Causality of KAG in learning and optimization

Determine whether Kolmogorov-Arnold geometry actively aids learning or instead emerges as a consequence of optimization dynamics in trained neural networks, assessing the causal role of KA geometric signatures in learning effectiveness.

Background

The paper demonstrates that KAG emerges spontaneously in shallow MLPs on MNIST and is robust across spatial scales and training procedures. However, the authors explicitly state that the causal status of KAG remains unresolved: whether KAG contributes to effective learning or merely results from optimization dynamics.

Earlier in the discussion, the authors suggest intervention experiments (e.g., frustration or explicit regularization) as potential approaches to address this causality, but they leave the core question explicitly open in the conclusion.