Deep Learning to Ternary Hash Codes by Continuation

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

Deep Learning to Ternary Hash Codes by Continuation

Recently, it has been observed that $\{0,\pm1\}$-ternary codes which are simply generated from deep features by hard thresholding, tend to outperform $\{-1, 1\}$-binary codes in image retrieval. To obtain better ternary codes, we for the first time propose to jointly learn the features with the codes by appending a smoothed function to the networks. During training, the function could evolve into a non-smoothed ternary function by a continuation method, and then generate ternary codes. The method circumvents the difficulty of directly training discrete functions and reduces the quantization errors of ternary codes. Experiments show that the proposed joint learning indeed could produce better ternary codes.

Review of the book «Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes»

Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes. Vol. 1. Moscow, Nauka publ., 2020, 611 p. ISBN 978-5-02-040758-9.Proceedings on the Self-Checking Embedded Control Circuits Synthesis Theory Based on Binary Redundant Codes. Vol. 2. Moscow, Nauka publ., 2021, 527 p. ISBN 978-5-02-040757-2.The first volume of the book includes papers devoted to three main areas of research in the field of synthesis of self-checking discrete systems: study of features of classical sum codes (Berger codes), modular sum codes, as well as their modifications proposed by the authors of the articles; study of features of codes for which check bits are obtained using convolutions modulo М = 2 of a part of data bits (polynomial codes and classical Hamming codes); research of the Boolean Complement method for organisation of self-checking discrete systems based on redundant binary codes. Materials are provided on detailed characteristics of error detection in data bits of redundant binary codes under the condition of errorfree check bits, descriptions of methods for constructing previously unknown modified sum codes and features of methods for synthesizing self-checking discrete systems based on binary redundant codes.The second volume of the book includes papers in the field of constructing binary sum codes weighted bits and transitions between bits occupying adjacent positions in data vectors of code words, as well as the results of studying their characteristics and methods of synthesising coding equipment. The issues of application of features of codes in organisation of self-checking discrete systems are considered. The reader will find on the pages of this volume materials on detailed characteristics of error detection in data bits of weight-based sum codes provided that the check bits are error-free, descriptions of methods for constructing previously unknown weight-based sum codes and features of methods for synthesising self-checking discrete systems based on them.The book can be useful for developers, researchers and engineers working in the field of technical diagnostics of discrete systems and synthesis of systems with fault detection, as well as students studying computer science, computer technology and automation.

About the Ultimate Efficiency of Interference Binary Codes

The digital representation of various signals allows, at the subsequent stages of their transmission, to apply correction codes that provide protection against possible errors arising from the action of interference in the communication channel. At the same time, it is important that, with the required correcting ability, these codes have the maximum possible speed. The article presents the results of calculations for linear codes, showing their really achievable limiting capabilities.

Scalable supervised online hashing for image retrieval

Online hashing methods aim to learn compact binary codes of the new data stream, and update the hash function to renew the codes of the existing data. However, the addition of new data streams has a vital impact on the retrieval performance of the entire retrieval system, especially the similarity measurement between new data streams and existing data, which has always been one of the focuses of online retrieval research. In this paper, we present a novel scalable supervised online hashing method, to solve the above problems within a unified framework. Specifically, the similarity matrix is established by the label matrix of the existing data and the new data stream. The projection of the existing data label matrix is then used as an intermediate term to approximate the binary codes of the existing data, which not only realizes the semantic information of the hash codes learning but also effectively alleviates the problem of data imbalance. In addition, an alternate optimization algorithm is proposed to efficiently make the solution of the model. Extensive experiments on three widely used datasets validate its superior performance over several state-of-the-art methods in terms of both accuracy and scalability for online retrieval task.

Reinterpreting the Stabilizer Formalism

<div>Stabilizer codes, introduced in [2], [3], have been a prominent example of quantum codes constructed via classical codes. The paper [3], introduces the stabilizer formalism for obtaining additive quantum codes of length n from Hermitian self-orthogonal codes of length n over GF(4). In the present work, we reinterpret the stabilizer formalism by considering binary codes over the symbol-pair metric (see [9]). Specifically, the present work constructs additive quantum codes of length n from certain binary codes of length n considered over the symbol-pair metric. We also present the Modified CSS Construction which is used to obtain quantum codes with parameters.</div>

Reinterpreting the Stabilizer Formalism

<div>Stabilizer codes, introduced in [2], [3], have been a prominent example of quantum codes constructed via classical codes. The paper [3], introduces the stabilizer formalism for obtaining additive quantum codes of length n from Hermitian self-orthogonal codes of length n over GF(4). In the present work, we reinterpret the stabilizer formalism by considering binary codes over the symbol-pair metric (see [9]). Specifically, the present work constructs additive quantum codes of length n from certain binary codes of length n considered over the symbol-pair metric. We also present the Modified CSS Construction which is used to obtain quantum codes with parameters.</div>

Label Consistent Flexible Matrix Factorization Hashing for Efficient Cross-modal Retrieval

Hashing methods have sparked a great revolution on large-scale cross-media search due to its effectiveness and efficiency. Most existing approaches learn unified hash representation in a common Hamming space to represent all multimodal data. However, the unified hash codes may not characterize the cross-modal data discriminatively, because the data may vary greatly due to its different dimensionalities, physical properties, and statistical information. In addition, most existing supervised cross-modal algorithms preserve the similarity relationship by constructing an n × n pairwise similarity matrix, which requires a large amount of calculation and loses the category information. To mitigate these issues, a novel cross-media hashing approach is proposed in this article, dubbed label flexible matrix factorization hashing (LFMH). Specifically, LFMH jointly learns the modality-specific latent subspace with similar semantic by the flexible matrix factorization. In addition, LFMH guides the hash learning by utilizing the semantic labels directly instead of the large n × n pairwise similarity matrix. LFMH transforms the heterogeneous data into modality-specific latent semantic representation. Therefore, we can obtain the hash codes by quantifying the representations, and the learned hash codes are consistent with the supervised labels of multimodal data. Then, we can obtain the similar binary codes of the corresponding modality, and the binary codes can characterize such samples flexibly. Accordingly, the derived hash codes have more discriminative power for single-modal and cross-modal retrieval tasks. Extensive experiments on eight different databases demonstrate that our model outperforms some competitive approaches.