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arXiv · 2611.02274

Invertible Graph Aggregation Can Increase ReLU Readout Width

Hiroyasu Usami·Masanori Tsukamoto·Kohei Hashiguchi
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Abstract

An invertible graph aggregation preserves the complete feature table, but can increase the size of a classifier that reads one node at a time. For every even $N\ge4$, we construct a labeled tree with $2N$ vertices and maximum degree three. A shared one-hidden-layer rectified linear unit (ReLU) classifier needs one hidden unit on the raw scalar features and exactly $N$ units after one lazy neighborhood mean. All aggregate values are distinct, and the mixing matrix has condition number at most 8. We determine the complete error curve for heads with a free affine term. The width separation persists under scalar perturbations. Under a specified bounded uniform-noise model with one nuisance coordinate, every one-unit aggregate head has expected error at least $1/12$, while a fixed $N$-unit head has zero error. Controlled fits compare trained heads with these explicit feasible scores. On Roman-empire and Tolokers, aggregation improves fitted prediction, and retaining raw features helps at the largest tested parameter budget. Training-only diagnostics include conditional output-layer optimality bounds for eight fixed runs.

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Hiroyasu Usami, Masanori Tsukamoto, Kohei Hashiguchi. 2026-11-01. Invertible Graph Aggregation Can Increase ReLU Readout Width. https://arxiv.org/abs/2611.02274

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