Optimization of machine learning models is commonly performed through
stochastic gradient updates on randomly ordered training examples. This
practice means that sub-epochs comprise of independent random samples of the
training data that may not preserve informative structure present in the full
data. We hypothesize that the training can be more effective with {\em
self-similar} arrangements that potentially allow each epoch to provide
benefits of multiple ones. We study this for "matrix factorization" -- the
common task of learning metric embeddings of entities such as queries, videos,
or words from example pairwise associations. We construct arrangements that
preserve the weighted Jaccard similarities of rows and columns and
experimentally observe training acceleration of 3\%-37\% on synthetic and
recommendation datasets. Principled arrangements of training examples emerge as
a novel and potentially powerful enhancement to SGD that merits further
exploration.

本研究证明，对机器学习模型进行随机梯度更新常常使子时期包括独立随机样本，可能无法保留完整数据中存在的信息结构，建立自相似的训练样本可以更有效地训练矩阵分解等任务，并且通过实验证明加速了训练。