Title: Towards Principled Representation Learning for Entity Alignment. Abstract: Knowledge graph (KG) representation learning for entity alignment has recently received great attention. Compared with conventional methods, these embedding-based ones are considered to be robuster for highly-heterogeneous and cross-lingual entity alignment scenarios as they do not rely on the quality of  machine translation or feature extraction. Despite the significant improvement that has been made, there is little understanding of how the embedding-based entity alignment methods actually work. Most existing methods rest on the foundation that a small number of pre-aligned entities can serve as anchors to connect the embedding spaces of two KGs. But no one investigates the rationality of such foundation. In this paper, we define a typical paradigm abstracted from the existing methods, and analyze how the representation discrepancy between two potentially-aligned entities is implicitly bounded by a predefined margin in the scoring function for embedding learning. However, such a margin cannot guarantee to be tight enough for alignment learning. We mitigate this problem by proposing a new approach that explicitly learns KG-invariant and principled entity representations, meanwhile preserves the original infrastructure of existing methods. In this sense, the model not only pursues the closeness of aligned entities on geometric distance, but also aligns the neural ontologies of two KGs to eliminate the discrepancy in feature distribution and underlying ontology knowledge. Our experiments demonstrate consistent and significant improvement in performance against the existing embedding-based entity alignment methods, including several state-of-the-art ones.