---
title: "Nonlinear Maps Between Irreducible Representations in Graph Neural Networks"
source: "arXiv AI/CL/LG（论文）"
source_tier: "t2"
url: "https://arxiv.org/abs/2610.41059v1"
permalink: "https://feed.astralor.com/items/itm_e582b6d2f7aaebbb4993b86c"
published: "2026-10-29T22:56:36.000Z"
score: 51
channel: "ai"
tags: ["Nonlinear Maps Between","Irreducible Representations","Graph Neural Networks","Equivariant","Specht Triple","GIN"]
---

# Nonlinear Maps Between Irreducible Representations in Graph Neural Networks

## At a glance

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 in…

## Key points

- 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…

## Full text

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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