Nonlinear Maps Between Irreducible Representations in Graph Neural Networks
Read the original on arXiv Machine Learning →The paper introduces a degree‑resolved framework for nonlinear interactions between irreducible representations in graph neural networks, enabling mixing of non‑isomorphic representations that linear equivariant maps cannot achieve. Using this framework, the authors build Specht Triple, a residual module for unordered graph triples, and demonstrate that it reduces aggregate standardised test MSE by 11.05% on a synthetic structural benchmark compared to a parameter‑matched linear baseline. The results highlight irreducible decomposition as a useful inductive bias for nonlinear higher‑order equivariant processing.
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