While language models (LMs) have demonstrated remarkable general-purpose capabilities across domains, including molecule generation using line notations such as SMILES and SELFIES, their direct application to 3D structure design remains constrained by two interdependent challenges. First, the difficulty in designing a 3D line notation that ensures SE(3)-invariant atomic coordinates and supports autoregressive generation. Second, the incompatibility between continuous spatial coordinates and the discrete token inputs required by LMs. To address this, we propose Mol-StrucTok, a unified framework for tokenizing 3D molecular structures. Our approach comprises two key innovations: (1) a 3D line notation—Spherical Coordinate Notation—that encodes local atomic environments in spherical coordinates, agnostic to 2D notations and inherently SE(3)-invariant; and (2) a structure-aware Vector Quantized Variational Autoencoder (VQ-VAE) for discretizing these coordinates into chemically valid tokens suitable for language model processing. Leveraging this tokenization framework, we train a GPT-2 style model for end-to-end 3D molecular generation. Empirical results demonstrate strong, task-dependent performance: in unconditional generation, Mol-StrucTok achieves diffusion-level stability with ~28× faster inference; in conditional generation, it reduces property-matching mean absolute error (MAE) by 5–8× compared to diffusion-based methods, highlighting the advantage of autoregressive contextual modeling for precise control of molecular attributes. Our code is available at https://github.com/KyGao/Mol-StrucTok.

Graph Transformers have demonstrated superiority in handling complex heterogeneous graphs in recent years. However, existing models still face several inherent challenges: (1) reliance on manually designed meta-paths to encode explicit local graph heterogeneity; (2) inability to capture fine-grained global information from distant yet relevant nodes. To address these limitations, we introduce THFormer, a novel node tokenized heterogeneous graph Transformer that learns expressive node representations by incorporating local and global perspectives. From the local perspective, we employ multiple subsequences for different heterogeneous types to explicitly encode local semantic relations, eliminating the need for manually designed meta-paths. From the global perspective, we design a local masking and global sampling mechanism to construct global structural (semantic) sequences, effectively capturing fine-grained global structural (semantic) information. Subsequently, THFormer separately feeds the resulting global and local sequences into standard Transformer layers as model inputs. Since these sequences represent two distinct views of the same target node, their corresponding outputs are naturally aligned to generate self-supervisory signals for model training, further enhancing the expressiveness and reliability of the target node representation. Extensive experiments are conducted to validate the efficacy of THFormer, and the quantitative performance gains are 0.24%, 0.31%, 0.51%, and 0.81% on DBLP, ACM, IMDB, and Freebase, respectively. The experimental results demonstrate the superiority of THFormer over representative heterogeneous graph neural networks and graph Transformer models.

Molecular docking is a pivotal process in drug discovery. While traditional techniques rely on extensive sampling and simulation governed by physical principles, deep learning has emerged as a promising alternative, offering improvements in both accuracy and efficiency. Building upon the foundational work of FABind, a model focused on speed and accuracy, we introduce FABind+, an enhanced iteration that significantly elevates the performance of its predecessor. We identify pocket prediction as a critical bottleneck in molecular docking and introduce an enhanced approach. In addition to the pocket prediction module, the docking module has also been upgraded with permutation loss and a more refined model design. These designs enable the regression-based FABind+ to surpass most of the generative models. In contrast, while sampling-based models often struggle with inefficiency, they excel in capturing a wide range of potential docking poses, leading to better overall performance. To bridge the gap between sampling and regression docking models, we incorporate a simple yet effective sampling technique coupled with a lightweight confidence model, transforming the regression-based FABind+ into a sampling version without requiring additional training. This involves the introduction of pocket clustering to capture multiple binding sites and dropout sampling for various conformations. The combination of a classification loss and a ranking loss enables the lightweight confidence model to select the most accurate prediction. Experimental results and analysis demonstrate that FABind+ (both the regression and sampling versions) not only significantly outperforms the original FABind, but also achieves competitive state-of-the-art performance. Our code is available at https://github.com/QizhiPei/FABind.

Molecular docking plays a crucial role in predicting the binding mode of ligands to target proteins, and covalent interactions, which involve the formation of a covalent bond between the ligand and the target, are particularly valuable due to their strong, enduring binding nature. However, most existing docking methods and deep learning approaches hardly account for the formation of covalent bonds and the associated structural changes. To address this gap, we introduce a comprehensive benchmark for covalent docking, CovDocker, which is designed to better capture the complexities of covalent binding. We decompose the covalent docking process into three main tasks: reactive location prediction, covalent reaction prediction, and covalent docking. By adapting state-of-the-art models, such as Uni-Mol and Chemformer, we establish baseline performances and demonstrate the effectiveness of the benchmark in accurately predicting interaction sites and modeling the molecular transformations involved in covalent binding. These results confirm the role of the benchmark as a rigorous framework for advancing research in covalent drug design. It underscores the potential of data-driven approaches to accelerate the discovery of selective covalent inhibitors and addresses critical challenges in therapeutic development.

Much of the complexity of social, biological, and engineering systems arises from the complicated interactions among the entities in the corresponding networks. A number of network analysis tools have been successfully used to discover latent structures termed communities in such networks. However, some communities with relatively weak structures can be difficult to uncover because they are obscured by other stronger connections. To cope with this situation, our previous work proposes an algorithm called HICODE to detect and amplify the dominant and hidden community structures. In this work, we conduct a comprehensive and systematic theoretical analysis on the impact of hidden community structure and the efficacy of the HICODE algorithm, as well as provide illustrations of the detection process and results. Specifically, we define a multi-layer stochastic block model and use this model to explain why the existence of hidden structure makes the detection of dominant structure harder than equivalent random noises, which can also explain why many community detection algorithms only focusing on the dominant structure do not work well as expected. We then provide theoretical analysis that the iterative reducing methods could help to enhance the discovery of hidden structure as well as the dominant structure in the multi-layer stochastic block model for the two cases of accurate and inaccurate detection. Finally, visual simulations and experimental results are presented to show the process of HICODE algorithm and the impact of different number of layers on the detection quality.

Antibodies are proteins that effectively protect the human body by binding to pathogens. Recently, deep learning-based computational antibody design has attracted popular attention since it automatically mines the antibody patterns from data that could be complementary to human experiences. However, the computational methods heavily rely on high-quality antibody structure data, which is quite limited. Besides, the complementarity-determining region (CDR), which is the key component of an antibody that determines the specificity and binding affinity, is highly variable and hard to predict. Therefore, the limited availability of high-quality antibody structure data exacerbates the difficulty of CDR generation. Fortunately, there is a large amount of sequence data for antibodies that can help model the CDR and reduce reliance on structure data. By witnessing the success of pre-training models for protein modeling, in this paper, we develop the antibody pre-training language model and incorporate it into the antigen-specific antibody design model in a systemic way. Specifically, we first pre-train a novel antibody language model based on the sequence data, then propose a one-shot way for sequence and structure generation of CDR to mitigate the high cost and error propagation associated with autoregressive methods, and finally leverage the pre-trained antibody model for the antigen-specific antibody generation model with some carefully designed modules. Our experiments demonstrate the superiority of our method over previous baselines in tasks such as sequence and structure generation, CDR-H3 design for antigen binding, and antibody optimization1. The code is available at https://github.com/KyGao/ABGNN.

Hidden community is a useful concept proposed recently for social network analysis. Hidden communities indicate some weak communities whose most members also belong to other stronger dominant communities. Dominant communities could form a layer that partitions all the individuals of a network, and hidden communities could form other layer(s) underneath. These layers could be natural structures in the real-world networks like students grouped by major, minor, hometown, and so on. To handle the rapid growth of network scale, in this work, we explore the detection of hidden communities from the local perspective, and propose a new method that detects and boosts each layer iteratively on a subgraph sampled from the original network. We first expand the seed set from a single seed node based on our modified local spectral method and detect an initial dominant local community. Then we temporarily remove the members of this community as well as their connections to other nodes, and detect all the neighborhood communities in the remaining subgraph, including some “broken communities” that only contain a fraction of members in the original network. The local community and neighborhood communities form a dominant layer, and by reducing the edge weights inside these communities, we weaken this layer’s structure to reveal the hidden layers. Eventually, we repeat the whole process, and all communities containing the seed node can be detected and boosted iteratively. We theoretically show that our method can avoid some situations that a broken community and the local community are regarded as one community in the subgraph, leading to the inaccuracy of detection which can be caused by global hidden community detection methods. Extensive experiments show that our method could significantly outperform the state-of-the-art baselines designed for either global hidden community detection or multiple local community detection.

Label propagation and graph neural networks are two main methods for the semi-supervised node classification problem on graphs. They share similar idea of propagating information over the network, exhibiting promising performance on the node classification task. Despite effectiveness, the limitations of these propagation methods are still not well understood. From the perspective of label propagation then training, we observe three major challenges of these propagation methods. The observations from both theoretical analyses and empirical studies reveal that the propagation operations can degrade performance on certain labels and suffers from structure noise, which is described by edges with two nodes belonging to distinct labels. To address the above issues, we propose a new method termed Robust Label Propagation (RLP). RLP contains two novel strategies, Robust Training and Ada-Mixup. Robust Training can utilize more attribute information to have the overall training correction ability and alleviate the impact of structure noise significantly. Ada-Mixup can help RLP mine useful structure information by integrating information before and after the propagation adaptively. Extensive empirical studies on real-world datasets demonstrate that RLP outperforms the mainstream baselines on the node classification task in terms of effectiveness, efficiency and robustness.

Hybrid Flow Shop Scheduling Problem (HFSP) is an essential problem in the automated warehouse scheduling, aiming at optimizing the sequence of jobs and the assignment of machines to utilize the makespan or other objectives. Existing algorithms adopt fixed search paradigm based on expert knowledge to seek satisfactory solutions. However, considering the varying data distribution and large scale of the practical HFSP, these methods fail to guarantee the quality of the obtained solution under the real-time requirement, especially facing extremely different data distribution. To address this challenge, we propose a novel Multi-Graph Attributed Reinforcement Learning based Optimization (MGRO) algorithm to better tackle the practical large-scale HFSP and improve the existing algorithm. Owing to incorporating the reinforcement learning-based policy search approach with classic search operators and the powerful multi-graph based representation, MGRO is capable of adjusting the search paradigm according to specific instances and enhancing the search efficiency. Specifically, we formulate the Gantt chart of the instance into the multi-graph-structured data. Then Graph Neural Network (GNN) and attention-based adaptive weighted pooling are employed to represent the state and make MGRO size-agnostic across arbitrary sizes of instances. In addition, a useful reward shaping approach is designed to facilitate model convergence. Extensive numerical experiments on both the publicly available dataset and real industrial dataset from Huawei Supply Chain Business Unit demonstrate the superiority of MGRO over existing baselines.

In this paper we make progress on the unsupervised task of mining arbitrarily shaped clusters in highly noisy datasets, which is a task present in many real-world applications. Based on the fundamental work that first applies a wavelet transform to data clustering, we propose an adaptive clustering algorithm, denoted as AdaWave, which exhibits favorable characteristics for clustering. By a self-adaptive thresholding technique, AdaWave is parameter free and can handle data in various situations. It is deterministic, fast in linear time, order-insensitive, shape-insensitive, robust to highly noisy data, and requires no pre-knowledge on data models. Moreover, AdaWave inherits the ability from the wavelet transform to cluster data in different resolutions. We adopt the "grid labeling" data structure to drastically reduce the memory consumption of the wavelet transform so that AdaWave can be used for relatively high dimensional data. Experiments on synthetic as well as natural datasets demonstrate the effectiveness and efficiency of our proposed method.

Community detection is an important information mining task to uncover modular structures in large networks. For increasingly common large network datasets, global community detection is prohibitively expensive, and attention has shifted to methods that mine local communities, i.e., identifying all latent members of a particular community from a few labeled seed members. To address such semi-supervised mining task, we systematically develop a local spectral (LOSP) subspace-based community detection method, called LOSP. We define a family of LOSP subspaces based on Krylov subspaces, and seek a sparse indicator for the target community via an ℓ 1 norm minimization over the Krylov subspace. Variants of LOSP depend on type of random walks with different diffusion speeds, type of random walks, dimension of the LOSP subspace, and step of diffusions. The effectiveness of the proposed LOSP approach is theoretically analyzed based on Rayleigh quotients, and it is experimentally verified on a wide variety of real-world networks across social, production, and biological domains, as well as on an extensive set of synthetic LFR benchmark datasets.

Existing works on local community detection in social networks focus on finding one single community a few seed members are most likely to be in. In this work, we address a much harder problem of multiple local community detection and propose a Nonnegative Matrix Factorization algorithm for finding multiple local communities for a single seed chosen randomly in multiple ground truth communities. The number of detected communities for the seed is determined automatically by the algorithm. We first apply a Breadth-First Search to sample the input graph up to several levels depending on the network density. We then use Nonnegative Matrix Factorization on the adjacency matrix of the sampled subgraph to estimate the number of communities, and then cluster the nodes of the subgraph into communities. Our proposed method differs from the existing NMF-based community detection methods as it does not use“ argmax ” function to assign nodes to communities. Our method has been evaluated on real-world networks and shows good accuracy as evaluated by the F1score when comparing with the state-of-the-art local community detection algorithm.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms for mining communities have focused on global graph structure, and often run in time proportional to the size of the entire graph. As we explore networks with millions of vertices and find communities of size in the hundreds, it becomes important to shift our attention from macroscopic structure to microscopic structure in large networks. A growing body of work has been adopting local expansion methods in order to identify communities from a few exemplary seed members. In this article, we propose a novel approach for finding overlapping communities called L emon ( L ocal E xpansion via M inimum O ne N orm). Provided with a few known seeds , the algorithm finds the community by performing a local spectral diffusion. The core idea of L emon is to use short random walks to approximate an invariant subspace near a seed set, which we refer to as local spectra . Local spectra can be viewed as the low-dimensional embedding that captures the nodes’ closeness in the local network structure. We show that L emon ’s performance in detecting communities is competitive with state-of-the-art methods. Moreover, the running time scales with the size of the community rather than that of the entire graph. The algorithm is easy to implement and is highly parallelizable. We further provide theoretical analysis of the local spectral properties, bounding the measure of tightness of extracted community using the eigenvalues of graph Laplacian. We thoroughly evaluate our approach using both synthetic and real-world datasets across different domains, and analyze the empirical variations when applying our method to inherently different networks in practice. In addition, the heuristics on how the seed set quality and quantity would affect the performance are provided.

Based on the definition of local spectral subspace, we propose a novel approach called LOSP for local overlapping community detection. Using the power method for a few steps, LOSP finds an approximate invariant subspace, which depicts the embedding of the local neighborhood structure around the seeds of interest. LOSP then identifies the local community expanded from the given seeds by seeking a sparse indicator vector in the subspace where the seeds are in its support. We provide a systematic investigation on LOSP, and thoroughly evaluate it on large real world networks across multiple domains. With the prior information of very few seed members, LOSP can detect the remaining members of a target community with high accuracy. Experiments demonstrate that LOSP outperforms the Heat Kernel and PageRank diffusions. Using LOSP as a subroutine, we further address the problem of multiple membership identification, which aims to find all the communities a single vertex belongs to. High F1 scores are achieved in detecting multiple local communities with respect to arbitrary single seed for various large real world networks.

Large graphs arise in a number of contexts and understanding their structure and extracting information from them is an important research area. Early algorithms on mining communities have focused on the global structure, and often run in time functional to the size of the entire graph. Nowadays, as we often explore networks with billions of vertices and find communities of size hundreds, it is crucial to shift our attention from macroscopic structure to microscopic structure when dealing with large networks. A growing body of work has been adopting local expansion methods in order to identify the community from a few exemplary seed members. %Very few approaches can systematically demonstrate both high efficiency and effectiveness that significantly stands out amongst the divergent approaches in finding communities.