Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is frequently limited by the substantial computational resources required to construct the Kohn-Sham Hamiltonian. In response to these limitations, current research has employed deep-learning models to efficiently predict molecular and solid Hamiltonians, with roto-translational symmetries encoded in their neural networks. However, the scalability of prior models may be problematic when applied to large molecules, resulting in non-physical predictions of ground-state properties. In this study, we generate a substantially larger training set (PubChemQH) than used previously and use it to create a scalable model for DFT calculations with physical accuracy. For our model, we introduce a loss function derived from physical principles, which we call Wavefunction Alignment Loss (WALoss). WALoss involves performing a basis change on the predicted Hamiltonian to align it with the observed one; thus, the resulting differences can serve as a surrogate for orbital energy differences, allowing models to make better predictions for molecular orbitals and total energies than previously possible. WALoss also substantially accelerates self-consistent-field (SCF) DFT calculations. Here, we show it achieves a reduction in total energy prediction error by a factor of 1347 and an SCF calculation speed-up by a factor of 18\%. These substantial improvements set new benchmarks for achieving accurate and applicable predictions in larger molecular systems.

Hamiltonian matrix prediction is pivotal in computational chemistry, serving as the foundation for determining a wide range of molecular properties. While SE(3) equivariant graph neural networks have achieved remarkable success in this domain, their substantial computational cost—driven by high-order tensor product (TP) operations—restricts their scalability to large molecular systems with extensive basis sets. To address this challenge, we introduce SPHNet, an efficient and scalable equivariant network, that incorporates adaptive SParsity into Hamiltonian prediction. SPHNet employs two innovative sparse gates to selectively constrain non-critical interaction combinations, significantly reducing tensor product computations while maintaining accuracy. To optimize the sparse representation, we develop a Three-phase Sparsity Scheduler, ensuring stable convergence and achieving high performance at sparsity rates of up to 70%. Extensive evaluations on QH9 and PubchemQH datasets demonstrate that SPHNet achieves state-of-the-art accuracy while providing up to a 7x speedup over existing models. Beyond Hamiltonian prediction, the proposed sparsification techniques also hold significant potential for improving the efficiency and scalability of other SE(3) equivariant networks, further broadening their applicability and impact.

Computational simulation of chemical and biological systems using *ab initio* molecular dynamics has been a challenge over decades. Researchers have attempted to address the problem with machine learning and fragmentation-based methods. However, the two approaches fail to give a satisfactory description of long-range and many-body interactions, respectively. Inspired by fragmentation-based methods, we propose the Long-Short-Range Message-Passing (LSR-MP) framework as a generalization of the existing equivariant graph neural networks (EGNNs) with the intent to incorporate long-range interactions efficiently and effectively. We apply the LSR-MP framework to the recently proposed ViSNet and demonstrate the state-of-the-art results with up to 40% MAE reduction for molecules in MD22 and Chignolin datasets. Consistent improvements to various EGNNs will also be discussed to illustrate the general applicability and robustness of our LSR-MP framework. The code for our experiments and trained model weights could be found at https://github.com/liyy2/LSR-MP.

Predicting the mean-field Hamiltonian matrix in density functional theory is a fundamental formulation to leverage machine learning for solving molecular science problems. Yet, its applicability is limited by insufficient labeled data for training. In this work, we highlight that Hamiltonian prediction possesses a self-consistency principle, based on which we propose self-consistency training, an exact training method that does not require labeled data. It distinguishes the task from predicting other molecular properties by the following benefits: (1) it enables the model to be trained on a large amount of unlabeled data, hence addresses the data scarcity challenge and enhances generalization; (2) it is more efficient than running DFT to generate labels for supervised training, since it amortizes DFT calculation over a set of queries. We empirically demonstrate the better generalization in data-scarce and out-of-distribution scenarios, and the better efficiency over DFT labeling. These benefits push forward the applicability of Hamiltonian prediction to an ever-larger scale.

Geometric graph neural networks (GNNs) have emerged as powerful tools for modeling molecular geometry. However, they encounter limitations in effectively capturing long-range interactions in large molecular systems. To address this challenge, we introduce **Neural P$^3$M**, a versatile enhancer of geometric GNNs to expand the scope of their capabilities by incorporating mesh points alongside atoms and reimaging traditional mathematical operations in a trainable manner. Neural P$^3$M exhibits flexibility across a wide range of molecular systems and demonstrates remarkable accuracy in predicting energies and forces, outperforming on benchmarks such as the MD22 dataset. It also achieves an average improvement of 22% on the OE62 dataset while integrating with various architectures. Codes are available at https://github.com/OnlyLoveKFC/Neural_P3M.

In this study, we introduce a unified neural network architecture, the Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) model, which incorporates Deep Equilibrium Models (DEQs) for predicting Density Functional Theory (DFT) Hamiltonians. The DEQH model inherently captures the self-consistency nature of Hamiltonian, a critical aspect often overlooked by traditional machine learning approaches for Hamiltonian prediction. By employing DEQ within our model architecture, we circumvent the need for DFT calculations during the training phase to introduce the Hamiltonian's self-consistency, thus addressing computational bottlenecks associated with large or complex systems. We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians. When benchmarked on the MD17 and QH9 datasets, DEQHNet, an instantiation of the DEQH framework, has demonstrated a significant improvement in prediction accuracy. Beyond a predictor, the DEQH model is a Hamiltonian solver, in the sense that it uses the fixed-point solving capability of the deep equilibrium model to iteratively solve for the Hamiltonian. Ablation studies of DEQHNet further elucidate the network's effectiveness, offering insights into the potential of DEQ-integrated networks for Hamiltonian learning. We open source our implementation at https://github.com/Zun-Wang/DEQHNet.

The widespread adoption of Transformer architectures in various data modalities has opened new avenues for the applications in molecular modeling. Nevertheless, it remains elusive that whether the Transformer-based architecture can do molecular modeling as good as equivariant GNNs. In this paper, by designing Interatomic Positional Encoding (IPE) that parameterizes atomic environments as Transformer's positional encodings, we propose Geoformer, a novel geometric Transformer to effectively model molecular structures for various molecular property prediction. We evaluate Geoformer on several benchmarks, including the QM9 dataset and the recently proposed Molecule3D dataset. Compared with both Transformers and equivariant GNN models, Geoformer outperforms the state-of-the-art (SoTA) algorithms on QM9, and achieves the best performance on Molecule3D for both random and scaffold splits. By introducing IPE, Geoformer paves the way for molecular geometric modeling based on Transformer architecture. Codes are available at https://github.com/microsoft/AI2BMD/tree/Geoformer.

Machine learning force fields (MLFFs) have instigated a groundbreaking shift in molecular dynamics (MD) simulations across a wide range of fields, such as physics, chemistry, biology, and materials science. Incorporating higher order many-body interactions can enhance the expressiveness and accuracy of models. Recent models have achieved this by explicitly including up to four-body interactions. However, five-body interactions, which have relevance in various fields, are still challenging to incorporate efficiently into MLFFs. In this work, we propose the quintuple network (QuinNet), an end-to-end graph neural network that efficiently expresses many-body interactions up to five-body interactions with \emph{ab initio} accuracy. By analyzing the topology of diverse many-body interactions, we design the model architecture to efficiently and explicitly represent these interactions. We evaluate QuinNet on public datasets of small molecules, such as MD17 and its revised version, and show that it is compatible with other state-of-the-art models on these benchmarks. Moreover, QuinNet surpasses many leading models on larger and more complex molecular systems, such as MD22 and Chignolin, without increasing the computational complexity. We also use QuinNet as a force field for molecular dynamics (MD) simulations to demonstrate its accuracy and stability, and conduct an ablation study to elucidate the significance of five-body interactions. We open source our implementation at https://github.com/Zun-Wang/QuinNet.

Drug-drug interaction (DDI) prediction identifies interactions of drug combinations in which the adverse side effects caused by the physicochemical incompatibility have attracted much attention. Previous studies usually model drug information from single or dual views of the whole drug molecules but ignore the detailed interactions among atoms, which leads to incomplete and noisy information and limits the accuracy of DDI prediction. In this work, we propose a novel dual-view drug representation learning network for DDI prediction ('DSN-DDI'), which employs local and global representation learning modules iteratively and learns drug substructures from the single drug ('intra-view') and the drug pair ('inter-view') simultaneously. Comprehensive evaluations demonstrate that DSN-DDI significantly improved performance on DDI prediction for the existing drugs by achieving a relatively improved accuracy of 13.01% and an over 99% accuracy under the transductive setting. More importantly, DSN-DDI achieves a relatively improved accuracy of 7.07% to unseen drugs and shows the usefulness for real-world DDI applications. Finally, DSN-DDI exhibits good transferability on synergistic drug combination prediction and thus can serve as a generalized framework in the drug discovery field.

Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In light of this, great efforts have been put on encoding this symmetry into deep neural networks, which has been shown to improve the generalization performance and data efficiency for downstream tasks. Constructing an equivariant neural network generally brings high computational costs to ensure expressiveness. Therefore, how to better trade-off the expressiveness and computational efficiency plays a core role in the design of the equivariant deep learning models. In this paper, we propose a framework to construct SE(3) equivariant graph neural networks that can approximate the geometric quantities efficiently. Inspired by differential geometry and physics, we introduce equivariant local complete frames to graph neural networks, such that tensor information at given orders can be projected onto the frames. The local frame is constructed to form an orthonormal basis that avoids direction degeneration and ensure completeness. Since the frames are built only by cross product operations, our method is computationally efficient. We evaluate our method on two tasks: Newton mechanics modeling and equilibrium molecule conformation generation. Extensive experimental results demonstrate that our model achieves the best or competitive performance in two types of datasets.

The identification of active binding drugs for target proteins (referred to as drug-target interaction prediction) is the key challenge in virtual screening, which plays an essential role in drug discovery. Although recent deep learning-based approaches achieve better performance than molecular docking, existing models often neglect topological or spatial of intermolecular information, hindering prediction performance. We recognize this problem and propose a novel approach called the Intermolecular Graph Transformer (IGT) that employs a dedicated attention mechanism to model intermolecular information with a three-way Transformer-based architecture. IGT outperforms state-of-the-art (SoTA) approaches by 9.1% and 20.5% over the second best option for binding activity and binding pose prediction, respectively, and exhibits superior generalization ability to unseen receptor proteins than SoTA approaches. Furthermore, IGT exhibits promising drug screening ability against severe acute respiratory syndrome coronavirus 2 by identifying 83.1% active drugs that have been validated by wet-lab experiments with near-native predicted binding poses. Source code and datasets are available at https://github.com/microsoft/IGT-Intermolecular-Graph-Transformer.

In this big data era, knowledge becomes increasingly linked, along with the rapid growth in data volume. Connected knowledge is naturally represented and stored as knowledge graphs, which are of more and more importance for many frontier research areas such as machine intelligence. Effectively finding relations between entities in a large knowledge graph plays a key role in many knowledge graph applications, as the most valuable part of a knowledge graph is its rich connectedness, which captures rich information about the objects in the real world. However, due to the intrinsic complexity of real-world knowledge, finding semantically close relations by navigation in a large knowledge graph is very challenging. Canonical graph exploration methods inevitably result in combinatorial explosion especially when the paths connecting two entities are long: the search space is$O(d^l)$, where$d$is the average graph node degree and$l$is the length of the path. In this paper, we will systematically study the semantic navigation problem for large knowledge graphs. Inspired by AlphaGo, which was overwhelmingly successful in the game Go, we designed an efficient semantic navigation method based on a well-tailored Monte Carlo Tree Search algorithm with the unique characteristics of knowledge graphs considered. Extensive experiments on different real-life knowledge bases show that our method is not only effective but also very efficient.

Proteins are the main machinery of life and protein functions are largely determined by their 3D structures. The measurement of the pairwise proximity between amino acids of a protein, known as inter-residue contact map, well characterizes the structural information of a protein. Protein contact prediction (PCP) is an essential building block of many protein structure related applications. The prevalent approach to contact prediction is based on estimating the inter-residue contacts using hand-crafted coevolutionary features derived from multiple sequence alignments (MSAs). To mitigate the information loss caused by hand-crafted features, some recently proposed methods try to learn residue co-evolutions directly from MSAs. These methods generally derive coevolutionary features by aggregating the learned residue representations from individual sequences with equal weights, which is inconsistent with the premise that residue co-evolutions are a reflection of collective covariation patterns of numerous homologous proteins. Moreover, non-homologous residues and gaps commonly exist in MSAs. By aggregating features from all homologs equally, the non-homologous information may cause misestimation of the residue co-evolutions. To overcome these issues, we propose an attention-based architecture, Co-evolution Transformer (CoT), for PCP. CoT jointly considers the information from all homologous sequences in the MSA to better capture global coevolutionary patterns. To mitigate the influence of the non-homologous information, CoT selectively aggregates the features from different homologs by assigning smaller weights to non-homologous sequences or residue pairs. Extensive experiments on two rigorous benchmark datasets demonstrate the effectiveness of CoT. In particular, CoT achieves a $51.6\%$ top-L long-range precision score for the Free Modeling (FM) domains on the CASP14 benchmark, which outperforms the winner group of CASP14 contact prediction challenge by $9.8\%$.

MOTIVATION: Gradient descent-based protein modeling is a popular protein structure prediction approach that takes as input the predicted inter-residue distances and other necessary constraints and folds protein structures by minimizing protein-specific energy potentials. The constraints from multiple predicted protein properties provide redundant and sometime conflicting information that can trap the optimization process into local minima and impairs the modeling efficiency. RESULTS: To address these issues, we developed a self-adaptive protein modeling framework, SAMF. It eliminates redundancy of constraints and resolves conflicts, folds protein structures in an iterative way, and picks up the best structures by a deep quality analysis system. Without a large amount of complicated domain knowledge and numerous patches as barriers, SAMF achieves the state-of-the-art performance by exploiting the power of cutting-edge techniques of deep learning. SAMF has a modular design and can be easily customized and extended. As the quality of input constraints is ever growing, the superiority of SAMF will be amplified over time. AVAILABILITY AND IMPLEMENTATION: The source code and data for reproducing the results is available at https://msracb.blob.core.windows.net/pub/psp/SAMF.zip. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Fragment libraries play a key role in fragment-assembly based protein structure prediction, where protein fragments are assembled to form a complete three-dimensional structure. Rich and accurate structural information embedded in fragment libraries has not been systematically extracted and used beyond fragment assembly. METHODS: To better leverage the valuable structural information for protein structure prediction, we extracted seven types of structural information from fragment libraries. We broadened the usage of such structural information by transforming fragment libraries into protein-specific potentials for gradient-descent based protein folding and encoding fragment libraries as structural features for protein property prediction. RESULTS: Fragment libraires improved the accuracy of protein folding and outperformed state-of-the-art algorithms with respect to predicted properties, such as torsion angles and inter-residue distances. CONCLUSION: Our work implies that the rich structural information extracted from fragment libraries can complement sequence-derived features to help protein structure prediction.

In recent years, knowledge graph embedding becomes a pretty hot research topic of artificial intelligence and plays increasingly vital roles in various downstream applications, such as recommendation and question answering.However, existing methods for knowledge graph embedding can not make a proper trade-off between the model complexity and the model expressiveness, which makes them still far from satisfactory.To mitigate this problem, we propose a lightweight modeling framework that can achieve highly competitive relational expressiveness without increasing the model complexity.Our framework focuses on the design of scoring functions and highlights two critical characteristics: 1) facilitating sufficient feature interactions; 2) preserving both symmetry and antisymmetry properties of relations.It is noteworthy that owing to the general and elegant design of scoring functions, our framework can incorporate many famous existing methods as special cases.Moreover, extensive experiments on public benchmarks demonstrate the efficiency and effectiveness of our framework.

Commonsense knowledge is fundamental to make machines reach human-level intelligence. However, conventional methods of commonsense extraction generally do not work well because commonsense by nature is usually not explicitly stated in texts or other data. Besides, commonsense knowledge graphs built in advance are difficult to cover all the knowledge required for practical tasks due to the incompleteness of knowledge graphs. In this paper, we propose an online commonsense oracle to achieve knowledge reasoning. Specifically, we focus on the on-demand inference of specific commonsense propositions. We use capableOf relation as an example due to its notable significance in daily life. For more effective capableOf reasoning, informative supporting features derived from an existing commonsense knowledge graph and a Web search engine are exploited. Finally, we conduct extensive experiments, and the results demonstrate the effectiveness of our approach.

RDF is one of the most commonly used knowledge representation forms. Many highly influential knowledge bases, such as Freebase and PubChemRDF, are in RDF format. An RDF data set is usually represented as a collection of subject-predicate-object triples. Despite the flexibility of RDF triples, it is challenging to serve SPARQL queries on RDF data efficiently by directly managing triples due to the following two reasons. First, heavy joins on a large number of triples are needed for query processing, resulting in a large number of data scans and large redundant intermediate results; Second, weakly-typed triple representation provides suboptimal random access - typically with logarithmic complexity. This data access challenge, unfortunately, cannot be easily met by a better query optimizer as large graph processing is extremely I/O-intensive. In this paper, we argue that strongly-typed graph representation is the key to high-performance RDF query processing. We propose Stylus - a strongly-typed store for serving massive RDF data. Stylus exploits a strongly-typed storage scheme to boost the performance of RDF query processing. The storage scheme is essentially a materialized join view on entities, it thus can eliminate a large number of unnecessary joins on triples. Moreover, it is equipped with a compact representation for intermediate results and an efficient graph-decomposition based query planner. Experimental results on both synthetic and real-life RDF data sets confirm that the proposed approach can dramatically boost the performance of SPARQL query processing.

A lot of real-life data are of graph nature. However, it is not until recently that business begins to exploit data's connectedness for business insights. On the other hand, RDBMSs are a mature technology for data management, but they are not for graph processing. Take graph traversal, a common graph operation for example, it heavily relies on a graph primitive that accesses a given node's neighborhood. We need to join tables following foreign keys to access the nodes in the neighborhood if an RDBMS is used to manage graph data. Graph exploration is a fundamental building block of many graph algorithms. But this simple operation is costly due to a large volume of I/O caused by the massive amount of table joins. In this paper, we present G-SQL, our effort toward the integration of a RDBMS and a native in-memory graph processing engine. G-SQL leverages the fast graph exploration capability provided by the graph engine to answer multi-way join queries. Meanwhile, it uses RDBMSs to provide mature data management functionalities, such as reliable data storage and additional data access methods. Specifically, G-SQL is a SQL dialect augmented with graph exploration functionalities and it dispatches query tasks to the in-memory graph engine and its underlying RDMBS. The G-SQL runtime coordinates the two query processors via a unified cost model to ensure the entire query is processed efficiently. Experimental results show that our approach greatly expands capabilities of RDBMs and delivers exceptional performance for SQL-graph hybrid queries.

Billion-node graphs pose significant challenges at all levels from storage infrastructures to programming models. It is critical to develop a general purpose platform for graph processing. A distributed memory system is considered a feasible platform supporting online query processing as well as offline graph analytics. In this paper, we study the problem of partitioning a billion-node graph on such a platform, an important consideration because it has direct impact on load balancing and communication overhead. It is challenging not just because the graph is large, but because we can no longer assume that the data can be organized in arbitrary ways to maximize the performance of the partitioning algorithm. Instead, the algorithm must adopt the same data and programming model adopted by the system and other applications. In this paper, we propose a multi-level label propagation (MLP) method for graph partitioning. Experimental results show that our solution can partition billion-node graphs within several hours on a distributed memory system consisting of merely several machines, and the quality of the partitions produced by our approach is comparable to state-of-the-art approaches applied on toy-size graphs.

Computations performed by graph algorithms are data driven, and require a high degree of random data access. Despite the great progresses made in disk technology, it still cannot provide the level of efficient random access required by graph computation. On the other hand, memory-based approaches usually do not scale due to the capacity limit of single machines. In this paper, we introduce Trinity, a general purpose graph engine over a distributed memory cloud. Through optimized memory management and network communication, Trinity supports fast graph exploration as well as efficient parallel computing. In particular, Trinity leverages graph access patterns in both online and offline computation to optimize memory and communication for best performance. These enable Trinity to support efficient online query processing and offline analytics on large graphs with just a few commodity machines. Furthermore, Trinity provides a high level specification language called TSL for users to declare data schema and communication protocols, which brings great ease-of-use for general purpose graph management and computing. Our experiments show Trinity's performance in both low latency graph queries as well as high throughput graph analytics on web-scale, billion-node graphs.

The emergence of real life graphs with billions of nodes poses significant challenges for managing and querying these graphs. One of the fundamental queries submitted to graphs is the shortest distance query. Online BFS (breadth-first search) and offline pre-computing pairwise shortest distances are prohibitive in time or space complexity for billion-node graphs. In this paper, we study the feasibility of building distance oracles for billion-node graphs. A distance oracle provides approximate answers to shortest distance queries by using a pre-computed data structure for the graph. Sketch-based distance oracles are good candidates because they assign each vertex a sketch of bounded size, which means they have linear space complexity. However, state-of-the-art sketch-based distance oracles lack efficiency or accuracy when dealing with big graphs. In this paper, we address the scalability and accuracy issues by focusing on optimizing the three key factors that affect the performance of distance oracles: landmark selection, distributed BFS , and answer generation. We conduct extensive experiments on both real networks and synthetic networks to show that we can build distance oracles of affordable cost and efficiently answer shortest distance queries even for billion-node graphs.

Much work has been devoted to supporting RDF data. But state-of-the-art systems and methods still cannot handle web scale RDF data effectively. Furthermore, many useful and general purpose graph-based operations (e.g., random walk, reachability, community discovery) on RDF data are not supported, as most existing systems store and index data in particular ways (e.g., as relational tables or as a bitmap matrix) to maximize one particular operation on RDF data: SPARQL query processing. In this paper, we introduce Trinity. RDF, a distributed, memory-based graph engine for web scale RDF data. Instead of managing the RDF data in triple stores or as bitmap matrices, we store RDF data in its native graph form. It achieves much better (sometimes orders of magnitude better) performance for SPARQL queries than the state-of-the-art approaches. Furthermore, since the data is stored in its native graph form, the system can support other operations (e.g., random walks, reachability) on RDF graphs as well. We conduct comprehensive experimental studies on real life, web scale RDF data to demonstrate the effectiveness of our approach.

We are facing challenges at all levels ranging from infrastructures to programming models for managing and mining large graphs. A lot of algorithms on graphs are ad-hoc in the sense that each of them assumes that the underlying graph data can be organized in a certain way that maximizes the performance of the algorithm. In other words, there is no standard graph systems based on which graph algorithms are developed and optimized. In response to this situation, a lot of graph systems have been proposed recently. In this tutorial, we discuss several representative systems. Still, we focus on providing perspectives from a variety of standpoints on the goals and the means for developing a general purpose graph system. We highlight the challenges posed by the graph data, the constraints of architectural design, the different types of application needs, and the power of different programming models that support such needs.

The ability to handle large scale graph data is crucial to an increasing number of applications. Much work has been dedicated to supporting basic graph operations such as subgraph matching, reachability, regular expression matching, etc. In many cases, graph indices are employed to speed up query processing. Typically, most indices require either super-linear indexing time or super-linear indexing space. Unfortunately, for very large graphs, super-linear approaches are almost always infeasible. In this paper, we study the problem of subgraph matching on billion-node graphs. We present a novel algorithm that supports efficient subgraph matching for graphs deployed on a distributed memory store. Instead of relying on super-linear indices, we use efficient graph exploration and massive parallel computing for query processing. Our experimental results demonstrate the feasibility of performing subgraph matching on web-scale graph data.