Symmetrical Synthesis for Deep Metric Learning

Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard sample generation are adopting autoencoders or generative adversarial networks, but this leads to more hyper-parameters, harder optimization, and slower training speed. In this paper, we address these problems by proposing a novel method of synthetic hard sample generation called symmetrical synthesis. Given two original feature points from the same class, the proposed method firstly generates synthetic points with each other as an axis of symmetry. Secondly, it performs hard negative pair mining within the original and synthetic points to select a more informative negative pair for computing the metric learning loss. Our proposed method is hyper-parameter free and plug-and-play for existing metric learning losses without network modification. We demonstrate the superiority of our proposed method over existing methods for a variety of loss functions on clustering and image retrieval tasks.

The Properties of Sets of Temporal Logic Subformulas

Summary This is a second preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [17]. We introduce two modified definitions of a subformula. In the former one we treat until-formula as indivisible. In the latter one, we extend the set of subformulas of until-formulas by a special disjunctive formula. This is needed to construct a temporal model. We also define an ordered positive-negative pair of finite sequences of formulas (PNP). PNPs represent states of a temporal model.