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随机梯度下降引入了有效的依赖于景观的规范化,有利于平面解决方案.
Ning Yang1, Chao Tang1,2,3, Yuhai Tu4
1Peking-Tsinghua Center for Life Science, Peking University, Beijing 100871, China.
Physical review letters
|June 24, 2023
概括
随机梯度下降 (SGD) 噪音有助于深度学习模型通过在损失景观中找到更平坦的最小值来概括. 这种规范化效应提高了通用化到关键噪声水平,提高了模型性能.
科学领域:
- 深度学习 (Deep Learning) 是一种深度学习.
- 优化理论 优化理论
- 机器学习 机器学习
背景情况:
- 一般化是深度学习的一个关键挑战,通常通过在损失格局中找到平面最小值来解决.
- 随机梯度下降 (SGD) 经验上与找到这些平面最小值有关,这对于良好的概括至关重要.
- 深度学习中的过度参数化导致了许多低损失的解决方案,这使得寻找可概括的模型变得复杂.
研究的目的:
- 阐明SGD噪声在找到平面最小值和改进概括方面的作用.
- 了解SGD固有的噪音如何影响损失格局和学习动态.
- 为高效的深度学习提供超参数选择的洞察力,没有分歧.
主要方法:
- 构建了一个简化的模型,连续设置了一组退化的最小值.
- 大致的迷你批量损失景观作为整体损失函数的随机转移.
- 执行了随机学习动态的直接模拟,并解决了相关的福克-普朗克方程.
主要成果:
- SGD噪声引入了一个异构的有效损失期,随着景观平坦度的下降而减少.
- 这种SGD诱导的损失起到规范化作用,打破退化,有利于更平坦的解决方案.
- 增加的SGD噪声强度导致整体损失景观更平坦,改善了通用化到一个关键点.
结论:
- 通过有效地规范学习过程以达到更平坦的最小值,SGD噪声在促进概括方面发挥着至关重要的作用.
- 这些发现提供了对SGD对损失景观几何和概括的影响的理论理解.
- 结果表明,选择最佳超参数,如学习率和批量大小,以平衡概括和收,有意义.
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