用机器学习自动简化含椭圆伽马函数的复杂表达式，准确率超99%。
Machine learning modularity
- 基于Transformer和动态批处理，学习应用模变换规则简化表达式
- 在分布内测试准确率超99%，外推到更深混淆仍保持90%以上准确率
- 首次实现用机器学习进行符号化简化，适合理论物理计算场景
基于Transformer序列到序列架构与动态批处理算法，本文提出一个机器学习框架，可自动简化涉及多个椭圆伽马函数（包括q-θ函数和椭圆伽马函数）的复杂表达式。模型学习应用代数恒等式，尤其是SL(2,Z)与SL(3,Z)模变换，将高度混乱的表达式化为标准形式。实验表明，模型在分布内测试中准确率超过99%，在显著外推情况下（如更深的混淆深度）仍保持超过90%的准确率，说明其已内化模变换的底层代数规则，而非仅记忆训练模式。本工作首次成功将机器学习应用于基于模恒等式的符号简化，为量子场论与弦论中的特殊函数计算提供自动化新工具。
原文摘要 · Abstract (English)
Based on a transformer based sequence-to-sequence architecture combined with a dynamic batching algorithm, this work introduces a machine learning framework for automatically simplifying complex expressions involving multiple elliptic Gamma functions, including the $q$-$θ$ function and the elliptic Gamma function. The model learns to apply algebraic identities, particularly the SL$(2,\mathbb{Z})$ and SL$(3,\mathbb{Z})$ modular transformations, to reduce heavily scrambled expressions to their canonical forms. Experimental results show that the model achieves over 99\% accuracy on in-distribution tests and maintains robust performance (exceeding 90\% accuracy) under significant extrapolation, such as with deeper scrambling depths. This demonstrates that the model has internalized the underlying algebraic rules of modular transformations rather than merely memorizing training patterns. Our work presents the first successful application of machine learning to perform symbolic simplification using modular identities, offering a new automated tool for computations with special functions in quantum field theory and the string theory.
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