PreprintarXiv licencearXiv
Nonlinear Maps Between Irreducible Representations in Graph Neural Networks
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
@misc{shayestehfar2026nonlinear,
title = {{Nonlinear Maps Between Irreducible Representations in Graph Neural Networks}},
author = {Mani Shayestehfar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41059},
eprint = {2610.41059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41059},
}
RIS
TY - UNPB
TI - Nonlinear Maps Between Irreducible Representations in Graph Neural Networks
AU - Mani Shayestehfar
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.41059
UR - https://arxiv.org/abs/2610.41059
AB - 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.
ER -