提出可分析无限宽网络的新型神经网络架构，揭示训练中核函数演化规律。
Mathematical Foundations of Neural Tangents and Infinite-Width Networks
- 设计融合傅里叶特征与层间缩放残差的NTK-ECRN结构
- 证明核矩阵特征值随训练稳定演化，提升泛化与优化稳定性
- 适合研究无限宽网络理论或追求训练鲁棒性的实践者
我们通过神经正切核（NTK）研究无限宽神经网络的数学基础。提出NTK-ECRN架构，结合傅里叶特征嵌入、分层缩放残差连接和随机深度，实现对训练过程中核演化行为的严格分析。理论贡献包括推导出NTK动态的上界，刻画特征值演化规律，并将谱特性与泛化能力及优化稳定性关联。在合成数据与基准数据集上的实验验证了预测的核行为，表明该架构具有更优的训练稳定性和泛化性能。本工作构建了无限宽理论与实际深度学习架构之间的完整框架。
原文摘要 · Abstract (English)
We investigate the mathematical foundations of neural networks in the infinite-width regime through the Neural Tangent Kernel (NTK). We propose the NTK-Eigenvalue-Controlled Residual Network (NTK-ECRN), an architecture integrating Fourier feature embeddings, residual connections with layerwise scaling, and stochastic depth to enable rigorous analysis of kernel evolution during training. Our theoretical contributions include deriving bounds on NTK dynamics, characterizing eigenvalue evolution, and linking spectral properties to generalization and optimization stability. Empirical results on synthetic and benchmark datasets validate the predicted kernel behavior and demonstrate improved training stability and generalization. This work provides a comprehensive framework bridging infinite-width theory and practical deep-learning architectures.
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