广义图变分自编码器：有界散度控制后验坍缩

中文摘要 AI 辅助

变分图自编码器（VGAE）通过Kullback-Leibler散度将其后验正则化到先验，这一选择继承自变分自编码器而非经过论证。我们引入了广义图变分自编码器（GGVA），该模型用Rényi-Tsallis族中任意阶$q$的成员替换该项，同时保持模型的其他部分不变。这两个成员对于对角高斯分布均具有闭式解，并且当$q \ o 1$时均精确恢复KL散度，因此VGAE是我们模型在$q=1$时的特例，而非独立的基线，任何测量到的差异都可归因于单个标量。我们的分析将有界性而非阶数确定为关键属性：对于$q<1$，Tsallis散度的上界为$1/(1-q)$，与潜在宽度无关，而KL散度和同阶的Rényi散度则是无界的。在跨越三个合成族、一个社交网络、三个引文网络、一个连接组、一个电网和一个道路网络的十个图上，$q$使保留的后验信息相对于VGAE最多变化$49\ imes$，而同阶的Rényi分支在所有六个较大的真实图上保持在VGAE的$1.02$-$1.30\ imes$范围内（将有界性隔离为原因）。保留的信息是可用的：探测冻结嵌入中的节点类别（该标签不在目标函数中），GGVA在CiteSeer上相对于VGAE最多获得$+0.14$的宏F1值，而Rényi对照再次跟踪VGAE。我们还报告了设计旨在揭示的内容：这些方法在六个较大的真实图上均未达到留出法链路预测的准确性，并且有界性延迟了后验坍缩而非阻止它。

英文摘要

The variational graph autoencoder (VGAE) regularizes its posterior toward the prior with the Kullback-Leibler divergence, a choice inherited from the variational autoencoder rather than argued for. We introduce the generalized graph variational autoencoder (GGVA), which replaces that term with any member of the Rényi-Tsallis family of order $q$ while leaving every other part of the model untouched. Both members admit closed forms for diagonal Gaussians and both recover the KL exactly as $q \to 1$, so the VGAE is the $q=1$ arm of our own model rather than a separate baseline, and any measured difference is attributable to a single scalar. Our analysis identifies boundedness, not the order, as the operative property: for $q<1$ the Tsallis divergence is bounded above by $1/(1-q)$, independently of the latent width, whereas the KL and the Rényi divergence of the same order are unbounded. On ten graphs spanning three synthetic families, a social network, three citation networks, a connectome, a power grid and a road network, $q$ moves the retained posterior information by up to $49\times$ relative to the VGAE, while the Rényi arm at the same order stays within $1.02$-$1.30\times$ of it on all six larger real graphs (isolating the bound as the cause). The retained information is usable: probing the frozen embedding for node class, a label absent from the objective, gives GGVA up to $+0.14$ macro-F1 over the VGAE on CiteSeer, with the Rényi control again tracking the VGAE. We also report what the design was built to expose: none of this reaches held-out link-prediction accuracy on any of the six larger real graphs, and boundedness delays posterior collapse rather than preventing it.

发表机构

• UCL（伦敦大学学院）
• Holistic AI
• University of Utah（犹他大学）
• PUC-Rio（里约热内卢天主教大学）

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