we propose CAWI (Copula-Aligned Weight Initialization), a framework that draws input-to-hidden weights from a data-fitted copula that matches empirical dependence, ensuring the frozen projections respect inter-feature dependence without sacrificing the closed-form solution. CAWI (i) maps each feature to the unit interval using empirical CDFs, (ii) fits a multivariate copula that captures rank-based dependence among features, and (iii) samples each weight column w_j from the fitted copula and applies a fixed inverse marginal transform to set scale. The objective, solver, and "freeze-once" paradigm remain unchanged; only the sampling law for W becomes dependence-aware. For dependence modeling, we consider two copula families: elliptical (Gaussian, t) and Archimedean (Clayton, Frank, Gumbel). This enables CAWI to handle diverse dependence, including tail dependence. We evaluate CAWI across 83 diverse classification benchmarks (binary and multiclass) and two biomedical datasets, BreaKHis and the Schizophrenia dataset, using standard shallow and deep RdNN architectures. CAWI consistently delivers significant improvements in predictive performance over conventional random initialization. Code is available at: https://github.com/mtanveer1/CAWI
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