Weight elimination in two dimensions when p=2p=2

We prove the `weight elimination' part of the weight part of Serre's conjecture for mod 2 Galois representations for rank two unitary groups, by modifying the results in arXiv:1203.2552 and arXiv:1309.0527.Comment: Adapts arguments from arXiv:1203.2552 and arXiv:1309.052

Business model innovation of Chinese internet enterprises a stakeholder perspective of BAT (Baidu, Alibaba, Tencent)

Driven by the tide of world economic development and the rapid development of information technology, China's Internet industry has developed rapidly and continuously, and the business model has been continuously innovated, which has effectively promoted the development of China's Internet industry economy. However, rapid development has led to conflicts and conflicts between business model innovation and stakeholders such as user interests, corporate ethics, and corporate performance. This study combs the relationship and interaction between business model theory, corporate ethics theory, and stakeholder theory, reviews the development history of Chinese Internet companies, analyzes the forms of Chinese Internet enterprise business model innovation, and discusses the contradiction and confusion within the innovation of China's Internet business model, and construct the "Business Model Innovation - Performance Structure Model". Through the case studies of Baidu, Alibaba, and Tencent, it verifies the inevitable relationship among the business model innovation - stakeholder relationship quality - corporate performance. And put forward relevant suggestions for the problems in the Internet business model innovation.Impulsionada pela tendência do desenvolvimento econômico mundial e pelo desenvolvimento rápido da tecnologia das informações, o setor de Internet da China desenvolveu- se rápida e continuamente, e o modelo de negócios foi continuamente inovado, o que efetivamente promoveu o desenvolvimento da economia chinesa da indústria da Internet. No entanto, o desenvolvimento rápido levou a conflitos entre a inovação do modelo de negócios e os stakeholders, como os interesses dos usuários, a ética corporativa e o desempenho corporativo. Este estudo combina a relação e interação entre a teoria do modelo de negócios, a da ética corporativa e a dos stakeholders, recorda a história de desenvolvimento de empresas de Internet chinesas, analisa as formas de inovação do modelo chinês de negócios e discute a contradição e confusão dentro da inovação de modelo de negócios da indústria de Internet na China, construindo o "Inovação do Modelo Empresarial - Modelo de Estrutura de Desempenho". Por meio dos estudos de caso do Baidu, Alibaba e Tencent, verifica-se a relação inevitável entre a inovação do modelo de negócios - qualidade do relacionamento com stakeholders - desempenho corporativo. E apresenta sugestões relevantes para os problemas na inovação do modelo de negócios na indústria de Internet

Graph Neural Network with Local Frame for Molecular Potential Energy Surface

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and fulfill symmetry requirement like rotation equivariance, leading to complicated architectures. To avoid these designs, we introduce a novel local frame method to molecule representation learning and analyze its expressivity. Projected onto a frame, equivariant features like 3D coordinates are converted to invariant features, so that we can capture geometric information with these projections and decouple the symmetry requirement from GNN design. Theoretically, we prove that given non-degenerate frames, even ordinary GNNs can encode molecules injectively and reach maximum expressivity with coordinate projection and frame-frame projection. In experiments, our model uses a simple ordinary GNN architecture yet achieves state-of-the-art accuracy. The simpler architecture also leads to higher scalability. Our model only takes about 30% inference time and 10% GPU memory compared to the most efficient baselines.Comment: Learning on Graphs (LoG) 202

Sequentially Sampled Chunk Conformer for Streaming End-to-End ASR

This paper presents an in-depth study on a Sequentially Sampled Chunk Conformer, SSC-Conformer, for streaming End-to-End (E2E) ASR. The SSC-Conformer first demonstrates the significant performance gains from using the sequentially sampled chunk-wise multi-head self-attention (SSC-MHSA) in the Conformer encoder by allowing efficient cross-chunk interactions while keeping linear complexities. Furthermore, it explores taking advantage of chunked convolution to make use of the chunk-wise future context and integrates with casual convolution in the convolution layers to further reduce CER. We verify the proposed SSC-Conformer on the AISHELL-1 benchmark and experimental results show that a state-of-the-art performance for streaming E2E ASR is achieved with CER 5.33% without LM rescoring. And, owing to its linear complexity, the SSC-Conformer can train with large batch sizes and infer more efficiently.Comment: This paper has been submitted to ICASSP 202

Neural Common Neighbor with Completion for Link Prediction

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor

On the essential torsion finiteness of abelian varieties over torsion fields

The classical Mordell-Weil theorem implies that an abelian variety $A$ over a number field $K$ has only finitely many $K$-rational torsion points. This finitude of torsion still holds even over the cyclotomic extension $K^{\rm cyc}=K\mathbb{Q}^{\mathrm{ab}}$ by a result of Ribet. In this article, we consider the finiteness of torsion points of an abelian variety $A$ over the infinite algebraic extension $K_B$ obtained by adjoining the coordinates of all torsion points of an abelian variety $B$. Assuming the Mumford-Tate conjecture, and up to a finite extension of the base field $K$, we give a necessary and sufficient condition for the finiteness of $A(K_B)_{\rm tors}$ in terms of Mumford--Tate groups. We give a complete answer when both abelian varieties have dimension both three, or when both have complex multiplication.Comment: 35 page

Facilitating Graph Neural Networks with Random Walk on Simplicial Complexes

Node-level random walk has been widely used to improve Graph Neural Networks. However, there is limited attention to random walk on edge and, more generally, on $k$-simplices. This paper systematically analyzes how random walk on different orders of simplicial complexes (SC) facilitates GNNs in their theoretical expressivity. First, on $0$-simplices or node level, we establish a connection between existing positional encoding (PE) and structure encoding (SE) methods through the bridge of random walk. Second, on $1$-simplices or edge level, we bridge edge-level random walk and Hodge $1$-Laplacians and design corresponding edge PE respectively. In the spatial domain, we directly make use of edge level random walk to construct EdgeRWSE. Based on the spectral analysis of Hodge $1$-Laplcians, we propose Hodge1Lap, a permutation equivariant and expressive edge-level positional encoding. Third, we generalize our theory to random walk on higher-order simplices and propose the general principle to design PE on simplices based on random walk and Hodge Laplacians. Inter-level random walk is also introduced to unify a wide range of simplicial networks. Extensive experiments verify the effectiveness of our random walk-based methods.Comment: Accepted by NeurIPS 202

P-vectors: A Parallel-Coupled TDNN/Transformer Network for Speaker Verification

Typically, the Time-Delay Neural Network (TDNN) and Transformer can serve as a backbone for Speaker Verification (SV). Both of them have advantages and disadvantages from the perspective of global and local feature modeling. How to effectively integrate these two style features is still an open issue. In this paper, we explore a Parallel-coupled TDNN/Transformer Network (p-vectors) to replace the serial hybrid networks. The p-vectors allows TDNN and Transformer to learn the complementary information from each other through Soft Feature Alignment Interaction (SFAI) under the premise of preserving local and global features. Also, p-vectors uses the Spatial Frequency-channel Attention (SFA) to enhance the spatial interdependence modeling for input features. Finally, the outputs of dual branches of p-vectors are combined by Embedding Aggregation Layer (EAL). Experiments show that p-vectors outperforms MACCIF-TDNN and MFA-Conformer with relative improvements of 11.5% and 13.9% in EER on VoxCeleb1-O.Comment: Accepted by INTERSPEECH 202

Some remarks on strong multiplicity one for paramodular forms

We establish several refined strong multiplicity one results for paramodular cusp forms by using the spinor and standard $L$-functions with the combination of the methods from both of automorphic side and Galois side.Comment: 28 page