提出一种新型神经网络初始化方法，可稳定训练超深网络。
Initialization of a Polyharmonic Cascade, Launch and Testing
- 用超八面体结构实现对称初始化，简化深层网络训练
- 500层无跳跃连接网络仍稳定训练，MNIST准确率达98.3%
- 适合追求极深架构、重视训练稳定性的研究者
本文总结了对多谐波级联（polyharmonic cascade）这一基于对称性原理与随机函数理论推导出的深度机器学习架构的研究。提出一种通用初始化方法，基于包含中心点的超八面体对称构型。该方法不仅确保了含数十至数百层（最多500层无跳跃连接）级联网络的稳定训练，还大幅简化计算过程。在MNIST（无需卷积或数据增强，准确率98.3%）、HIGGS（1100万样本，AUC约0.885）和Epsilon（2000个特征，AUC约0.963）数据集上验证了其可扩展性与鲁棒性。所有线性代数运算被简化为二维操作，可在GPU上高效执行。提供公开代码仓库与归档快照，确保完全可复现。
原文摘要 · Abstract (English)
This paper concludes a series of studies on the polyharmonic cascade, a deep machine learning architecture theoretically derived from indifference principles and the theory of random functions. A universal initialization procedure is proposed, based on symmetric constellations in the form of hyperoctahedra with a central point. This initialization not only ensures stable training of cascades with tens and hundreds of layers (up to 500 layers without skip connections), but also radically simplifies the computations. Scalability and robustness are demonstrated on MNIST (98.3% without convolutions or augmentations), HIGGS (AUC approximately 0.885 on 11M examples), and Epsilon (AUC approximately 0.963 with 2000 features). All linear algebra is reduced to 2D operations and is efficiently executed on GPUs. A public repository and an archived snapshot are provided for full reproducibility.
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