arXiv：cs.LG· Yi Fan, Vishnu Jejjala, Yang Lei·· 4 小时前AI 评分34
基于 Transformer 的机器学习框架实现椭圆 Gamma 函数符号化简
Machine learning modularity
AI 导读
一个基于 Transformer 序列到序列架构结合动态批处理算法的机器学习框架，可自动化简包含椭圆 Gamma 函数与 q-θ 函数的复杂表达式，通过学习 SL(2,Z) 和 SL(3,Z) 模变换将混乱表达式约简为规范形式。
正文
Abstract: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 $q$-$\theta$ 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.
| Comments: | 48 pages, 7 figures, 6 tables; v2: to be published in PRD, discussions and applications added |
| Subjects: | High Energy Physics - Theory (hep-th); Machine Learning (cs.LG) |
| Cite as: | arXiv:2601.01779 [hep-th] |
| (or arXiv:2601.01779v2 [hep-th] for this version) | |
| https://doi.org/10.48550/arXiv.2601.01779 arXiv-issued DOI via DataCite |
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| Related DOI: | https://doi.org/10.1103/j99v-l6zq
DOI(s) linking to related resources |
Submission history
From: Yang Lei [view email]
[v1]
Mon, 5 Jan 2026 04:17:55 UTC (18,795 KB)
[v2]
Wed, 7 Oct 2026 13:43:08 UTC (18,806 KB)
来源：arXiv：cs.LG · arxiv.org