arXiv：cs.LG· F\'elix Marcoccia·· 6 小时前AI 评分34
为消息传递网络缓解过度压缩：可寻址与支持感知的全局记忆
Escaping Oversquashing: Addressable and Support-Aware Global Memory for Message Passing Networks
AI 导读
研究针对消息传递网络过度压缩问题的虚拟节点全局记忆，提出可寻址性与支持感知两项性质：在恒定边距地址码与放大该边距的非线性下，乘性读写映射仅用 O(log M) 维地址码即可提供 M 条可选记忆行，cross-attention 槽与受限 ELU+1 双线性记忆均满足条件。
正文
Abstract:Virtual nodes are a natural tool against oversquashing: they replace long message-passing paths by a two-hop global route. But when many nodes share one global state, that shortcut can become a bottleneck itself. We study two properties of this global memory. First, addressability: under constant-margin address codes and a nonlinearity that amplifies this margin, multiplicative write/read maps provide $M$ selectable memory rows with only $O(\log M)$ address-code dimensions. Cross-attention slots and a constrained $ELU+1$ bilinear memory both satisfy these conditions. Second, support awareness: normalized cross-attention has no self-key for a latent query to use as a reference. A learned private anchor supplies this reference, keeps the read bounded, and exposes the strength of the matching source mass. We demonstrate the merits of such properties on several instances of Two-Radius and Tree-NeighborsMatch: both addressable realizations solve the controlled tasks through depth $5$, where pooled VNs of comparable or larger size reach about $10.6\%$.
| Comments: | preliminary work |
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2608.02709 [cs.LG] |
| (or arXiv:2608.02709v2 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2608.02709 arXiv-issued DOI via DataCite |
Submission history
From: Félix Marcoccia [view email]
[v1]
Mon, 3 Aug 2026 17:44:10 UTC (31 KB)
[v2]
Fri, 2 Oct 2026 14:30:43 UTC (51 KB)
来源：arXiv：cs.LG · arxiv.org