  Predicting missing facts in a knowledge graph (KG) is crucial as modern KGs
are far from complete. Due to labor-intensive human labeling, this phenomenon
deteriorates when handling knowledge represented in various languages. In this
paper, we explore multilingual KG completion, which leverages limited seed
alignment as a bridge, to embrace the collective knowledge from multiple
languages. However, language alignment used in prior works is still not fully
exploited: (1) alignment pairs are treated equally to maximally push parallel
entities to be close, which ignores KG capacity inconsistency; (2) seed
alignment is scarce and new alignment identification is usually in a noisily
unsupervised manner. To tackle these issues, we propose a novel self-supervised
adaptive graph alignment (SS-AGA) method. Specifically, SS-AGA fuses all KGs as
a whole graph by regarding alignment as a new edge type. As such, information
propagation and noise influence across KGs can be adaptively controlled via
relation-aware attention weights. Meanwhile, SS-AGA features a new pair
generator that dynamically captures potential alignment pairs in a
self-supervised paradigm. Extensive experiments on both the public multilingual
DBPedia KG and newly-created industrial multilingual E-commerce KG empirically
demonstrate the effectiveness of SS-AG
