梳理非凸光滑性条件，评估其在训练线性神经网络中的有效性

Recent Advances in Non-convex Smoothness Conditions and Applicability to Deep Linear Neural Networks

• 提出系统性排序的非凸光滑性条件
• 验证这些条件在二分类线性网络中的适用性
• 为优化理论提供可检验的判据，适合研究者参考

深度学习中的平滑优化问题普遍存在非凸性，催生了文献中一系列新的光滑性条件及其对应的收敛性分析。本文系统讨论这些光滑性条件，对其进行排序，给出判定其成立的充分条件，并评估它们在训练用于二分类任务的深层线性神经网络中的实际适用性。结果表明，部分条件在特定结构下可满足，但整体适用范围受限，揭示了当前理论对真实模型的刻画局限性。

原文摘要 · Abstract (English)

The presence of non-convexity in smooth optimization problems arising from deep learning have sparked new smoothness conditions in the literature and corresponding convergence analyses. We discuss these smoothness conditions, order them, provide conditions for determining whether they hold, and evaluate their applicability to training a deep linear neural network for binary classification.

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