Title: From Graph Local Embedding to Deep Metric Learning. Abstract: Deep metric learning continues to play a crucial role in many computer vision applications, while its various mining and weighting strategies have been extensively investigated. Techniques based on pairwise learning often use excessive random sampling and end up in slow convergence and model degradation. Further, neural network approaches mostly employ MLP layers for metric learning. The tactic can indeed be thought of as graph convolutions with only self-connections, indicating that local neighborhood relationships are neglected. We comprehensively identify the missing neighborhood  relationships issue of conventional embedding and propose a novel approach, termed as Graph Local Embedding (GLE), to deep metric learning. Our method explores the local relationships and draws on the graph convolution networks to construct a discriminative mapping for embedding learning. The strategy can enhance metric learning by exploring the manifold-to-manifold relationships. By focusing on an essential variety of neighboring relations within GLE, burdens of redundant pairs can be substantially eased, and the context of each encoded data is greatly enriched. We demonstrate in the experiments that coupling GLE with existing metric learning techniques can yield impressive performance gains on popular benchmark datasets for fine-grained retrieval.