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改进了基于多层感知子的分数顺序梯度下降方法
Xiaojun Zhou1, Chunna Zhao1, Yaqun Huang1
1School of Information Science and Engineering, Yunnan University, Kunming, 650091, China.
改进的分数顺序梯度下降 (IFOGD) 方法将分数顺序的差异化应用于人工神经网络 (ANN) 中的隐藏层. 这提高了深度学习任务的灵活性和性能.
科学领域:
- 人工智能的人工智能
- 机器学习 机器学习
- 深度学习 (Deep Learning) 是一种深度学习.
背景情况:
- 分数级梯度下降 (FOGD) 在人工神经网络 (ANN) 中使用,但通常只适用于损失函数.
- 将FOGD扩展到隐藏层,为新型深度学习优化器提供了更大的灵活性和潜力.
研究的目的:
- 提出一种改进的分数顺序梯度下降 (IFOGD) 方法,适用于多层感知子 (MLP) 的隐藏层.
- 在PyTorch中开发一个分数顺序的Autograd (FOAutograd) 系统,以增强深度学习.
- 在各种任务中验证IFOGD方法的性能和稳定性.
主要方法:
- 开发了一个分数矩阵差异化算法和MLP隐藏层的解决方案.
- 解决了绝对值函数引起的反向传播分歧问题.
- 通过重建PyTorch的线性层和平均平方误差损失模块来实现FOAutograd.
- 集成的FOAutograd与适应性优化器用于分数顺序梯度更新.
主要成果:
- 拟议的IFOGD方法可以在ANN的隐藏层中成功应用.
- 该方法确保稳定的损失函数值,避免分歧.
- 模拟实验和时间序列预测任务显示了IFOGD的竞争性表现.
结论:
- IFOGD方法提供了一种强大而灵活的方法,用于将分数微积分纳入深度学习.
- 这项工作为一个新的分数顺序深度学习优化器家族奠定了基础.
- IFOGD在各种应用中显示出改善ANN性能的巨大潜力.
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