用Transformer自动生成符合标准模型对称性的粒子物理拉格朗日量
Generating particle physics Lagrangians with transformers
- 将拉格朗日量视为规则性语言，用Transformer模型根据粒子列表生成
- 在六种物质场内准确率超90%，能泛化到训练数据外的组合
- 模型学会内部表示群论概念，适合理论物理与AI交叉研究者
在物理学中，拉格朗日量为描述物理系统规律提供了系统方法。在粒子物理中，它们编码了宇宙基本组分之间的相互作用与行为。我们将拉格朗日量视为类似语言表达的复杂规则结构，训练了一个在自然语言任务中表现优异的Transformer模型，以根据给定粒子列表预测对应的拉格朗日量。我们报告了该模型在构建遵守标准模型 $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)$ 规范对称性的拉格朗日量方面的表现。结果表明，对于包含最多六种物质场的拉格朗日量，模型准确率超过90%，且具备在架构限制内超越训练分布的泛化能力。通过输入嵌入的分析，我们发现模型在生成过程中已内化群表示和共轭运算等概念。模型与训练数据集已向社区公开，交互式演示可通过链接访问：\url{https://huggingface.co/spaces/JoseEliel/generate-lagrangians}。
原文摘要 · Abstract (English)
In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)$ gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: \url{https://huggingface.co/spaces/JoseEliel/generate-lagrangians}.
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