高度过度参数化的神经网络是否普遍化,因为糟糕的解决方案很少?
概括
在过度参数化的分类器中,许多解决方案产生零训练错误. 随着更多的数据,具有高真错误的"坏"解决方案呈指数级下降,解释了神经网络中良好的概括.
科学领域:
- 机器学习 机器学习
- 优化优化 优化优化
- 统计学学习理论
背景情况:
- 过度参数化的分类器经常通过实证风险最小化 (ERM) 实现零训练错误.
- 在这些设置中存在多个全局最小值,它们的概括性能各不相同.
- 在高度参数化的模型中理解概括仍然是一个关键的挑战.
研究的目的:
- 从理论上分析过度参数化的分类器的概括性质.
- 为了确定条件,在这些条件下,不良的概括解决方案的比例随着数据的增加而减少.
- 为过度参数化的神经网络的有效概括提供解释.
主要方法:
- 在过度参数化的环境中,对全球最小值分布的理论分析.
- 在基于真错分布的"坏"全球最小值的分数上推导边界.
- 使用合成数据集和基准图像数据集进行实证验证 (MNIST,Caltech101).
主要成果:
- "糟糕"全球最小值的比例随着训练样本的数量 (n) 呈指数下降.
- 这种衰变率取决于真错分布,不一定取决于模型的复杂性.
- 理论发现得到了合成和现实世界的数据实验的支持.
结论:
- 该研究为理解过度参数化的分类器中的概括提供了一个理论框架.
- "坏"最小值与数据大小的指数式衰减解释了有效的神经网络概括.
- 这些发现强调了错误分布在函数空间中的重要性,用于概括分析.
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