研究人员提出了一种新颖的浅层神经网络变分表述，将离散训练问题视为连续变分代理。该方法利用加权 Sobolev 空间中的 $\lambda$-凸泛函，证明了全局适定性和稳定性以及出乎意料的正则性。与现有方法不同，这种表述提供了对椭圆正则性和凸分析的直接访问，通过单个线性系统求解最优参数密度，从而完全绕过了迭代优化。该工作还建立了明确的泛化误差控制，并证明了有限宽度网络以 $O(1/N)$ 的速率达到连续体最优值，弥合了神经切线核和特征学习机制之间的差距。 AI
影响 为理解和简化神经网络优化提供了新的理论框架。
排序理由 详细介绍神经网络训练新理论方法的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]
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arXiv:2607.02003v1 Announce Type: new Abstract: Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochastic heuristics. In this work, we propose a paradigm sh…
Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochastic heuristics. In this work, we propose a paradigm shift by replacing the discrete training problem o…