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概括 对于浅层神经网络的梯度下降的保证
Puyu Wang1, Yunwen Lei2, Di Wang3
1Hong Kong Baptist University, Hong Kong wangpuyu1026@gmail.com.
Neural computation
|November 18, 2024
概括
本研究分析了使用算法稳定性的神经网络 (NN) 的概括,将以前的工作扩展到两层和三层网络. 我们展示了梯度下降 (GD) 可以达到01/n的风险率,揭示了有效培训的条件.
科学领域:
- 机器学习 机器学习
- 深度学习理论 深度学习理论
- 算法稳定性 算法稳定性
背景情况:
- 了解神经网络 (NN) 概括对于可靠的AI至关重要.
- 算法稳定性为分析概括提供了一个框架.
- 以前的研究主要集中在单隐层网络上,忽视了网络扩展效应.
研究的目的:
- 将算法稳定性和概括分析扩展到由梯度下降 (GD) 训练的两层和三层神经网络.
- 调查网络扩展对通用化的影响.
- 导出在NNs中实现最佳风险率的条件.
主要方法:
- 对二层和三层NNs的GD进行了全面的稳定性和概括性分析.
- 在一般网络扩展下放松双层NN的先前条件.
- 使用一种新的诱导策略来证明三层NNN的几乎共同强制性属性,考虑到过度参数化.
主要成果:
- 在两层和三层的NN中,GD的风险过剩率为O(1/n).
- 确定了不足和过度参数化的NN的足够和必要条件,以实现O (n) 风险率.
- 已证明,扩展因子增加或网络复杂性降低可以减少为最佳错误率所需的过度参数化.
- 在低噪音条件下实现了两种网络类型的快速O{\displaystyle O}1/n) 风险率.
结论:
- 该研究为更深层次的网络提供了对GD概括的概括理解.
- 网络扩展和复杂性是影响泛化性能的关键因素.
- 这些发现为培训NN提供了实际见解,以提高概括和错误率.
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