Real-world event sequences are often generated by different temporal point processes (TPPs) and thus have clustering structures. Nonetheless, in the modeling and prediction of event sequences, most existing TPPs ignore the inherent clustering structures of the event sequences, leading to the models with unsatisfactory interpretability. In this study, we learn structure-enhanced TPPs with the help of Gromov-Wasserstein (GW) regularization, which imposes clustering structures on the sequence-level embeddings of the TPPs in the maximum likelihood estimation framework.In the training phase, the proposed method leverages a nonparametric TPP kernel to regularize the similarity matrix derived based on the sequence embeddings. In large-scale applications, we sample the kernel matrix and implement the regularization as a Gromov-Wasserstein (GW) discrepancy term, which achieves a trade-off between regularity and computational efficiency.The TPPs learned through this method result in clustered sequence embeddings and demonstrate competitive predictive and clustering performance, significantly improving the model interpretability without compromising prediction accuracy.

Protein backbone generation plays a central role in de novo protein design and is significant for many biological and medical applications. Although diffusion and flow-based generative models provide potential solutions to this challenging task, they often generate proteins with undesired designability and suffer computational inefficiency. In this study, we propose a novel rectified quaternion flow (ReQFlow) matching method for fast and high-quality protein backbone generation. In particular, our method generates a local translation and a 3D rotation from random noise for each residue in a protein chain, which represents each 3D rotation as a unit quaternion and constructs its flow by spherical linear interpolation (SLERP) in an exponential format. We train the model by quaternion flow (QFlow) matching with guaranteed numerical stability and rectify the QFlow model to accelerate its inference and improve the designability of generated protein backbones, leading to the proposed ReQFlow model. Experiments show that ReQFlow achieves state-of-the-art performance in protein backbone generation while requiring much fewer sampling steps and significantly less inference time (e.g., being 37x faster than RFDiffusion and 62x faster than Genie2 when generating a backbone of length 300), demonstrating its effectiveness and efficiency. The code is available at https://github.com/AngxiaoYue/ReQFlow.

Premise selection is a crucial yet challenging step in mathematical formalization, especially for users with limited experience. Due to the lack of available formalization projects, existing approaches that leverage language models often suffer from data scarcity. In this work, we introduce an innovative method for training a premise retriever to support the formalization of mathematics. Our approach employs a BERT model to embed proof states and premises into a shared latent space. The retrieval model is trained within a contrastive learning framework and incorporates a domain-specific tokenizer along with a fine-grained similarity computation method. Experimental results show that our model is highly competitive compared to existing baselines, achieving strong performance while requiring fewer computational resources. Performance is further enhanced through the integration of a re-ranking module. To streamline the formalization process, we will release a search engine that enables users to query Mathlib theorems directly using proof states, significantly improving accessibility and efficiency. Codes are available at https://github.com/ruc-ai4math/Premise-Retrieval.

An event sequence generated by a temporal point process is often associated with a hidden and structured event branching process that captures the triggering relations between its historical and current events. In this study, we design a new plug-and-play module based on the Bregman ADMM (BADMM) algorithm, which infers event branches associated with event sequences in the maximum likelihood estimation framework of temporal point processes (TPPs). Specifically, we formulate the inference of event branches as an optimization problem for the event transition matrix under sparse and low-rank constraints, which is embedded in existing TPP models or their learning paradigms. We can implement this optimization problem based on subspace clustering and sparse group-lasso, respectively, and solve it using the Bregman ADMM algorithm, whose unrolling leads to the proposed BADMM module. When learning a classic TPP (e.g., Hawkes process) by the expectation-maximization algorithm, the BADMM module helps derive structured responsibility matrices in the E-step. Similarly, the BADMM module helps derive low-rank and sparse attention maps for the neural TPPs with self-attention layers. The structured responsibility matrices and attention maps, which work as learned event transition matrices, indicate event branches, e.g., inferring isolated events and those key events triggering many subsequent events. Experiments on both synthetic and real-world data show that plugging our BADMM module into existing TPP models and learning paradigms can improve model performance and provide us with interpretable structured event branches.

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey intrinsic physics, and struggle to cope with the various domains. While geometry-based methods, e.g., graph neural networks (GNNs), have been proposed to further tackle these challenges, they still need to find the implicit physical laws from large datasets and rely excessively on rich labeled data. In this paper, we herein introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework, to learn spatiotemporal dynamics based on limited training data. The network is designed to conform to the general conservation law via symmetry, where conservative and non-conservative information passes over a multiscale space enhanced by a latent temporal marching strategy. The efficacy of our model has been verified in various spatiotemporal systems based on synthetic and real-world datasets, showing superiority over baseline models. Results demonstrate that CiGNN exhibits remarkable accuracy and generalizability, and is readily applicable to learning for prediction of various spatiotemporal dynamics in a spatial domain with complex geometry.

Asynchronous event sequence clustering aims to group similar event sequences in an unsupervised manner. Mixture models of temporal point processes have been proposed to solve this problem, but they often suffer from overfitting, leading to excessive cluster generation with a lack of diversity. To overcome these limitations, we propose a Bayesian mixture model of Temporal Point Processes with Determinantal Point Process prior (TP$^2$DP$^2$) and accordingly an efficient posterior inference algorithm based on conditional Gibbs sampling. Our work provides a flexible learning framework for event sequence clustering, enabling automatic identification of the potential number of clusters and accurate grouping of sequences with similar features. It is applicable to a wide range of parametric temporal point processes, including neural network-based models. Experimental results on both synthetic and real-world data suggest that our framework could produce moderately fewer yet more diverse mixture components, and achieve outstanding results across multiple evaluation metrics.

Predicting ground-state conformation from the corresponding molecular graph is crucial for many chemical applications, such as molecular modeling, molecular docking, and molecular property prediction. Recently, many learning-based methods have been proposed to replace time-consuming simulations for this task. However, these methods are often inefficient and sub-optimal as they merely rely on molecular graph information to make predictions from scratch. In this work, considering that molecular low-quality conformations are readily available, we propose a novel framework called ConfOpt to predict molecular ground-state conformation from the perspective of conformation optimization. Specifically, ConfOpt takes the molecular graph and corresponding low-quality 3D conformation as inputs, and then derives the ground-state conformation by iteratively optimizing the low-quality conformation under the guidance of the molecular graph. During training, ConfOpt concurrently optimizes the predicted atomic 3D coordinates and the corresponding interatomic distances, resulting in a strong predictive model. Extensive experiments demonstrate that ConfOpt significantly outperforms existing methods, thus providing a new paradigm for efficiently and accurately predicting molecular ground-state conformation.

Transformer [48] has been widely adopted in the deep learning domain. Recent large language models like GPT [4, 36] and LLaMA [45, 46] series are built based on the Transformer and its variants, which demonstrate their remarkable abilities in natural language processing. In the field of computer vision, Vision Transformers (ViTs) [14], such as EfficientViT [5, 26] and SHViT [53], exhibit exceptional performance and consistently push their limits. In addition, the Transformer-based models have been designed for the complex structured data in various applications, including the Informer [57] for time series broadcasting, the Transformer Hawkes process [58] for continuous-time event sequence prediction, the Graphormer [51] for molecular representation, the Mesh Transformer [24] for 3D mesh representation, the Set-Transformer [22] and Point-Transformer [56] for point cloud modeling, and so on. Although some new alternatives like Mamba [15] and RWKV [33] have been proposed and shown their competitiveness in some aspects, Transformer still maintains a dominant position when developing deep learning models because of its strong performance and outstanding universality. The effectiveness of Transformer is mainly attributed to its multi-head attention (MHA) mechanism [48]. However, MHA's quadratic complexity concerning sequence length leads to a heavy, even Hongteng Xu is the corresponding author of this work.

In the past few decades, polymers, high-molecular-weight compounds formed by bonding numerous identical or similar monomers covalently, have played an essential role in various scientific fields. In this context, accurate prediction of their properties is becoming increasingly crucial. Typically, the properties of a polymer, such as plasticity, conductivity, bio-compatibility, and so on, are highly correlated with its 3D structure. However, current methods for predicting polymer properties heavily rely on information from polymer SMILES sequences (P-SMILES strings) while ignoring crucial 3D structural information, leading to sub-optimal performance. In this work, we propose MMPolymer, a novel multimodal multitask pretraining framework incorporating both polymer 1D sequential information and 3D structural information to enhance downstream polymer property prediction tasks. Besides, to overcome the limited availability of polymer 3D data, we further propose the "Star Substitution" strategy to extract 3D structural information effectively. During pretraining, MMPolymer not only predicts masked tokens and recovers 3D coordinates but also achieves the cross-modal alignment of latent representation. Subsequently, we further fine-tune the pretrained MMPolymer for downstream polymer property prediction tasks in the supervised learning paradigm. Experimental results demonstrate that MMPolymer achieves state-of-the-art performance in various polymer property prediction tasks. Moreover, leveraging the pretrained MMPolymer and using only one modality (either P-SMILES string or 3D conformation) during fine-tuning can also surpass existing polymer property prediction methods, highlighting the exceptional capability of MMPolymer in polymer feature extraction and utilization. Our online platform for polymer property prediction is available at https://app.bohrium.dp.tech/mmpolymer.

As a promising individualized treatment effect (ITE) estimation method, counterfactual regression (CFR) maps individuals' covariates to a latent space and predicts their counterfactual outcomes. However, the selection bias between control and treatment groups often imbalances the two groups' latent distributions and negatively impacts this method's performance. In this study, we revisit counterfactual regression through the lens of information bottleneck and propose a novel learning paradigm called Gromov-Wasserstein information bottleneck (GWIB). In this paradigm, we learn CFR by maximizing the mutual information between covariates' latent representations and outcomes while penalizing the kernelized mutual information between the latent representations and the covariates. We demonstrate that the upper bound of the penalty term can be implemented as a new regularizer consisting of $i)$ the fused Gromov-Wasserstein distance between the latent representations of different groups and $ii)$ the gap between the transport cost generated by the model and the cross-group Gromov-Wasserstein distance between the latent representations and the covariates. GWIB effectively learns the CFR model through alternating optimization, suppressing selection bias while avoiding trivial latent distributions. Experiments on ITE estimation tasks show that GWIB consistently outperforms state-of-the-art CFR methods. To promote the research community, we release our project at https://github.com/peteryang1031/Causal-GWIB.