UniSymNet:一个统一的符号网络,具有稀疏编码和双层优化.
Xinxin Li1, Juan Zhang2, Da Li3
1School of Mathematical Sciences, East China Normal University, Shang Hai, 200241, China.
概括
本研究介绍了一个统一的符号网络 (UniSymNet),以改进数学表达式的发现. UniSymNet 统一了运营商,使得自然现象的建模复杂度降低,性能更好.
科学领域:
- 人工智能的人工智能
- 机器学习 机器学习
- 计算数学 计算数学 计算数学
背景情况:
- 符号回归 (SR) 是发现数学表达式以建模自然现象的关键.
- 传统的SR方法与复杂的树结构作斗争,限制了性能.
- 现有的符号网络面临着多变量运营商和固定架构的挑战,导致过度装配.
研究的目的:
- 提出一个新的统一符号网络 (UniSymNet),克服现有符号网络的局限性.
- 为了增强表达力,并减少发现的数学表达式的复杂性.
- 开发一个灵活的培训框架,适应各种数据集.
主要方法:
- 将非线性二进制运算符统一为嵌套的单元运算符,以创建多变量运算符.
- 开发一个双层优化框架:用于结构选择和目标特定参数优化的变压器预训练.
- 严格的理论证明,以确定UniSymNet的能力.
主要成果:
- UniSymNet 在复杂性和表现性方面展示了理论上的优势.
- 双层优化框架使灵活的结构适应和减少表达式的复杂性.
- 标准基准和SRBench的评估显示了高的符号解决率,合适的准确性和低复杂性.
结论:
- UniSymNet提供了一个有前途的新范式,用于具有增强功能的符号回归.
- 拟议的培训框架有效指导结构选择和参数优化.
- 在发现准确而简洁的数学表达式方面,UniSymNet 实现了卓越的性能.
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