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Jia Gong, Lin Geng Foo, Yixuan He, Hossein Rahmani, Jun Liu

Sign Language Translation (SLT) is a challenging task that aims to translate sign videos into spoken language. Inspired by the strong translation capabilities of large language models (LLMs) that are trained on extensive multilingual text corpora, we aim to harness off-the-shelf LLMs to handle SLT. In this paper, we regularize the sign videos to embody linguistic characteristics of spoken language, and propose a novel SignLLM framework to transform sign videos into a language-like representation for improved readability by off-the-shelf LLMs. SignLLM comprises two key modules: (1) The Vector-Quantized Visual Sign module converts sign videos into a sequence of discrete character-level sign tokens, and (2) the Codebook Reconstruction and Alignment module converts these character-level tokens into word-level sign representations using an optimal transport formulation. A sign-text alignment loss further bridges the gap between sign and text tokens, enhancing semantic compatibility. We achieve state-of-the-art gloss-free results on two widely-used SLT benchmarks.

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Gholamali Aminian, Yixuan He, Gesine Reinert, Łukasz Szpruch, Samuel N. Cohen

This work provides a theoretical framework for assessing the generalization error of graph classification tasks via graph neural networks in the over-parameterized regime, where the number of parameters surpasses the quantity of data points. We explore two widely utilized types of graph neural networks: graph convolutional neural networks and message passing graph neural networks. Prior to this study, existing bounds on the generalization error in the over-parametrized regime were uninformative, limiting our understanding of over-parameterized network performance. Our novel approach involves deriving upper bounds within the mean-field regime for evaluating the generalization error of these graph neural networks. We establish upper bounds with a convergence rate of $O(1/n)$, where $n$ is the number of graph samples. These upper bounds offer a theoretical assurance of the networks' performance on unseen data in the challenging over-parameterized regime and overall contribute to our understanding of their performance.

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Yixuan He, Gesine Reinert, David Wipf, Mihai Cucuringu

The angular synchronization problem aims to accurately estimate (up to a constant additive phase) a set of unknown angles $\theta_1, \dots, \theta_n\in[0, 2\pi)$ from $m$ noisy measurements of their offsets $\theta_i-\theta_j \;\mbox{mod} \; 2\pi.$ Applications include, for example, sensor network localization, phase retrieval, and distributed clock synchronization. An extension of the problem to the heterogeneous setting (dubbed $k$-synchronization) is to estimate $k$ groups of angles simultaneously, given noisy observations (with unknown group assignment) from each group. Existing methods for angular synchronization usually perform poorly in high-noise regimes, which are common in applications. In this paper, we leverage neural networks for the angular synchronization problem, and its heterogeneous extension, by proposing GNNSync, a theoretically-grounded end-to-end trainable framework using directed graph neural networks. In addition, new loss functions are devised to encode synchronization objectives. Experimental results on extensive data sets demonstrate that GNNSync attains competitive, and often superior, performance against a comprehensive set of baselines for the angular synchronization problem and its extension, validating the robustness of GNNSync even at high noise levels.

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Qitian Wu, Chenxiao Yang, Wentao Zhao, Yixuan He, David Wipf, Junchi Yan

Real-world data generation often involves complex inter-dependencies among instances, violating the IID-data hypothesis of standard learning paradigms and posing a challenge for uncovering the geometric structures for learning desired instance representations. To this end, we introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states that progressively incorporate other instances' information by their interactions. The diffusion process is constrained by descent criteria w.r.t.~a principled energy function that characterizes the global consistency of instance representations over latent structures. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs, which gives rise to a new class of neural encoders, dubbed as DIFFormer (diffusion-based Transformers), with two instantiations: a simple version with linear complexity for prohibitive instance numbers, and an advanced version for learning complex structures. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks, such as node classification on large graphs, semi-supervised image/text classification, and spatial-temporal dynamics prediction.

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Yixuan He, Michael Permultter, Gesine Reinert, Mihai Cucuringu

Signed and directed networks are ubiquitous in real-world applications. However, there has been relatively little work proposing spectral graph neural networks (GNNs) for such networks. Here we introduce a signed directed Laplacian matrix, which we call the magnetic signed Laplacian, as a natural generalization of both the signed Laplacian on signed graphs and the magnetic Laplacian on directed graphs. We then use this matrix to construct a novel efficient spectral GNN architecture and conduct extensive experiments on both node clustering and link prediction tasks. In these experiments, we consider tasks related to signed information, tasks related to directional information, and tasks related to both signed and directional information. We demonstrate that our proposed spectral GNN is effective for incorporating both signed and directional information, and attains leading performance on a wide range of data sets. Additionally, we provide a novel synthetic network model, which we refer to as the signed directed stochastic block model, and a number of novel real-world data sets based on lead-lag relationships in financial time series.

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Xuhong Wang, Sirui Chen, Yixuan He, Minjie Wang, Quan Gan, Yupu Yang, Junchi Yan

Many real world applications can be formulated as event forecasting on Continuous Time Dynamic Graphs (CTDGs) where the occurrence of a timed event between two entities is represented as an edge along with its occurrence timestamp in the graphs.However, most previous works approach the problem in compromised settings, either formulating it as a link prediction task on the graph given the event time or a time prediction problem given which event will happen next. In this paper, we propose a novel model combining Graph Neural Networks and Marked Temporal Point Process (MTPP) that jointly forecasts multiple link events and their timestamps on communities over a CTDG. Moreover, to scale our model to large graphs, we factorize the jointly event prediction problem into three easier conditional probability modeling problems.To evaluate the effectiveness of our model and the rationale behind such a decomposition, we establish a set of benchmarks and evaluation metrics for this event forecasting task. Our experiments demonstrate the superior performance of our model in terms of both model accuracy and training efficiency.

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Yixuan He, Xitong Zhang, Junjie Huang, Mihai Cucuringu, Gesine Reinert

Signed networks are ubiquitous in many real-world applications (e.g., social networks encoding trust/distrust relationships, correlation networks arising from time series data). While many signed networks are directed, there is a lack of survey papers and software packages on graph neural networks (GNNs) specially designed for directed networks. In this paper, we present PyTorch Geometric Signed Directed, a survey and software on GNNs for signed and directed networks. We review typical tasks, loss functions and evaluation metrics in the analysis of signed and directed networks, discuss data used in related experiments, and provide an overview of methods proposed. The deep learning framework consists of easy-to-use GNN models, synthetic and real-world data, as well as task-specific evaluation metrics and loss functions for signed and directed networks. The software is presented in a modular fashion, so that signed and directed networks can also be treated separately. As an extension library for PyTorch Geometric, our proposed software is maintained with open-source releases, detailed documentation, continuous integration, unit tests and code coverage checks. Our code is publicly available at \url{https://github.com/SherylHYX/pytorch_geometric_signed_directed}.

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Yixuan He, Quan Gan, David Wipf, Gesine Reinert, Junchi Yan, Mihai Cucuringu

Recovering global rankings from pairwise comparisons is an important problem with many applications, ranging from time synchronization to sports team ranking. Pairwise comparisons corresponding to matches in a competition can naturally be construed as edges in a directed graph (digraph), whose nodes represent competitors with an unknown rank or skill strength. However, existing methods addressing the rank estimation problem have thus far not utilized powerful neural network architectures to optimize ranking objectives. Hence, we propose to augment an algorithm with neural network, in particular graph neural network (GNN) for its coherence to the problem at hand. In this paper, we introduce GNNRank, a modeling framework that is compatible with any GNN capable of learning digraph embeddings, and we devise trainable objectives to encode ranking upsets/violations. This framework includes a ranking score estimation approach, and adds a useful inductive bias by unfolding the Fiedler vector computation of the graph constructed from a learnable similarity matrix. Experimental results on a wide range of data sets show that our methods attain competitive and often superior performance compared with existing approaches. It also shows promising transfer ability to new data based on the trained GNN model.

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Yixuan He, Gesine Reinert, Songchao Wang, Mihai Cucuringu

Node embeddings are a powerful tool in the analysis of networks; yet, their full potential for the important task of node clustering has not been fully exploited. In particular, most state-of-the-art methods generating node embeddings of signed networks focus on link sign prediction, and those that pertain to node clustering are usually not graph neural network (GNN) methods. Here, we introduce a novel probabilistic balanced normalized cut loss for training nodes in a GNN framework for semi-supervised signed network clustering, called SSSNET. The method is end-to-end in combining embedding generation and clustering without an intermediate step; it has node clustering as main focus, with an emphasis on polarization effects arising in networks. The main novelty of our approach is a new take on the role of social balance theory for signed network embeddings. The standard heuristic for justifying the criteria for the embeddings hinges on the assumption that "an enemy's enemy is a friend". Here, instead, a neutral stance is assumed on whether or not the enemy of an enemy is a friend. Experimental results on various data sets, including a synthetic signed stochastic block model, a polarized version of it, and real-world data at different scales, demonstrate that SSSNET can achieve comparable or better results than state-of-the-art spectral clustering methods, for a wide range of noise and sparsity levels. SSSNET complements existing methods through the possibility of including exogenous information, in the form of node-level features or labels.

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Yixuan He, Gesine Reinert, Mihai Cucuringu

Node clustering is a powerful tool in the analysis of networks. Here, we introduce a graph neural network framework with a novel scalable Directed Mixed Path Aggregation(DIMPA) scheme to obtain node embeddings for directed networks in a self-supervised manner, including a novel probabilistic imbalance loss. The method is end-to-end in combining embedding generation and clustering without an intermediate step. In contrast to standard approaches in the literature, in this paper, directionality is not treated as a nuisance, but rather contains the main signal. In particular, we leverage the recently introduced cut flow imbalance measure, which is tightly related to directionality; cut flow imbalance is optimized without resorting to spectral methods or cluster labels. Experimental results on synthetic data, in the form of directed stochastic block models and real-world data at different scales, demonstrate that our method attains state-of-the-art results on directed clustering, for a wide range of noise and sparsity levels, as well as graph structures.

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