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Danmaku, a system of scene-aligned, time-synced, floating comments, can augment video content to create 'collective knowledge'. However, its chaotic nature often hinders viewers from effectively assimilating the collective knowledge, especially in knowledge-intensive science videos. With a formative study, we examined viewers' practices for processing collective knowledge and the specific barriers they encountered. Building on these insights, we designed a processing pipeline to filter, classify, and cluster danmaku, leading to the development of CoKnowledge - a tool incorporating a video abstract, knowledge graphs, and supplementary danmaku features to support viewers' assimilation of collective knowledge in science videos. A within-subject study (N=24) showed that CoKnowledge significantly enhanced participants' comprehension and recall of collective knowledge compared to a baseline with unprocessed live comments. Based on our analysis of user interaction patterns and feedback on design features, we presented design considerations for developing similar support tools.

Diffusion models have gained popularity in graph generation tasks; however, the extent of their expressivity concerning the graph distributions they can learn is not fully understood. Unlike models in other domains, popular backbones for graph diffusion models, such as Graph Transformers, do not possess universal expressivity to accurately model the distribution scores of complex graph data. Our work addresses this limitation by focusing on the frequency of specific substructures as a key characteristic of target graph distributions. When evaluating existing models using this metric, we find that they fail to maintain the distribution of substructure counts observed in the training set when generating new graphs. To address this issue, we establish a theoretical connection between the expressivity of Graph Neural Networks (GNNs) and the overall performance of graph diffusion models, demonstrating that more expressive GNN backbones can better capture complex distribution patterns. By integrating advanced GNNs into the backbone architecture, we achieve significant improvements in substructure generation., Comment: Under Review

Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures tailored to exploit noise for specific tasks excel yet lack broad applicability. This paper tackles these issues by laying down a theoretical framework that elucidates the increased sample complexity when introducing random noise into GNNs without careful design. We further propose Equivariant Noise GNN (ENGNN), a novel architecture that harnesses the symmetrical properties of noise to mitigate sample complexity and bolster generalization. Our experiments demonstrate that using noise equivariantly significantly enhances performance on node-level, link-level, subgraph, and graph-level tasks and achieves comparable performance to models designed for specific tasks, thereby offering a general method to boost expressivity across various graph tasks., Comment: Under review

Graph neural networks (GNNs) have become a prevalent framework for graph tasks. Many recent studies have proposed the use of graph convolution methods over the numerous subgraphs of each graph, a concept known as subgraph graph neural networks (subgraph GNNs), to enhance GNNs' ability to distinguish non-isomorphic graphs. To maximize the expressiveness, subgraph GNNs often require each subgraph to have equal size to the original graph. Despite their impressive performance, subgraph GNNs face challenges due to the vast number and large size of subgraphs which lead to a surge in training data, resulting in both storage and computational inefficiencies. In response to this problem, this paper introduces Ego-Nets-Fit-All (ENFA), a model that uniformly takes the smaller ego nets as subgraphs, thereby providing greater storage and computational efficiency, while at the same time guarantees identical outputs to the original subgraph GNNs even taking the whole graph as subgraphs. The key is to identify and eliminate the redundant computation among subgraphs. For example, a node $v_i$ may appear in multiple subgraphs but is far away from all of their centers (the unsymmetric part between subgraphs). Therefore, its first few rounds of message passing within each subgraph can be computed once in the original graph instead of being computed multiple times within each subgraph. Such strategy enables our ENFA to accelerate subgraph GNNs in an exact way, unlike previous sampling approaches that often lose the performance. Extensive experiments across various datasets reveal that compared with the conventional subgraph GNNs, ENFA can reduce storage space by 29.0% to 84.5% and improve training efficiency by up to 1.66x.

The deployment of large language models (LLMs) in diverse applications requires a thorough understanding of their decision-making strategies and behavioral patterns. As a supplement to a recent study on the behavioral Turing test, this paper presents a comprehensive analysis of five leading LLM-based chatbot families as they navigate a series of behavioral economics games. By benchmarking these AI chatbots, we aim to uncover and document both common and distinct behavioral patterns across a range of scenarios. The findings provide valuable insights into the strategic preferences of each LLM, highlighting potential implications for their deployment in critical decision-making roles., Comment: Presented at The First Workshop on AI Behavioral Science (AIBS 2024)

Recent research on integrating Large Language Models (LLMs) with Graph Neural Networks (GNNs) typically follows two approaches: LLM-centered models, which convert graph data into tokens for LLM processing, and GNN-centered models, which use LLMs to encode text features into node and edge representations for GNN input. LLM-centered models often struggle to capture graph structures effectively, while GNN-centered models compress variable-length textual data into fixed-size vectors, limiting their ability to understand complex semantics. Additionally, GNN-centered approaches require converting tasks into a uniform, manually-designed format, restricting them to classification tasks and preventing language output. To address these limitations, we introduce a new architecture that deeply integrates GNN with LLM, featuring three key innovations: (1) Structure-Aware Transformers, which incorporate GNN's message-passing capabilities directly into LLM's transformer layers, allowing simultaneous processing of textual and structural information and generating outputs from both GNN and LLM; (2) Graph-Text Cross-Attention, which processes full, uncompressed text from graph nodes and edges, ensuring complete semantic integration; and (3) GNN-LLM Twin Predictor, enabling LLM's flexible autoregressive generation alongside GNN's scalable one-pass prediction. GL-Fusion achieves outstand performance on various tasks. Notably, it achieves state-of-the-art performance on OGBN-Arxiv and OGBG-Code2., Comment: under review

Various graph neural networks (GNNs) with advanced training techniques and model designs have been proposed for link prediction tasks. However, outdated baseline models may lead to an overestimation of the benefits provided by these novel approaches. To address this, we systematically investigate the potential of Graph Autoencoders (GAE) by meticulously tuning hyperparameters and utilizing the trick of orthogonal embedding and linear propagation. Our findings reveal that a well-optimized GAE can match the performance of more complex models while offering greater computational efficiency.

Graph neural networks (GNNs) have achieved remarkable success in a variety of machine learning tasks over graph data. Existing GNNs usually rely on message passing, i.e., computing node representations by gathering information from the neighborhood, to build their underlying computational graphs. They are known fairly limited in expressive power, and often fail to capture global characteristics of graphs. To overcome the issue, a popular solution is to use Laplacian eigenvectors as additional node features, as they contain global positional information of nodes, and can serve as extra node identifiers aiding GNNs to separate structurally similar nodes. For such an approach, properly handling the orthogonal group symmetry among eigenvectors with equal eigenvalue is crucial for its stability and generalizability. However, using a naive orthogonal group invariant encoder for each separate eigenspace may not keep the full expressivity in the Laplacian eigenvectors. Moreover, computing such invariants inevitably entails a hard split of Laplacian eigenvalues according to their numerical identity, which suffers from great instability when the graph structure is perturbed. In this paper, we propose a novel method exploiting Laplacian eigenvectors to generate stable and globally expressive graph representations. The main difference from previous works is that (i) our method utilizes learnable orthogonal group invariant representations for each Laplacian eigenspace, based upon powerful orthogonal group equivariant neural network layers already well studied in the literature, and that (ii) our method deals with numerically close eigenvalues in a smooth fashion, ensuring its better robustness against perturbations. Experiments on various graph learning benchmarks witness the competitive performance of our method, especially its great potential to learn global properties of graphs.

Recent advancements in molecular generative models have demonstrated substantial potential in accelerating scientific discovery, particularly in drug design. However, these models often face challenges in generating high-quality molecules, especially in conditional scenarios where specific molecular properties must be satisfied. In this work, we introduce GeoRCG, a general framework to enhance the performance of molecular generative models by integrating geometric representation conditions with provable theoretical guarantees. We decompose the molecule generation process into two stages: first, generating an informative geometric representation; second, generating a molecule conditioned on the representation. Compared to directly generating a molecule, the relatively easy-to-generate representation in the first stage guides the second-stage generation to reach a high-quality molecule in a more goal-oriented and much faster way. Leveraging EDM and SemlaFlow as the base generators, we observe significant quality improvements in unconditional molecule generation tasks on the widely-used QM9 and GEOM-DRUG datasets. More notably, in the challenging conditional molecular generation task, our framework achieves an average 31\% performance improvement over state-of-the-art approaches, highlighting the superiority of conditioning on semantically rich geometric representations over conditioning on individual property values as in previous approaches. Furthermore, we show that, with such representation guidance, the number of diffusion steps can be reduced to as small as 100 while largely preserving the generation quality achieved with 1,000 steps, thereby significantly accelerating the generation process.

Temporal graphs are ubiquitous in real-world scenarios, such as social network, trade and transportation. Predicting dynamic links between nodes in a temporal graph is of vital importance. Traditional methods usually leverage the temporal neighborhood of interaction history to generate node embeddings first and then aggregate the source and target node embeddings to predict the link. However, such methods focus on learning individual node representations, but overlook the pairwise representation learning nature of link prediction and fail to capture the important pairwise features of links such as common neighbors (CN). Motivated by the success of Neural Common Neighbor (NCN) for static graph link prediction, we propose TNCN, a temporal version of NCN for link prediction in temporal graphs. TNCN dynamically updates a temporal neighbor dictionary for each node, and utilizes multi-hop common neighbors between the source and target node to learn a more effective pairwise representation. We validate our model on five large-scale real-world datasets from the Temporal Graph Benchmark (TGB), and find that it achieves new state-of-the-art performance on three of them. Additionally, TNCN demonstrates excellent scalability on large datasets, outperforming popular GNN baselines by up to 6.4 times in speed. Our code is available at https: //github.com/GraphPKU/TNCN.

Let $(\rho_\lambda\colon G_{\mathbb Q}\to \operatorname{GL}_5(\overline{E}_\lambda))_\lambda$ be a strictly compatible system of Galois representations such that no Hodge--Tate weight has multiplicity $5$. We show that if $\rho_{\lambda_0}$ is irreducible for some $\lambda_0$, then $\rho_\lambda$ is irreducible for all but finitely many $\lambda$. More generally, if $(\rho_\lambda)_\lambda$ is essentially self-dual, we show that either $\rho_\lambda$ is irreducible for all but finitely many $\lambda$, or the compatible system $(\rho_\lambda)_\lambda$ decomposes as a direct sum of lower-dimensional compatible systems. We apply our results to study the Tate conjecture for elliptic surfaces. For example, if $X_0\colon y^2 + (t+3)xy + y= x^3$, we prove the codimension one $\ell$-adic Tate conjecture for all but finitely many $\ell$, for all but finitely many general, degree $3$, genus $2$ branched multiplicative covers of $X_0$. To prove this result, we classify the elliptic surfaces into six families, and prove, using perverse sheaf theory and a result of Cadoret--Tamagawa, that if one surface in a family satisfies the Tate conjecture, then all but finitely many do. We then verify the Tate conjecture for one representative of each family by making our irreducibility result explicit: for the compatible system arising from the transcendental part of $H^2_{\mathrm{et}}(X_{\overline{\mathbb Q}}, \mathbb{Q}_\ell(1))$ for a representative $X$, we formulate an algorithm that takes as input the characteristic polynomials of Frobenius, and terminates if and only if the compatible system is irreducible., Comment: 52 pages. Comments welcome!

Graph is a fundamental data structure to model interconnections between entities. Set, on the contrary, stores independent elements. To learn graph representations, current Graph Neural Networks (GNNs) primarily use message passing to encode the interconnections. In contrast, this paper introduces a novel graph-to-set conversion method that bijectively transforms interconnected nodes into a set of independent points and then uses a set encoder to learn the graph representation. This conversion method holds dual significance. Firstly, it enables using set encoders to learn from graphs, thereby significantly expanding the design space of GNNs. Secondly, for Transformer, a specific set encoder, we provide a novel and principled approach to inject graph information losslessly, different from all the heuristic structural/positional encoding methods adopted in previous graph transformers. To demonstrate the effectiveness of our approach, we introduce Point Set Transformer (PST), a transformer architecture that accepts a point set converted from a graph as input. Theoretically, PST exhibits superior expressivity for both short-range substructure counting and long-range shortest path distance tasks compared to existing GNNs. Extensive experiments further validate PST's outstanding real-world performance. Besides Transformer, we also devise a Deepset-based set encoder, which achieves performance comparable to representative GNNs, affirming the versatility of our graph-to-set method., Comment: accepted in ICML 2024

Invariant models, one important class of geometric deep learning models, are capable of generating meaningful geometric representations by leveraging informative geometric features in point clouds. These models are characterized by their simplicity, good experimental results and computational efficiency. However, their theoretical expressive power still remains unclear, restricting a deeper understanding of the potential of such models. In this work, we concentrate on characterizing the theoretical expressiveness of a wide range of invariant models. We first rigorously bound the expressiveness of the most classic invariant model, message-passing neural networks incorporating distance (DisGNN), restricting its unidentifiable cases to be only highly symmetric point clouds. We then show that GeoNGNN, the geometric counterpart of one of the simplest subgraph graph neural networks (subgraph GNNs), can effectively break these corner cases' symmetry and thus achieve E(3)-completeness. By leveraging GeoNGNN as a theoretical tool, we further prove that: 1) most subgraph GNNs developed in traditional graph learning can be seamlessly extended to geometric scenarios with E(3)-completeness; 2) DimeNet, GemNet and SphereNet, three well-established invariant models, are also all capable of achieving E(3)-completeness. Our theoretical results fill the gap in the theoretical power of invariant models, contributing to a rigorous and comprehensive understanding of their capabilities. We also empirically evaluated GeoNGNN, the simplest model within the large E(3)-complete family we established, which achieves competitive results to models relying on high-order invariant/equivariant representations on molecule-relevant tasks.

In this paper, we propose the first framework that enables solving graph learning tasks of all levels (node, edge and graph) and all types (generation, regression and classification) using one formulation. We first formulate prediction tasks including regression and classification into a generic (conditional) generation framework, which enables diffusion models to perform deterministic tasks with provable guarantees. We then propose Latent Graph Diffusion (LGD), a generative model that can generate node, edge, and graph-level features of all categories simultaneously. We achieve this goal by embedding the graph structures and features into a latent space leveraging a powerful encoder and decoder, then training a diffusion model in the latent space. LGD is also capable of conditional generation through a specifically designed cross-attention mechanism. Leveraging LGD and the ``all tasks as generation'' formulation, our framework is capable of solving graph tasks of various levels and types. We verify the effectiveness of our framework with extensive experiments, where our models achieve state-of-the-art or highly competitive results across a wide range of generation and regression tasks., Comment: Accepted to NeurIPS 2024

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 2023

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 pages

The ability of graph neural networks (GNNs) to count certain graph substructures, especially cycles, is important for the success of GNNs on a wide range of tasks. It has been recently used as a popular metric for evaluating the expressive power of GNNs. Many of the proposed GNN models with provable cycle counting power are based on subgraph GNNs, i.e., extracting a bag of subgraphs from the input graph, generating representations for each subgraph, and using them to augment the representation of the input graph. However, those methods require heavy preprocessing, and suffer from high time and memory costs. In this paper, we overcome the aforementioned limitations of subgraph GNNs by proposing a novel class of GNNs -- $d$-Distance-Restricted FWL(2) GNNs, or $d$-DRFWL(2) GNNs. $d$-DRFWL(2) GNNs use node pairs whose mutual distances are at most $d$ as the units for message passing to balance the expressive power and complexity. By performing message passing among distance-restricted node pairs in the original graph, $d$-DRFWL(2) GNNs avoid the expensive subgraph extraction operations in subgraph GNNs, making both the time and space complexity lower. We theoretically show that the discriminative power of $d$-DRFWL(2) GNNs strictly increases as $d$ increases. More importantly, $d$-DRFWL(2) GNNs have provably strong cycle counting power even with $d=2$: they can count all 3, 4, 5, 6-cycles. Since 6-cycles (e.g., benzene rings) are ubiquitous in organic molecules, being able to detect and count them is crucial for achieving robust and generalizable performance on molecular tasks. Experiments on both synthetic datasets and molecular datasets verify our theory. To the best of our knowledge, our model is the most efficient GNN model to date (both theoretically and empirically) that can count up to 6-cycles.

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: 37 pages. Fix the gaps in the previous version, especially the proof of case 1 in Theorem 5.14

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 2023

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel $k,l$-WL algorithm, a more general framework than $k$-WL. Theoretically, we analyze the expressivity of $k,l$-WL with respect to $k$ and $l$ and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical $k,l$-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our $k,l$-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework., Comment: To be published in ICML 2023. 27 pages, 5 figures

In this paper, we provide a theory of using graph neural networks (GNNs) for \textit{multi-node representation learning}, where we are interested in learning a representation for a set of more than one node such as a link. Existing GNNs are mainly designed to learn single-node representations. When we want to learn a node-set representation involving multiple nodes, a common practice in previous works is to directly aggregate the single-node representations obtained by a GNN. In this paper, we show a fundamental limitation of such an approach, namely the inability to capture the dependence among multiple nodes in a node set, and argue that directly aggregating individual node representations fails to produce an effective joint representation for multiple nodes. A straightforward solution is to distinguish target nodes from others. Formalizing this idea, we propose \text{labeling trick}, which first labels nodes in the graph according to their relationships with the target node set before applying a GNN and then aggregates node representations obtained in the labeled graph for multi-node representations. The labeling trick also unifies a few previous successful works for multi-node representation learning, including SEAL, Distance Encoding, ID-GNN, and NBFNet. Besides node sets in graphs, we also extend labeling tricks to posets, subsets and hypergraphs. Experiments verify that the labeling trick technique can boost GNNs on various tasks, including undirected link prediction, directed link prediction, hyperedge prediction, and subgraph prediction. Our work explains the superior performance of previous node-labeling-based methods and establishes a theoretical foundation for using GNNs for multi-node representation learning.

Graph Neural Networks (GNNs) are often used for tasks involving the 3D geometry of a given graph, such as molecular dynamics simulation. While incorporating Euclidean distance into Message Passing Neural Networks (referred to as Vanilla DisGNN) is a straightforward way to learn the geometry, it has been demonstrated that Vanilla DisGNN is geometrically incomplete. In this work, we first construct families of novel and symmetric geometric graphs that Vanilla DisGNN cannot distinguish even when considering all-pair distances, which greatly expands the existing counterexample families. Our counterexamples show the inherent limitation of Vanilla DisGNN to capture symmetric geometric structures. We then propose $k$-DisGNNs, which can effectively exploit the rich geometry contained in the distance matrix. We demonstrate the high expressive power of $k$-DisGNNs from three perspectives: 1. They can learn high-order geometric information that cannot be captured by Vanilla DisGNN. 2. They can unify some existing well-designed geometric models. 3. They are universal function approximators from geometric graphs to scalars (when $k\geq 2$) and vectors (when $k\geq 3$). Most importantly, we establish a connection between geometric deep learning (GDL) and traditional graph representation learning (GRL), showing that those highly expressive GNN models originally designed for GRL can also be applied to GDL with impressive performance, and that existing complicated, equivariant models are not the only solution. Experiments verify our theory. Our $k$-DisGNNs achieve many new state-of-the-art results on MD17., Comment: NeurIPS 2023. This new version includes corrections of some minor typos and potentially unclear notations

In this work, we propose a novel link prediction model and further boost it by studying graph incompleteness. First, we introduce MPNN-then-SF, an innovative architecture leveraging structural feature (SF) to guide MPNN's representation pooling, with its implementation, namely Neural Common Neighbor (NCN). NCN exhibits superior expressiveness and scalability compared with existing models, which can be classified into two categories: SF-then-MPNN, augmenting MPNN's input with SF, and SF-and-MPNN, decoupling SF and MPNN. Second, we investigate the impact of graph incompleteness -- the phenomenon that some links are unobserved in the input graph -- on SF, like the common neighbor. Through dataset visualization, we observe that incompleteness reduces common neighbors and induces distribution shifts, significantly affecting model performance. To address this issue, we propose to use a link prediction model to complete the common neighbor structure. Combining this method with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins, and NCNC further surpasses state-of-the-art models in standard link prediction benchmarks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor., Comment: ICLR 2024

Let $K$ be a finite unramified extension of $\mathbb{Q}_p$, where $p>2$. [CEGS22b] and [EG23] construct a moduli stack of two dimensional mod $p$ representations of the absolute Galois group of $K$. We show that most irreducible components of this stack (including several non-generic components) are isomorphic to quotients of smooth affine schemes. We also use this quotient presentation to compute global sections on these components., Comment: Final version. To appear in Transactions of the AMS

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) 2022

Promotions are commonly used by e-commerce merchants to boost sales. The efficacy of different promotion strategies can help sellers adapt their offering to customer demand in order to survive and thrive. Current approaches to designing promotion strategies are either based on econometrics, which may not scale to large amounts of sales data, or are spontaneous and provide little explanation of sales volume. Moreover, accurately measuring the effects of promotion designs and making bootstrappable adjustments accordingly remains a challenge due to the incompleteness and complexity of the information describing promotion strategies and their market environments. We present PromotionLens, a visual analytics system for exploring, comparing, and modeling the impact of various promotion strategies. Our approach combines representative multivariant time-series forecasting models and well-designed visualizations to demonstrate and explain the impact of sales and promotional factors, and to support "what-if" analysis of promotions. Two case studies, expert feedback, and a qualitative user study demonstrate the efficacy of PromotionLens., Comment: IEEE Transactions on Visualization and Computer Graphics (Proc. IEEE VIS 2022)

Link prediction is one important application of graph neural networks (GNNs). Most existing GNNs for link prediction are based on one-dimensional Weisfeiler-Lehman (1-WL) test. 1-WL-GNNs first compute node representations by iteratively passing neighboring node features to the center, and then obtain link representations by aggregating the pairwise node representations. As pointed out by previous works, this two-step procedure results in low discriminating power, as 1-WL-GNNs by nature learn node-level representations instead of link-level. In this paper, we study a completely different approach which can directly obtain node pair (link) representations based on \textit{two-dimensional Weisfeiler-Lehman (2-WL) tests}. 2-WL tests directly use links (2-tuples) as message passing units instead of nodes, and thus can directly obtain link representations. We theoretically analyze the expressive power of 2-WL tests to discriminate non-isomorphic links, and prove their superior link discriminating power than 1-WL. Based on different 2-WL variants, we propose a series of novel 2-WL-GNN models for link prediction. Experiments on a wide range of real-world datasets demonstrate their competitive performance to state-of-the-art baselines and superiority over plain 1-WL-GNNs.

Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral GNNs. This paper studies spectral GNNs' expressive power theoretically. We first prove that even spectral GNNs without nonlinearity can produce arbitrary graph signals and give two conditions for reaching universality. They are: 1) no multiple eigenvalues of graph Laplacian, and 2) no missing frequency components in node features. We also establish a connection between the expressive power of spectral GNNs and Graph Isomorphism (GI) testing, the latter of which is often used to characterize spatial GNNs' expressive power. Moreover, we study the difference in empirical performance among different spectral GNNs with the same expressive power from an optimization perspective, and motivate the use of an orthogonal basis whose weight function corresponds to the graph signal density in the spectrum. Inspired by the analysis, we propose JacobiConv, which uses Jacobi basis due to its orthogonality and flexibility to adapt to a wide range of weight functions. JacobiConv deserts nonlinearity while outperforming all baselines on both synthetic and real-world datasets., Comment: To be published in ICML2022

In this work, we introduce the pattern-domain pilot design paradigm based on a "superposition of orthogonal-building-blocks" with significantly larger contention space to enhance the massive machine-type communications (mMTC) random access (RA) performance in massive multiple-input multiple-output (MIMO) systems.Specifically, the pattern-domain pilot is constructed based on the superposition of $L$ cyclically-shifted Zadoff-Chu (ZC) sequences. The pattern-domain pilots exhibit zero correlation values between non-colliding patterns from the same root and low correlation values between patterns from different roots. The increased contention space, i.e., from N to $\binom{N}{L}$, where $\binom{N}{L}$ denotes the number of all L-combinations of a set N, and low correlation valueslead to a significantly lower pilot collision probability without compromising excessively on channel estimation performance for mMTC RA in massive MIMO systems.We present the framework and analysis of the RA success probability of the pattern-domain based scheme with massive MIMO systems.Numerical results demonstrate that the proposed pattern division random access (PDRA) scheme achieves an appreciable performance gain over the conventional one,while preserving the existing physical layer virtually unchanged. The extension of the "superposition of orthogonal-building-blocks" scheme to "superposition of quasi-orthogonal-building-blocks" is straightforward.

Let $K/k$ be a finite Galois extension of number fields, and let $H_K$ be the Hilbert class field of $K$. We find a way to verify the nonsplitting of the short exact sequence $$1\to Cl_K\to \text{Gal}(H_K/k)\to\text{Gal}(K/k)\to 1$$ by finite calculation. Our method is based on the study of the principal version of the Chebotarev density theorem, which represents the density of the prime ideals of $k$ that factor into the product of principal prime ideals in $K$. We also find explicit equations to express the principal density in terms of the invariants of $K/k$. In particular, we prove that the group structure of the ideal class group of $K$ can be determined by reading the principal densities.

Decentralized baseband processing (DBP) architecture, which partitions the base station antennas into multiple antenna clusters, has been recently proposed to alleviate the excessively high interconnect bandwidth, chip input/output data rates, and detection complexity for massive multi-user multiple-input multiple-output (MU-MIMO) systems. In this paper, we develop a novel decentralized Gaussian message passing (GMP) detection for the DBP architecture. By projecting the discrete probability distribution into a complex Gaussian function, the local means and variances iteratively calculated in each antenna cluster are fused to generate the global symbol beliefs based on the proposed message fusion rule in the centralized processing unit. We present the framework and analysis of the convergence of the decentralized GMP detection based on state evolution under the assumptions of large-system limit and Gaussian sources. Analytical results corroborated by simulations demonstrate that nonuniform antenna cluster partition scheme exhibits higher convergence rate than the uniform counterpart. Simulation results illustrate that the proposed decentralized GMP detection outperforms the recently proposed decentralized algorithms.

Using Calegari's result on the Fontaine-Mazur conjecture, we study the irreducibility of pure, regular, rank 3 weakly compatible systems of self-dual l-adic representations. As a consequence, we prove that the Tate conjecture holds for a family of elliptic surfaces defined over Q with geometric genus bigger than 1., Comment: Minor changes. To appear in Math. Res. Lett