You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
At present, the great achievements of convolutional neural network(CNN) in feature and metric learning have attracted many researchers. However, the vast majority of deep network architectures have been used to represent based on real values. The research of complex-valued networks is seldom concerned due to the absence of effective models and suitable distance of complex-valued vector. Motived by recent works, complex vectors have been shown to have a richer representational capacity and efficient complex blocks have been reported, we propose a new approach for learning image descriptors with complex numbers to compare image patches. We also propose a new architecture to learn image similarity function directly based on complex-valued network. We show that our models can perform competitive results on benchmark datasets. We make the source code of our models publicly available.

Cited Abstract(s):
[1]: Deep learning has proven itself as a successful set of models for learning useful semantic representations of data. These, however, are mostly implicitly learned as part of a classification task. In this paper we propose the triplet network model, which aims to learn useful representations by distance comparisons. A similar model was defined by (2014), tailor made for learning a ranking for image information retrieval. Here we demonstrate using various datasets that our model learns a better representation than that of its immediate competitor, the Siamese network. We also discuss future possible usage as a framework for unsupervised learning.

[2]: Despite significant recent advances in the field of face recognition [10, 14, 15, 17], implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors.

[3]: Motivated by large-scale multimedia applications we propose to learn mappings from high-dimensional data to binary codes that preserve semantic similarity. Binary codes are well suited to large-scale applications as they are storage efficient and permit exact sub-linear kNN search. The framework is applicable to broad families of mappings, and uses a flexible form of triplet ranking loss. We overcome discontinuous optimization of the discrete mappings by minimizing a piecewise-smooth upper bound on empirical loss, inspired by latent structural SVMs. We develop a new loss-augmented inference algorithm that is quadratic in the code length. We show strong retrieval performance on CIFAR-10 and MNIST, with promising classification results using no more than kNN on the binary codes.

[4]: In this paper we propose a new approach for learning local descriptors for matching image patches. It has recently been demonstrated that descriptors based on convolutional neural networks (CNN) can significantly improve the matching performance. Unfortunately their computational complexity is prohibitive for any practical application. We address this problem and propose a CNN based descriptor with improved matching performance, significantly reduced training and execution time, as well as low dimensionality. We propose to train the network with triplets of patches that include a positive and negative pairs. To that end we introduce a new loss function that exploits the relations within the triplets. We compare our approach to recently introduced MatchNet and DeepCompare and demonstrate the advantages of our descriptor in terms of performance, memory footprint and speed i.e. when run in GPU, the extraction time of our 128 dimensional feature is comparable to the fastest available binary descriptors such as BRIEF and ORB.
In the paper [1] [3] , the triplet network is proposed to change the twice branches structure into three branches. Its advantage lies in the distinction of details, that is, if input images are similar, triple net can be used to describe the details better. The idea of triple net equivalent to adding two measures of input differences and learning a better representation of the inputs. Triplet net is also utilized for face recognition due to its advantage in descriptor learning [2] . In further work, the author of [4] improved the loss function of triple net, named PNSoft Loss.