Interpretable Machine Learning for Kronecker Coefficients

TL;DR

This paper explores the use of interpretable machine learning models, including neural networks and transformers, to predict the vanishing of Kronecker coefficients with high accuracy, providing insights and explicit decision formulas.

Contribution

It introduces novel interpretable ML approaches and transformer models for predicting Kronecker coefficients, achieving high accuracy and deriving explicit decision formulas.

Findings

Neural network models reach about 83% accuracy.

Transformer models achieve over 99% accuracy.

Explicit formulas for decision functions are derived.

Abstract

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%.