用可解释模型预测对称群克罗内克系数是否为零，准确率超99%。
Interpretable Machine Learning for Kronecker Coefficients
- 以分拆三元组和主成分导出的b-loadings为输入特征
- 最高准确率达99%，并推导出基于b-loadings的显式决策公式
- 适合代数表示论与机器学习交叉研究者阅读
我们分析神经网络的显著性，并采用可解释机器学习模型预测对称群的克罗内克系数是否为零。模型输入为分拆三元组以及由捕捉分拆差异嵌入的主成分导出的b-loadings。所有方法中准确率均约为83%，并推导出基于b-loadings的显式决策函数。此外，我们开发了基于Transformer的模型，达到目前报告的最高准确率超过99%。
原文摘要 · Abstract (English)
We analyze the saliency of neural networks and employ interpretable machine learning models to predict whether the Kronecker coefficients of the symmetric group are zero or not. Our models use triples of partitions as input features, as well as b-loadings derived from the principal component of an embedding that captures the differences between partitions. Across all approaches, we achieve an accuracy of approximately 83% and derive explicit formulas for a decision function in terms of b-loadings. Additionally, we develop transformer-based models for prediction, achieving the highest reported accuracy of over 99%.
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