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梯度下降可能在浅浅的RELU网络的培训中避免了点
Patrick Cheridito1, Arnulf Jentzen2,3, Florian Rossmannek1,4
1Department of Mathematics and RiskLab, ETH Zurich, Zurich, Switzerland.
概括
梯度下降可以避免在机器学习优化中的点,即使在放松的条件下. 这项研究证明了在特定初始化下,直线单元 (ReLU) 网络的全球最小值的趋同.
科学领域:
- 优化理论 优化理论
- 动态系统是动态系统.
- 机器学习 机器学习
背景情况:
- 梯度下降被广泛用于机器学习中的优化.
- 动态系统理论表明,梯度下降可以绕过严格的位.
- 标准理论需要严格的规律性条件,在实践中并不总是满足.
研究的目的:
- 为了证明中心稳定多重体定理的一个变体,具有放松的规律性条件.
- 在机器学习任务中分析梯度下降的行为,特别是浅层神经网络.
- 调查避免坐点和接近全球最小值的情况.
主要方法:
- 应用动态系统理论来分析优化算法.
- 放松中心稳定多重体定理的规律性条件.
- 检查浅层ReLU和泄漏的ReLU网络的损失函数的关键点.
- 分析梯度下降动力学与标量输入和亲属目标函数.
主要成果:
- 中心稳定的多重数定理的一个变体被证明具有放松的规律性.
- 梯度下降被证明可以在浅的ReLU和漏洞的ReLU网络中绕过大多数点.
- 在有利的初始化条件下,向全球最小值的收被证明.
- 限制损失的明确门量化了趋同条件.
结论:
- 放松动态系统的结果与实际机器学习应用相关.
- 梯度下降在导航浅层神经网络的损失景观时表现出强大的行为.
- 了解关键点和初始化是保证全球优化趋同的关键.
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