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PostDeg: Placement Beats Parameterization in LayerNorm GNNs
arXiv:2606.14022v2 Announce Type: replace Abstract: LayerNorm-based GNNs routinely erase the topology signals (degree, centrality, $k$-core) that node-selection policies should depend on, but the literature has not located where in the residual block the erasure happens. We answer that question: a positive per-node scalar inserted before LayerNorm is divided out up to a stabilizer term, while the same scalar inserted after LayerNorm reaches the score head as representation magnitude. The surviving slot is the post-LayerNorm position. We instantiate it with PostDeg, a parameter-free post-LayerNorm inverse-degree scale, and pre-register four falsifiers (graphwise scalars, extra LayerNorm, expressive same-slot capacity, backbone-agnostic source) that would reject the rule. PostDeg gains $+3.5\%/+2.5\%/+5.6\%$ over the LN backbone on influence maximization, network dismantling, and maximum independent set, with $10/10$ paired-seed wins per task; none of the four falsifiers fires. The takeaway is that placement, not parameterization, carries the gain -- a small invariance check that generalizes to any positive topology scalar in any normalized residual stack.
Abstract:LayerNorm-based GNNs routinely erase the topology signals (degree, centrality, $k$-core) that node-selection policies should depend on, but the literature has not located where in the residual block the erasure happens. We answer that question: a positive per-node scalar inserted before LayerNorm is divided out up to a stabilizer term, while the same scalar inserted after LayerNorm reaches the score head as representation magnitude. The surviving slot is the post-LayerNorm position. We instantiate it with PostDeg, a parameter-free post-LayerNorm inverse-degree scale, and pre-register four falsifiers (graphwise scalars, extra LayerNorm, expressive same-slot capacity, backbone-agnostic source) that would reject the rule. PostDeg gains $+3.5\%/+2.5\%/+5.6\%$ over the LN backbone on influence maximization, network dismantling, and maximum independent set, with $10/10$ paired-seed wins per task; none of the four falsifiers fires. The takeaway is that placement, not parameterization, carries the gain -- a small invariance check that generalizes to any positive topology scalar in any normalized residual stack.
After reviews and such, significant methodological issues surfaced that ultimately warranted a complete withdrawal of our paper. Thank you for understanding
Machine Learning (cs.LG)
arXiv:2606.14022 [cs.LG]
(or arXiv:2606.14022v2 [cs.LG] for this version)
Full text under the publisher's open licence · 185 words
