Nonlinear Maps Between Irreducible Representations in Graph Neural Networks

Mani Shayestehfar

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arXiv · 2610.41059

Nonlinear Maps Between Irreducible Representations in Graph Neural Networks

Mani Shayestehfar

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Abstract

Equivariant linear maps cannot mix non-isomorphic irreducible representations, whereas nonlinear activations can. We develop a degree-resolved version of this nonlinear interaction picture and use the resulting block inventory to construct Specht Triple, a residual on unordered graph triples. On a synthetic structural benchmark with a frozen GIN backbone, Specht Triple reduces aggregate standardised test MSE by 11.05% relative to a parameter-matched Projector Control using the same irreducible projectors and complete linear equivariant space. The results support irreducible decomposition as an inductive bias for nonlinear higher-order equivariant processing.

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BibTeX RIS

Mani Shayestehfar. 2026-10-29. Nonlinear Maps Between Irreducible Representations in Graph Neural Networks. https://arxiv.org/abs/2610.41059

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