Ziming Liu, Pingchuan Ma, Yixuan Wang, Wojciech Matusik, Max Tegmark
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引用次数: 0
摘要
当今的人工智能主要基于连接主义，而科学则依赖于符号主义。为了沟通这两个世界，我们提出了一个将科尔莫哥罗夫-阿诺德网络（KANs）与科学无缝协同的框架。该框架强调了 KAN 在科学发现三个方面的用途：识别相关特征、揭示模块结构和发现符号公式。协同作用是双向的：科学到 KAN（将科学知识纳入 KAN），KAN 到科学（从 KAN 中提取科学见解）。我们重点介绍 pykanpackage 中的主要新功能：(1) MultKAN：带有乘法节点的 KAN。(2) kanpiler：将符号公式编译成 KAN 的 KAN 编译器。(3) 树状图转换器：将 KAN（或任何神经网络）转换为树状图。基于这些工具，我们展示了 KAN 发现各类物理定律的能力，包括守恒量、拉格朗日、对称性和构成定律。
A major challenge of AI + Science lies in their inherent incompatibility:
today's AI is primarily based on connectionism, while science depends on
symbolism. To bridge the two worlds, we propose a framework to seamlessly
synergize Kolmogorov-Arnold Networks (KANs) and science. The framework
highlights KANs' usage for three aspects of scientific discovery: identifying
relevant features, revealing modular structures, and discovering symbolic
formulas. The synergy is bidirectional: science to KAN (incorporating
scientific knowledge into KANs), and KAN to science (extracting scientific
insights from KANs). We highlight major new functionalities in the pykan
package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN
compiler that compiles symbolic formulas into KANs. (3) tree converter: convert
KANs (or any neural networks) to tree graphs. Based on these tools, we
demonstrate KANs' capability to discover various types of physical laws,
including conserved quantities, Lagrangians, symmetries, and constitutive laws.
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