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弥合差距:Rademacher复杂性在强大和标准的泛化中
Jiancong Xiao1, Ruoyu Sun2, Qi Long1
1University of Pennsylvania.
概括
这项研究通过引入一种新的统一覆盖数来改善深度神经网络 (DNN) 的对抗性概括. 这种方法实现了更严格的Rademacher复杂度限制,与DNN的标准概括性能相匹配.
科学领域:
- 机器学习 机器学习
- 深度学习理论 深度学习理论
- 竞争力强度 竞争力强度
背景情况:
- 用对抗性示例训练深度神经网络 (DNN) 通常会导致对抗性数据的概括性差.
- 关于对抗性强大的概括的现有研究在实现令人满意的边界方面面临挑战,通常比标准概括产生更宽松的结果.
研究的目的:
- 为了研究使用Rademacher复杂度在DNN中对抗性强大的泛化.
- 为对抗性拉德马切尔复杂度推导出与标准概括界限相匹配的更严格的上限.
主要方法:
- 这项研究使用Rademacher复杂度来分析对抗性概括.
- 引入了一个新概念,即"统一覆盖数",用于计算对抗函数类的覆盖数.
- 拟议的统一覆盖号码是为了与对抗性示例的兼容性和与标准设置相比的精度而设计的.
主要成果:
- 这篇论文为DNN的对抗性Rademacher复杂性设定了新的上限.
- 这些边界与标准设置中最知名的上限相匹配,对宽度和维度的依赖性.
- 提出的方法成功地弥合了Rademacher复杂性之间的差距,在强大的和标准的概括中.
结论:
- 统一覆盖号的引入在理解和提高DNN的对抗性稳定性方面取得了重大进展.
- 衍生的边界表明,在某些条件下,DNN可以实现与标准概括相比较的强大概括.
- 这项工作为开发更强大的深度神经网络来应对敌对攻击提供了理论基础.
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