Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure

Fermionic symmetry-protected topological state in strained graphene

The low-energy physics of graphene is described by relativistic Dirac fermions with spin and valley degrees of freedom. Mechanical strain can be used to create a pseudo magnetic field pointing to opposite directions in the two valleys. We study interacting electrons in graphene exposed to both an external real magnetic field and a strain-induced pseudo magnetic field. For a certain ratio between these two fields, it is proposed that a fermionic symmetry-protected topological state can be realized. The state is characterized in detail using model wave functions, Chern-Simons field theory, and numerical calculations. Our paper suggests that graphene with artificial gauge fields may host a rich set of topological states.Comment: 8 pages, 4 figure

Click-aware Structure Transfer with Sample Weight Assignment for Post-Click Conversion Rate Estimation

Post-click Conversion Rate (CVR) prediction task plays an essential role in industrial applications, such as recommendation and advertising. Conventional CVR methods typically suffer from the data sparsity problem as they rely only on samples where the user has clicked. To address this problem, researchers have introduced the method of multi-task learning, which utilizes non-clicked samples and shares feature representations of the Click-Through Rate (CTR) task with the CVR task. However, it should be noted that the CVR and CTR tasks are fundamentally different and may even be contradictory. Therefore, introducing a large amount of CTR information without distinction may drown out valuable information related to CVR. This phenomenon is called the curse of knowledge problem in this paper. To tackle this issue, we argue that a trade-off should be achieved between the introduction of large amounts of auxiliary information and the protection of valuable information related to CVR. Hence, we propose a Click-aware Structure Transfer model with sample Weight Assignment, abbreviated as CSTWA. It pays more attention to the latent structure information, which can filter the input information that is related to CVR, instead of directly sharing feature representations. Meanwhile, to capture the representation conflict between CTR and CVR, we calibrate the representation layer and reweight the discriminant layer to excavate the click bias information from the CTR tower. Moreover, it incorporates a sample weight assignment algorithm biased towards CVR modeling, to make the knowledge from CTR would not mislead the CVR. Extensive experiments on industrial and public datasets have demonstrated that CSTWA significantly outperforms widely used and competitive models

MixEdit: Revisiting Data Augmentation and Beyond for Grammatical Error Correction

Data Augmentation through generating pseudo data has been proven effective in mitigating the challenge of data scarcity in the field of Grammatical Error Correction (GEC). Various augmentation strategies have been widely explored, most of which are motivated by two heuristics, i.e., increasing the distribution similarity and diversity of pseudo data. However, the underlying mechanism responsible for the effectiveness of these strategies remains poorly understood. In this paper, we aim to clarify how data augmentation improves GEC models. To this end, we introduce two interpretable and computationally efficient measures: Affinity and Diversity. Our findings indicate that an excellent GEC data augmentation strategy characterized by high Affinity and appropriate Diversity can better improve the performance of GEC models. Based on this observation, we propose MixEdit, a data augmentation approach that strategically and dynamically augments realistic data, without requiring extra monolingual corpora. To verify the correctness of our findings and the effectiveness of the proposed MixEdit, we conduct experiments on mainstream English and Chinese GEC datasets. The results show that MixEdit substantially improves GEC models and is complementary to traditional data augmentation methods.Comment: Accepted to Findings of EMNLP 202