Jianzhu Ma

Shitong Luo, Jiahan Li, Jiaqi Guan et al. · mit

Equivariance has been a long-standing concern in various fields ranging from computer vision to physical modeling. Most previous methods struggle with generality, simplicity, and expressiveness -- some are designed ad hoc for specific data types, some are too complex to be accessible, and some sacrifice flexible transformations. In this work, we propose a novel and simple framework to achieve equivariance for point cloud analysis based on the message passing (graph neural network) scheme. We find the equivariant property could be obtained by introducing an orientation for each point to decouple the relative position for each point from the global pose of the entire point cloud. Therefore, we extend current message passing networks with a module that learns orientations for each point. Before aggregating information from the neighbors of a point, the networks transforms the neighbors' coordinates based on the point's learned orientations. We provide formal proofs to show the equivariance of the proposed framework. Empirically, we demonstrate that our proposed method is competitive on both point cloud analysis and physical modeling tasks. Code is available at https://github.com/luost26/Equivariant-OrientedMP .

Xingang Peng, Shitong Luo, Jiaqi Guan et al. · mit

Deep generative models have achieved tremendous success in designing novel drug molecules in recent years. A new thread of works have shown the great potential in advancing the specificity and success rate of in silico drug design by considering the structure of protein pockets. This setting posts fundamental computational challenges in sampling new chemical compounds that could satisfy multiple geometrical constraints imposed by pockets. Previous sampling algorithms either sample in the graph space or only consider the 3D coordinates of atoms while ignoring other detailed chemical structures such as bond types and functional groups. To address the challenge, we develop Pocket2Mol, an E(3)-equivariant generative network composed of two modules: 1) a new graph neural network capturing both spatial and bonding relationships between atoms of the binding pockets and 2) a new efficient algorithm which samples new drug candidates conditioned on the pocket representations from a tractable distribution without relying on MCMC. Experimental results demonstrate that molecules sampled from Pocket2Mol achieve significantly better binding affinity and other drug properties such as druglikeness and synthetic accessibility.

Xingchao Liu, Xiwen Zhang, Jianzhu Ma et al.

Diffusion models have revolutionized text-to-image generation with its exceptional quality and creativity. However, its multi-step sampling process is known to be slow, often requiring tens of inference steps to obtain satisfactory results. Previous attempts to improve its sampling speed and reduce computational costs through distillation have been unsuccessful in achieving a functional one-step model. In this paper, we explore a recent method called Rectified Flow, which, thus far, has only been applied to small datasets. The core of Rectified Flow lies in its \emph{reflow} procedure, which straightens the trajectories of probability flows, refines the coupling between noises and images, and facilitates the distillation process with student models. We propose a novel text-conditioned pipeline to turn Stable Diffusion (SD) into an ultra-fast one-step model, in which we find reflow plays a critical role in improving the assignment between noise and images. Leveraging our new pipeline, we create, to the best of our knowledge, the first one-step diffusion-based text-to-image generator with SD-level image quality, achieving an FID (Frechet Inception Distance) of $23.3$ on MS COCO 2017-5k, surpassing the previous state-of-the-art technique, progressive distillation, by a significant margin ($37.2$ $\rightarrow$ $23.3$ in FID). By utilizing an expanded network with 1.7B parameters, we further improve the FID to $22.4$. We call our one-step models \emph{InstaFlow}. On MS COCO 2014-30k, InstaFlow yields an FID of $13.1$ in just $0.09$ second, the best in $\leq 0.1$ second regime, outperforming the recent StyleGAN-T ($13.9$ in $0.1$ second). Notably, the training of InstaFlow only costs 199 A100 GPU days. Codes and pre-trained models are available at \url{github.com/gnobitab/InstaFlow}.

Shitong Luo, Jiaqi Guan, Jianzhu Ma et al. · mit

We study a fundamental problem in structure-based drug design -- generating molecules that bind to specific protein binding sites. While we have witnessed the great success of deep generative models in drug design, the existing methods are mostly string-based or graph-based. They are limited by the lack of spatial information and thus unable to be applied to structure-based design tasks. Particularly, such models have no or little knowledge of how molecules interact with their target proteins exactly in 3D space. In this paper, we propose a 3D generative model that generates molecules given a designated 3D protein binding site. Specifically, given a binding site as the 3D context, our model estimates the probability density of atom's occurrences in 3D space -- positions that are more likely to have atoms will be assigned higher probability. To generate 3D molecules, we propose an auto-regressive sampling scheme -- atoms are sampled sequentially from the learned distribution until there is no room for new atoms. Combined with this sampling scheme, our model can generate valid and diverse molecules, which could be applicable to various structure-based molecular design tasks such as molecule sampling and linker design. Experimental results demonstrate that molecules sampled from our model exhibit high binding affinity to specific targets and good drug properties such as drug-likeness even if the model is not explicitly optimized for them.

Jiaqi Guan, Wesley Wei Qian, Xingang Peng et al.

Rich data and powerful machine learning models allow us to design drugs for a specific protein target \textit{in silico}. Recently, the inclusion of 3D structures during targeted drug design shows superior performance to other target-free models as the atomic interaction in the 3D space is explicitly modeled. However, current 3D target-aware models either rely on the voxelized atom densities or the autoregressive sampling process, which are not equivariant to rotation or easily violate geometric constraints resulting in unrealistic structures. In this work, we develop a 3D equivariant diffusion model to solve the above challenges. To achieve target-aware molecule design, our method learns a joint generative process of both continuous atom coordinates and categorical atom types with a SE(3)-equivariant network. Moreover, we show that our model can serve as an unsupervised feature extractor to estimate the binding affinity under proper parameterization, which provides an effective way for drug screening. To evaluate our model, we propose a comprehensive framework to evaluate the quality of sampled molecules from different dimensions. Empirical studies show our model could generate molecules with more realistic 3D structures and better affinities towards the protein targets, and improve binding affinity ranking and prediction without retraining.

Haotian Ye, Haowei Lin, Jiaqi Han et al. · pku

Given an unconditional diffusion model and a predictor for a target property of interest (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. Existing methods, though effective in various individual applications, often lack theoretical grounding and rigorous testing on extensive benchmarks. As a result, they could even fail on simple tasks, and applying them to a new problem becomes unavoidably difficult. This paper introduces a novel algorithmic framework encompassing existing methods as special cases, unifying the study of training-free guidance into the analysis of an algorithm-agnostic design space. Via theoretical and empirical investigation, we propose an efficient and effective hyper-parameter searching strategy that can be readily applied to any downstream task. We systematically benchmark across 7 diffusion models on 16 tasks with 40 targets, and improve performance by 8.5% on average. Our framework and benchmark offer a solid foundation for conditional generation in a training-free manner.

Jing Gong, Minsheng Hao, Xingyi Cheng et al.

Advances in high-throughput sequencing technology have led to significant progress in measuring gene expressions at the single-cell level. The amount of publicly available single-cell RNA-seq (scRNA-seq) data is already surpassing 50M records for humans with each record measuring 20,000 genes. This highlights the need for unsupervised representation learning to fully ingest these data, yet classical transformer architectures are prohibitive to train on such data in terms of both computation and memory. To address this challenge, we propose a novel asymmetric encoder-decoder transformer for scRNA-seq data, called xTrimoGene$^α$ (or xTrimoGene for short), which leverages the sparse characteristic of the data to scale up the pre-training. This scalable design of xTrimoGene reduces FLOPs by one to two orders of magnitude compared to classical transformers while maintaining high accuracy, enabling us to train the largest transformer models over the largest scRNA-seq dataset today. Our experiments also show that the performance of xTrimoGene improves as we scale up the model sizes, and it also leads to SOTA performance over various downstream tasks, such as cell type annotation, perturb-seq effect prediction, and drug combination prediction. xTrimoGene model is now available for use as a service via the following link: https://api.biomap.com/xTrimoGene/apply.

Yinan Huang, Xingang Peng, Jianzhu Ma et al.

Deep learning has achieved tremendous success in designing novel chemical compounds with desirable pharmaceutical properties. In this work, we focus on a new type of drug design problem -- generating a small "linker" to physically attach two independent molecules with their distinct functions. The main computational challenges include: 1) the generation of linkers is conditional on the two given molecules, in contrast to generating full molecules from scratch in previous works; 2) linkers heavily depend on the anchor atoms of the two molecules to be connected, which are not known beforehand; 3) 3D structures and orientations of the molecules need to be considered to avoid atom clashes, for which equivariance to E(3) group are necessary. To address these problems, we propose a conditional generative model, named 3DLinker, which is able to predict anchor atoms and jointly generate linker graphs and their 3D structures based on an E(3) equivariant graph variational autoencoder. So far as we know, there are no previous models that could achieve this task. We compare our model with multiple conditional generative models modified from other molecular design tasks and find that our model has a significantly higher rate in recovering molecular graphs, and more importantly, accurately predicting the 3D coordinates of all the atoms.

Yinan Huang, Xingang Peng, Jianzhu Ma et al.

Message Passing Neural Networks (MPNNs) are a widely used class of Graph Neural Networks (GNNs). The limited representational power of MPNNs inspires the study of provably powerful GNN architectures. However, knowing one model is more powerful than another gives little insight about what functions they can or cannot express. It is still unclear whether these models are able to approximate specific functions such as counting certain graph substructures, which is essential for applications in biology, chemistry and social network analysis. Motivated by this, we propose to study the counting power of Subgraph MPNNs, a recent and popular class of powerful GNN models that extract rooted subgraphs for each node, assign the root node a unique identifier and encode the root node's representation within its rooted subgraph. Specifically, we prove that Subgraph MPNNs fail to count more-than-4-cycles at node level, implying that node representations cannot correctly encode the surrounding substructures like ring systems with more than four atoms. To overcome this limitation, we propose I$^2$-GNNs to extend Subgraph MPNNs by assigning different identifiers for the root node and its neighbors in each subgraph. I$^2$-GNNs' discriminative power is shown to be strictly stronger than Subgraph MPNNs and partially stronger than the 3-WL test. More importantly, I$^2$-GNNs are proven capable of counting all 3, 4, 5 and 6-cycles, covering common substructures like benzene rings in organic chemistry, while still keeping linear complexity. To the best of our knowledge, it is the first linear-time GNN model that can count 6-cycles with theoretical guarantees. We validate its counting power in cycle counting tasks and demonstrate its competitive performance in molecular prediction benchmarks.

Dongting Li, Xingyu Chen, Qianyang Wu et al.

Humanoid robots show promise for complex whole-body tasks in unstructured environments. Although Human-Object Interaction (HOI) has advanced, most methods focus on fully actuated objects rigidly coupled to the robot, ignoring underactuated objects with independent dynamics and non-holonomic constraints. These introduce control challenges from coupling forces and occlusions. We present HAIC, a unified framework for robust interaction across diverse object dynamics without external state estimation. Our key contribution is a dynamics predictor that estimates high-order object states (velocity, acceleration) solely from proprioceptive history. These predictions are projected onto static geometric priors to form a spatially grounded dynamic occupancy map, enabling the policy to infer collision boundaries and contact affordances in blind spots. We use asymmetric fine-tuning, where a world model continuously adapts to the student policy's exploration, ensuring robust state estimation under distribution shifts. Experiments on a humanoid robot show HAIC achieves high success rates in agile tasks (skateboarding, cart pushing/pulling under various loads) by proactively compensating for inertial perturbations, and also masters multi-object long-horizon tasks like carrying a box across varied terrain by predicting the dynamics of multiple objects.

Zhizhou Ren, Anji Liu, Yitao Liang et al.

Learning new task-specific skills from a few trials is a fundamental challenge for artificial intelligence. Meta reinforcement learning (meta-RL) tackles this problem by learning transferable policies that support few-shot adaptation to unseen tasks. Despite recent advances in meta-RL, most existing methods require the access to the environmental reward function of new tasks to infer the task objective, which is not realistic in many practical applications. To bridge this gap, we study the problem of few-shot adaptation in the context of human-in-the-loop reinforcement learning. We develop a meta-RL algorithm that enables fast policy adaptation with preference-based feedback. The agent can adapt to new tasks by querying human's preference between behavior trajectories instead of using per-step numeric rewards. By extending techniques from information theory, our approach can design query sequences to maximize the information gain from human interactions while tolerating the inherent error of non-expert human oracle. In experiments, we extensively evaluate our method, Adaptation with Noisy OracLE (ANOLE), on a variety of meta-RL benchmark tasks and demonstrate substantial improvement over baseline algorithms in terms of both feedback efficiency and error tolerance.

Ruiyang Chen, Yingheng Tang, Jianzhu Ma et al.

Diffractive optical neural networks (DONNs) have been emerging as a high-throughput and energy-efficient hardware platform to perform all-optical machine learning (ML) in machine vision systems. However, the current demonstrated applications of DONNs are largely straightforward image classification tasks, which undermines the prospect of developing and utilizing such hardware for other ML applications. Here, we numerically and experimentally demonstrate the deployment of an all-optical reconfigurable DONNs system for scientific computing, including guiding two-dimensional quantum material synthesis, predicting the properties of nanomaterials and small molecular cancer drugs, predicting the device response of nanopatterned integrated photonic power splitters, and the dynamic stabilization of an inverted pendulum with reinforcement learning. Despite a large variety of input data structures, we develop a universal feature engineering approach to convert categorical input features to the images that can be processed in the DONNs system. Our results open up new opportunities of employing DONNs systems for a broad range of ML applications.

Jieming Cui, Ziren Gong, Baoxiong Jia et al.

The challenge of replicating research results has posed a significant impediment to the field of molecular biology. The advent of modern intelligent systems has led to notable progress in various domains. Consequently, we embarked on an investigation of intelligent monitoring systems as a means of tackling the issue of the reproducibility crisis. Specifically, we first curate a comprehensive multimodal dataset, named ProBio, as an initial step towards this objective. This dataset comprises fine-grained hierarchical annotations intended for the purpose of studying activity understanding in BioLab. Next, we devise two challenging benchmarks, transparent solution tracking and multimodal action recognition, to emphasize the unique characteristics and difficulties associated with activity understanding in BioLab settings. Finally, we provide a thorough experimental evaluation of contemporary video understanding models and highlight their limitations in this specialized domain to identify potential avenues for future research. We hope ProBio with associated benchmarks may garner increased focus on modern AI techniques in the realm of molecular biology.

Jiaqi Guan, Xiangxin Zhou, Yuwei Yang et al.

Designing 3D ligands within a target binding site is a fundamental task in drug discovery. Existing structured-based drug design methods treat all ligand atoms equally, which ignores different roles of atoms in the ligand for drug design and can be less efficient for exploring the large drug-like molecule space. In this paper, inspired by the convention in pharmaceutical practice, we decompose the ligand molecule into two parts, namely arms and scaffold, and propose a new diffusion model, DecompDiff, with decomposed priors over arms and scaffold. In order to facilitate the decomposed generation and improve the properties of the generated molecules, we incorporate both bond diffusion in the model and additional validity guidance in the sampling phase. Extensive experiments on CrossDocked2020 show that our approach achieves state-of-the-art performance in generating high-affinity molecules while maintaining proper molecular properties and conformational stability, with up to -8.39 Avg. Vina Dock score and 24.5 Success Rate. The code is provided at https://github.com/bytedance/DecompDiff

Fan Ding, Yijie Wang, Jianzhu Ma et al.

Provably solving stochastic convex optimization problems with constraints is essential for various problems in science, business, and statistics. Recently proposed XOR-Stochastic Gradient Descent (XOR-SGD) provides a convergence rate guarantee solving the constraints-free version of the problem by leveraging XOR-Sampling. However, the task becomes more difficult when additional equality and inequality constraints are needed to be satisfied. Here we propose XOR-PGD, a novel algorithm based on Projected Gradient Descent (PGD) coupled with the XOR sampler, which is guaranteed to solve the constrained stochastic convex optimization problem still in linear convergence rate by choosing proper step size. We show on both synthetic stochastic inventory management and real-world road network design problems that the rate of constraints satisfaction of the solutions optimized by XOR-PGD is $10\%$ more than the competing approaches in a very large searching space. The improved XOR-PGD algorithm is demonstrated to be more accurate and efficient than both XOR-SGD and SGD coupled with MCMC based samplers. It is also shown to be more scalable with respect to the number of samples and processor cores via experiments with large dimensions.

Ruidong Wu, Ruihan Guo, Rui Wang et al.

Despite the striking success of general protein folding models such as AlphaFold2(AF2, Jumper et al. (2021)), the accurate computational modeling of antibody-antigen complexes remains a challenging task. In this paper, we first analyze AF2's primary loss function, known as the Frame Aligned Point Error (FAPE), and raise a previously overlooked issue that FAPE tends to face gradient vanishing problem on high-rotational-error targets. To address this fundamental limitation, we propose a novel geodesic loss called Frame Aligned Frame Error (FAFE, denoted as F2E to distinguish from FAPE), which enables the model to better optimize both the rotational and translational errors between two frames. We then prove that F2E can be reformulated as a group-aware geodesic loss, which translates the optimization of the residue-to-residue error to optimizing group-to-group geodesic frame distance. By fine-tuning AF2 with our proposed new loss function, we attain a correct rate of 52.3\% (DockQ $>$ 0.23) on an evaluation set and 43.8\% correct rate on a subset with low homology, with substantial improvement over AF2 by 182\% and 100\% respectively.

Jiahan Li, Tong Chen, Shitong Luo et al.

Peptides, short chains of amino acids, interact with target proteins, making them a unique class of protein-based therapeutics for treating human diseases. Recently, deep generative models have shown great promise in peptide generation. However, several challenges remain in designing effective peptide binders. First, not all residues contribute equally to peptide-target interactions. Second, the generated peptides must adopt valid geometries due to the constraints of peptide bonds. Third, realistic tasks for peptide drug development are still lacking. To address these challenges, we introduce PepHAR, a hot-spot-driven autoregressive generative model for designing peptides targeting specific proteins. Building on the observation that certain hot spot residues have higher interaction potentials, we first use an energy-based density model to fit and sample these key residues. Next, to ensure proper peptide geometry, we autoregressively extend peptide fragments by estimating dihedral angles between residue frames. Finally, we apply an optimization process to iteratively refine fragment assembly, ensuring correct peptide structures. By combining hot spot sampling with fragment-based extension, our approach enables de novo peptide design tailored to a target protein and allows the incorporation of key hot spot residues into peptide scaffolds. Extensive experiments, including peptide design and peptide scaffold generation, demonstrate the strong potential of PepHAR in computational peptide binder design. Source code will be available at https://github.com/Ced3-han/PepHAR.

Xinheng He, Yijia Zhang, Haowei Lin et al.

Structure-based drug design has seen significant advancements with the integration of artificial intelligence (AI), particularly in the generation of hit and lead compounds. However, most AI-driven approaches neglect the importance of endogenous protein interactions with peptides, which may result in suboptimal molecule designs. In this work, we present Peptide2Mol, an E(3)-equivariant graph neural network diffusion model that generates small molecules by referencing both the original peptide binders and their surrounding protein pocket environments. Trained on large datasets and leveraging sophisticated modeling techniques, Peptide2Mol not only achieves state-of-the-art performance in non-autoregressive generative tasks, but also produces molecules with similarity to the original peptide binder. Additionally, the model allows for molecule optimization and peptidomimetic design through a partial diffusion process. Our results highlight Peptide2Mol as an effective deep generative model for generating and optimizing bioactive small molecules from protein binding pockets.

Yinghao Shuai, Ran Yu, Yuantao Chen et al.

Current robotic systems can understand the categories and poses of objects well. But understanding physical properties like mass, friction, and hardness, in the wild, remains challenging. We propose a new method that reconstructs 3D objects using the Gaussian splatting representation and predicts various physical properties in a zero-shot manner. We propose two techniques during the reconstruction phase: a geometry-aware regularization loss function to improve the shape quality and a region-aware feature contrastive loss function to promote region affinity. Two other new techniques are designed during inference: a feature-based property propagation module and a volume integration module tailored for the Gaussian representation. Our framework is named as zero-shot physical understanding with Gaussian splatting, or PUGS. PUGS achieves new state-of-the-art results on the standard benchmark of ABO-500 mass prediction. We provide extensive quantitative ablations and qualitative visualization to demonstrate the mechanism of our designs. We show the proposed methodology can help address challenging real-world grasping tasks. Our codes, data, and models are available at https://github.com/EverNorif/PUGS

Jiahan Li, Shitong Luo, Congyue Deng et al.

By folding into particular 3D structures, proteins play a key role in living beings. To learn meaningful representation from a protein structure for downstream tasks, not only the global backbone topology but the local fine-grained orientational relations between amino acids should also be considered. In this work, we propose the Orientation-Aware Graph Neural Networks (OAGNNs) to better sense the geometric characteristics in protein structure (e.g. inner-residue torsion angles, inter-residue orientations). Extending a single weight from a scalar to a 3D vector, we construct a rich set of geometric-meaningful operations to process both the classical and SO(3) representations of a given structure. To plug our designed perceptron unit into existing Graph Neural Networks, we further introduce an equivariant message passing paradigm, showing superior versatility in maintaining SO(3)-equivariance at the global scale. Experiments have shown that our OAGNNs have a remarkable ability to sense geometric orientational features compared to classical networks. OAGNNs have also achieved state-of-the-art performance on various computational biology applications related to protein 3D structures. The code is available at https://github.com/Ced3-han/OAGNN/tree/main.

Haowei Lin, Baizhou Huang, Haotian Ye et al. · pku

The ever-growing ecosystem of LLMs has posed a challenge in selecting the most appropriate pre-trained model to fine-tune amidst a sea of options. Given constrained resources, fine-tuning all models and making selections afterward is unrealistic. In this work, we formulate this resource-constrained selection task into predicting fine-tuning performance and illustrate its natural connection with Scaling Law. Unlike pre-training, we find that the fine-tuning scaling curve includes not just the well-known "power phase" but also the previously unobserved "pre-power phase". We also explain why existing Scaling Law fails to capture this phase transition phenomenon both theoretically and empirically. To address this, we introduce the concept of "pre-learned data size" into our Rectified Scaling Law, which overcomes theoretical limitations and fits experimental results much better. By leveraging our law, we propose a novel LLM selection algorithm that selects the near-optimal model with hundreds of times less resource consumption, while other methods may provide negatively correlated selection. The project page is available at rectified-scaling-law.github.io.

Haotian Ye, Haowei Lin, Jingyi Tang et al.

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.

Xiangcheng Zhang, Haowei Lin, Haotian Ye et al.

Classical search algorithms have long underpinned modern artificial intelligence. In this work, we tackle the challenge of inference-time control in diffusion models -- adapting generated outputs to meet diverse test-time objectives -- using principles from classical search. We propose a general framework that orchestrates local and global search to efficiently navigate the generative space. It employs a theoretically grounded local search via annealed Langevin MCMC and performs compute-efficient global exploration using breadth-first and depth-first tree search. We evaluate our approach on a range of challenging domains, including planning, offline reinforcement learning, and image generation. Across all tasks, we observe significant gains in both performance and efficiency. These results show that classical search provides a principled and practical foundation for inference-time scaling in diffusion models. Project page at https://diffusion-inference-scaling.github.io/.

Xiangxin Zhou, Jiaqi Guan, Yijia Zhang et al.

Dual-target therapeutic strategies have become a compelling approach and attracted significant attention due to various benefits, such as their potential in overcoming drug resistance in cancer therapy. Considering the tremendous success that deep generative models have achieved in structure-based drug design in recent years, we formulate dual-target drug design as a generative task and curate a novel dataset of potential target pairs based on synergistic drug combinations. We propose to design dual-target drugs with diffusion models that are trained on single-target protein-ligand complex pairs. Specifically, we align two pockets in 3D space with protein-ligand binding priors and build two complex graphs with shared ligand nodes for SE(3)-equivariant composed message passing, based on which we derive a composed drift in both 3D and categorical probability space in the generative process. Our algorithm can well transfer the knowledge gained in single-target pretraining to dual-target scenarios in a zero-shot manner. We also repurpose linker design methods as strong baselines for this task. Extensive experiments demonstrate the effectiveness of our method compared with various baselines.

Xiangzhe Kong, Zishen Zhang, Ziting Zhang et al.

The design of target-specific molecules such as small molecules, peptides, and antibodies is vital for biological research and drug discovery. Existing generative methods are restricted to single-domain molecules, failing to address versatile therapeutic needs or utilize cross-domain transferability to enhance model performance. In this paper, we introduce Unified generative Modeling of 3D Molecules (UniMoMo), the first framework capable of designing binders of multiple molecular domains using a single model. In particular, UniMoMo unifies the representations of different molecules as graphs of blocks, where each block corresponds to either a standard amino acid or a molecular fragment. Subsequently, UniMoMo utilizes a geometric latent diffusion model for 3D molecular generation, featuring an iterative full-atom autoencoder to compress blocks into latent space points, followed by an E(3)-equivariant diffusion process. Extensive benchmarks across peptides, antibodies, and small molecules demonstrate the superiority of our unified framework over existing domain-specific models, highlighting the benefits of multi-domain training.

Xiangxin Zhou, Mingyu Li, Yi Xiao et al.

Cyclic peptides offer inherent advantages in pharmaceuticals. For example, cyclic peptides are more resistant to enzymatic hydrolysis compared to linear peptides and usually exhibit excellent stability and affinity. Although deep generative models have achieved great success in linear peptide design, several challenges prevent the development of computational methods for designing diverse types of cyclic peptides. These challenges include the scarcity of 3D structural data on target proteins and associated cyclic peptide ligands, the geometric constraints that cyclization imposes, and the involvement of non-canonical amino acids in cyclization. To address the above challenges, we introduce CpSDE, which consists of two key components: AtomSDE, a generative structure prediction model based on harmonic SDE, and ResRouter, a residue type predictor. Utilizing a routed sampling algorithm that alternates between these two models to iteratively update sequences and structures, CpSDE facilitates the generation of cyclic peptides. By employing explicit all-atom and bond modeling, CpSDE overcomes existing data limitations and is proficient in designing a wide variety of cyclic peptides. Our experimental results demonstrate that the cyclic peptides designed by our method exhibit reliable stability and affinity.

Haowei Lin, Xiangyu Wang, Ruilin Yan et al. · pku

With powerful large language models (LLMs) demonstrating superhuman reasoning capabilities, a critical question arises: Do LLMs genuinely reason, or do they merely recall answers from their extensive, web-scraped training datasets? Publicly released benchmarks inevitably become contaminated once incorporated into subsequent LLM training sets, undermining their reliability as faithful assessments. To address this, we introduce KUMO, a generative evaluation framework designed specifically for assessing reasoning in LLMs. KUMO synergistically combines LLMs with symbolic engines to dynamically produce diverse, multi-turn reasoning tasks that are partially observable and adjustable in difficulty. Through an automated pipeline, KUMO continuously generates novel tasks across open-ended domains, compelling models to demonstrate genuine generalization rather than memorization. We evaluated 23 state-of-the-art LLMs on 5,000 tasks across 100 domains created by KUMO, benchmarking their reasoning abilities against university students. Our findings reveal that many LLMs have outperformed university-level performance on easy reasoning tasks, and reasoning-scaled LLMs reach university-level performance on complex reasoning challenges. Moreover, LLM performance on KUMO tasks correlates strongly with results on newly released real-world reasoning benchmarks, underscoring KUMO's value as a robust, enduring assessment tool for genuine LLM reasoning capabilities.

Jiaqi Guan, Jiahan Li, Xiangxin Zhou et al.

Molecular docking is a key task in computational biology that has attracted increasing interest from the machine learning community. While existing methods have achieved success, they generally treat each protein-ligand pair in isolation. Inspired by the biochemical observation that ligands binding to the same target protein tend to adopt similar poses, we propose \textsc{GroupBind}, a novel molecular docking framework that simultaneously considers multiple ligands docking to a protein. This is achieved by introducing an interaction layer for the group of ligands and a triangle attention module for embedding protein-ligand and group-ligand pairs. By integrating our approach with diffusion-based docking model, we set a new S performance on the PDBBind blind docking benchmark, demonstrating the effectiveness of our proposed molecular docking paradigm.

Haowei Lin, Shanda Li, Haotian Ye et al.

Given an unconditional generative model and a predictor for a target property (e.g., a classifier), the goal of training-free guidance is to generate samples with desirable target properties without additional training. As a highly efficient technique for steering generative models toward flexible outcomes, training-free guidance has gained increasing attention in diffusion models. However, existing methods only handle data in continuous spaces, while many scientific applications involve both continuous and discrete data (referred to as multimodality). Another emerging trend is the growing use of the simple and general flow matching framework in building generative foundation models, where guided generation remains under-explored. To address this, we introduce TFG-Flow, a novel training-free guidance method for multimodal generative flow. TFG-Flow addresses the curse-of-dimensionality while maintaining the property of unbiased sampling in guiding discrete variables. We validate TFG-Flow on four molecular design tasks and show that TFG-Flow has great potential in drug design by generating molecules with desired properties.

Jiahan Li, Chaoran Cheng, Jianzhu Ma et al.

Shape assembly, which aims to reassemble separate parts into a complete object, has gained significant interest in recent years. Existing methods primarily rely on networks to predict the poses of individual parts, but often fail to effectively capture the geometric interactions between the parts and their poses. In this paper, we present the Geometric Point Attention Transformer (GPAT), a network specifically designed to address the challenges of reasoning about geometric relationships. In the geometric point attention module, we integrate both global shape information and local pairwise geometric features, along with poses represented as rotation and translation vectors for each part. To enable iterative updates and dynamic reasoning, we introduce a geometric recycling scheme, where each prediction is fed into the next iteration for refinement. We evaluate our model on both the semantic and geometric assembly tasks, showing that it outperforms previous methods in absolute pose estimation, achieving accurate pose predictions and high alignment accuracy.

Jie Ying, Haowei Lin, Chao Yue et al.

In this study, we unveil a new AI model, termed PhyE2E, to discover physical formulas through symbolic regression. PhyE2E simplifies symbolic regression by decomposing it into sub-problems using the second-order derivatives of an oracle neural network, and employs a transformer model to translate data into symbolic formulas in an end-to-end manner. The resulting formulas are refined through Monte-Carlo Tree Search and Genetic Programming. We leverage a large language model to synthesize extensive symbolic expressions resembling real physics, and train the model to recover these formulas directly from data. A comprehensive evaluation reveals that PhyE2E outperforms existing state-of-the-art approaches, delivering superior symbolic accuracy, precision in data fitting, and consistency in physical units. We deployed PhyE2E to five applications in space physics, including the prediction of sunspot numbers, solar rotational angular velocity, emission line contribution functions, near-Earth plasma pressure, and lunar-tide plasma signals. The physical formulas generated by AI demonstrate a high degree of accuracy in fitting the experimental data from satellites and astronomical telescopes. We have successfully upgraded the formula proposed by NASA in 1993 regarding solar activity, and for the first time, provided the explanations for the long cycle of solar activity in an explicit form. We also found that the decay of near-Earth plasma pressure is proportional to r^2 to Earth, where subsequent mathematical derivations are consistent with satellite data from another independent study. Moreover, we found physical formulas that can describe the relationships between emission lines in the extreme ultraviolet spectrum of the Sun, temperatures, electron densities, and magnetic fields. The formula obtained is consistent with the properties that physicists had previously hypothesized it should possess.

Xiangxin Zhou, Yi Xiao, Haowei Lin et al.

The dynamic nature of proteins, influenced by ligand interactions, is essential for comprehending protein function and progressing drug discovery. Traditional structure-based drug design (SBDD) approaches typically target binding sites with rigid structures, limiting their practical application in drug development. While molecular dynamics simulation can theoretically capture all the biologically relevant conformations, the transition rate is dictated by the intrinsic energy barrier between them, making the sampling process computationally expensive. To overcome the aforementioned challenges, we propose to use generative modeling for SBDD considering conformational changes of protein pockets. We curate a dataset of apo and multiple holo states of protein-ligand complexes, simulated by molecular dynamics, and propose a full-atom flow model (and a stochastic version), named DynamicFlow, that learns to transform apo pockets and noisy ligands into holo pockets and corresponding 3D ligand molecules. Our method uncovers promising ligand molecules and corresponding holo conformations of pockets. Additionally, the resultant holo-like states provide superior inputs for traditional SBDD approaches, playing a significant role in practical drug discovery.

Jiawei Xue, Ruichen Tan, Jianzhu Ma et al.

Data mining in transportation networks (DMTNs) refers to using diverse types of spatio-temporal data for various transportation tasks, including pattern analysis, traffic prediction, and traffic controls. Graph neural networks (GNNs) are essential in many DMTN problems due to their capability to represent spatial correlations between entities. Between 2016 and 2024, the notable applications of GNNs in DMTNs have extended to multiple fields such as traffic prediction and operation. However, existing reviews have primarily focused on traffic prediction tasks. To fill this gap, this study provides a timely and insightful summary of GNNs in DMTNs, highlighting new progress in prediction and operation from academic and industry perspectives since 2023. First, we present and analyze various DMTN problems, followed by classical and recent GNN models. Second, we delve into key works in three areas: (1) traffic prediction, (2) traffic operation, and (3) industry involvement, such as Google Maps, Amap, and Baidu Maps. Along these directions, we discuss new research opportunities based on the significance of transportation problems and data availability. Finally, we compile resources such as data, code, and other learning materials to foster interdisciplinary communication. This review, driven by recent trends in GNNs in DMTN studies since 2023, could democratize abundant datasets and efficient GNN methods for various transportation problems including prediction and operation.

Yuchen Hua, Xingang Peng, Jianzhu Ma et al.

Generative modeling of three-dimensional (3D) molecules is a fundamental yet challenging problem in drug discovery and materials science. Existing approaches typically represent molecules as 3D graphs and co-generate discrete atom types with continuous atomic coordinates, leading to intrinsic learning difficulties such as heterogeneous modality entanglement and geometry-chemistry coherence constraints. We propose VecMol, a paradigm-shifting framework that reimagines molecular representation by modeling 3D molecules as continuous vector fields over Euclidean space, where vectors point toward nearby atoms and implicitly encode molecular structure. The vector field is parameterized by a neural field and generated using a latent diffusion model, avoiding explicit graph generation and decoupling structure learning from discrete atom instantiation. Experiments on the QM9 and GEOM-Drugs benchmarks validate the feasibility of this novel approach, suggesting vector-field-based representations as a promising new direction for 3D molecular generation.

Haowei Lin, Haotian Ye, Wenzheng Feng et al.

Discovering scaling laws for predicting model performance at scale is a fundamental and open-ended challenge, mostly reliant on slow, case specific human experimentation. To investigate the potential for LLMs to automate this process, we collect over 5,000 experiments from existing literature and curate seven diverse scaling law discovery tasks. While existing agents struggle to produce accurate law formulas, this paper introduces SLDAgent, an evolution-based agent that co-optimize the scaling law model and the parameters, enabling it to autonomously explore complex relationships between variables. For the first time, we demonstrates that SLDAgent can automatically discover laws that exhibit consistently more accurate extrapolation than their established, human-derived counterparts across all tasks. Through comprehensive analysis, we elucidate why these discovered laws are superior and verify their practical utility in both pretraining and finetuning applications. This work establishes a new paradigm for agentic scientific discovery, showing that AI systems can understand their own scaling behavior, and can contribute novel and practical knowledge back to the research community.

Dapeng Jiang, Xiangzhe Kong, Jiaqi Han et al.

Cyclic peptides, characterized by geometric constraints absent in linear peptides, offer enhanced biochemical properties, presenting new opportunities to address unmet medical needs. However, designing target-specific cyclic peptides remains underexplored due to limited training data. To bridge the gap, we propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation via composable geometric constraints. Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model through geometric conditioning on nodes and edges. During training, the model learns from unit constraints and their random combinations in linear peptides, while at inference, novel constraint combinations required for cyclization are imposed as input. Experiments show that our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38% to 84% on different cyclization strategies.

Jiahan Li, Chaoran Cheng, Zuofan Wu et al.

Peptides, short chains of amino acid residues, play a vital role in numerous biological processes by interacting with other target molecules, offering substantial potential in drug discovery. In this work, we present PepFlow, the first multi-modal deep generative model grounded in the flow-matching framework for the design of full-atom peptides that target specific protein receptors. Drawing inspiration from the crucial roles of residue backbone orientations and side-chain dynamics in protein-peptide interactions, we characterize the peptide structure using rigid backbone frames within the $\mathrm{SE}(3)$ manifold and side-chain angles on high-dimensional tori. Furthermore, we represent discrete residue types in the peptide sequence as categorical distributions on the probability simplex. By learning the joint distributions of each modality using derived flows and vector fields on corresponding manifolds, our method excels in the fine-grained design of full-atom peptides. Harnessing the multi-modal paradigm, our approach adeptly tackles various tasks such as fix-backbone sequence design and side-chain packing through partial sampling. Through meticulously crafted experiments, we demonstrate that PepFlow exhibits superior performance in comprehensive benchmarks, highlighting its significant potential in computational peptide design and analysis.

Xingang Peng, Jiaqi Guan, Qiang Liu et al.

Deep generative models have recently achieved superior performance in 3D molecule generation. Most of them first generate atoms and then add chemical bonds based on the generated atoms in a post-processing manner. However, there might be no corresponding bond solution for the temporally generated atoms as their locations are generated without considering potential bonds. We define this problem as the atom-bond inconsistency problem and claim it is the main reason for current approaches to generating unrealistic 3D molecules. To overcome this problem, we propose a new diffusion model called MolDiff which can generate atoms and bonds simultaneously while still maintaining their consistency by explicitly modeling the dependence between their relationships. We evaluated the generation ability of our proposed model and the quality of the generated molecules using criteria related to both geometry and chemical properties. The empirical studies showed that our model outperforms previous approaches, achieving a three-fold improvement in success rate and generating molecules with significantly better quality.

Xuesong Wang, Zhihang Hu, Tingyang Yu et al.

Muilti-modality data are ubiquitous in biology, especially that we have entered the multi-omics era, when we can measure the same biological object (cell) from different aspects (omics) to provide a more comprehensive insight into the cellular system. When dealing with such multi-omics data, the first step is to determine the correspondence among different modalities. In other words, we should match data from different spaces corresponding to the same object. This problem is particularly challenging in the single-cell multi-omics scenario because such data are very sparse with extremely high dimensions. Secondly, matched single-cell multi-omics data are rare and hard to collect. Furthermore, due to the limitations of the experimental environment, the data are usually highly noisy. To promote the single-cell multi-omics research, we overcome the above challenges, proposing a novel framework to align and integrate single-cell RNA-seq data and single-cell ATAC-seq data. Our approach can efficiently map the above data with high sparsity and noise from different spaces to a low-dimensional manifold in a unified space, making the downstream alignment and integration straightforward. Compared with the other state-of-the-art methods, our method performs better in both simulated and real single-cell data. The proposed method is helpful for the single-cell multi-omics research. The improvement for integration on the simulated data is significant.

Andersen Ang, Jianzhu Ma, Nianjun Liu et al.

We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's method is able to solve the projection problem to high precision with a complexity roughly about O(n), which has a much lower computational cost compared with the existing sorting-based methods proposed in the literature. We provide a theory for partial explanation and justification of the method. We demonstrate that the proposed algorithm can produce a solution of the projection problem with high precision on large scale datasets, and the algorithm is able to significantly outperform the state-of-the-art methods in terms of runtime (about 6-8 times faster than a commercial software with respect to CPU time for input vector with 1 million variables or more). We further illustrate the effectiveness of the proposed algorithm on solving sparse regression in a bioinformatics problem. Empirical results on the GWAS dataset (with 1,500,000 single-nucleotide polymorphisms) show that, when using the proposed method to accelerate the Projected Quasi-Newton (PQN) method, the accelerated PQN algorithm is able to handle huge-scale regression problem and it is more efficient (about 3-6 times faster) than the current state-of-the-art methods.

Susheel Suresh, Vinith Budde, Jennifer Neville et al.

Graph neural networks (GNNs) have achieved tremendous success on multiple graph-based learning tasks by fusing network structure and node features. Modern GNN models are built upon iterative aggregation of neighbor's/proximity features by message passing. Its prediction performance has been shown to be strongly bounded by assortative mixing in the graph, a key property wherein nodes with similar attributes mix/connect with each other. We observe that real world networks exhibit heterogeneous or diverse mixing patterns and the conventional global measurement of assortativity, such as global assortativity coefficient, may not be a representative statistic in quantifying this mixing. We adopt a generalized concept, node-level assortativity, one that is based at the node level to better represent the diverse patterns and accurately quantify the learnability of GNNs. We find that the prediction performance of a wide range of GNN models is highly correlated with the node level assortativity. To break this limit, in this work, we focus on transforming the input graph into a computation graph which contains both proximity and structural information as distinct type of edges. The resulted multi-relational graph has an enhanced level of assortativity and, more importantly, preserves rich information from the original graph. We then propose to run GNNs on this computation graph and show that adaptively choosing between structure and proximity leads to improved performance under diverse mixing. Empirically, we show the benefits of adopting our transformation framework for semi-supervised node classification task on a variety of real world graph learning benchmarks.

Yunyu Liu, Jianzhu Ma, Pan Li

Dynamic systems that consist of a set of interacting elements can be abstracted as temporal networks. Recently, higher-order patterns that involve multiple interacting nodes have been found crucial to indicate domain-specific laws of different temporal networks. This posts us the challenge of designing more sophisticated hypergraph models for these higher-order patterns and the associated new learning algorithms. Here, we propose the first model, named HIT, for full-spectrum higher-order pattern prediction in temporal hypergraphs. Particularly, we focus on predicting three types of common but important interaction patterns involving three interacting elements in temporal networks, which could be extended to even higher-order patterns. HIT extracts the structural representation of a node triplet of interest on the temporal hypergraph and uses it to tell what type of, when, and why the interaction expansion could happen in this triplet. HIT could achieve significant improvement (averaged 20% AUC gain to identify the interaction type, uniformly more accurate time estimation) compared to both heuristic and other neural-network-based baselines on 5 real-world large temporal hypergraphs. Moreover, HIT provides a certain degree of interpretability by identifying the most discriminatory structural features on the temporal hypergraphs for predicting different higher-order patterns.

Jiawei Xue, Nan Jiang, Senwei Liang et al.

Quantifying the topological similarities of different parts of urban road networks (URNs) enables us to understand the urban growth patterns. While conventional statistics provide useful information about characteristics of either a single node's direct neighbors or the entire network, such metrics fail to measure the similarities of subnetworks considering local indirect neighborhood relationships. In this study, we propose a graph-based machine-learning method to quantify the spatial homogeneity of subnetworks. We apply the method to 11,790 urban road networks across 30 cities worldwide to measure the spatial homogeneity of road networks within each city and across different cities. We find that intra-city spatial homogeneity is highly associated with socioeconomic statuses such as GDP and population growth. Moreover, inter-city spatial homogeneity obtained by transferring the model across different cities, reveals the inter-city similarity of urban network structures originating in Europe, passed on to cities in the US and Asia. Socioeconomic development and inter-city similarity revealed using our method can be leveraged to understand and transfer insights across cities. It also enables us to address urban policy challenges including network planning in rapidly urbanizing areas and combating regional inequality.

Sheng Wang, Jian Peng, Jianzhu Ma et al.

Protein secondary structure (SS) prediction is important for studying protein structure and function. When only the sequence (profile) information is used as input feature, currently the best predictors can obtain ~80% Q3 accuracy, which has not been improved in the past decade. Here we present DeepCNF (Deep Convolutional Neural Fields) for protein SS prediction. DeepCNF is a Deep Learning extension of Conditional Neural Fields (CNF), which is an integration of Conditional Random Fields (CRF) and shallow neural networks. DeepCNF can model not only complex sequence-structure relationship by a deep hierarchical architecture, but also interdependency between adjacent SS labels, so it is much more powerful than CNF. Experimental results show that DeepCNF can obtain ~84% Q3 accuracy, ~85% SOV score, and ~72% Q8 accuracy, respectively, on the CASP and CAMEO test proteins, greatly outperforming currently popular predictors. As a general framework, DeepCNF can be used to predict other protein structure properties such as contact number, disorder regions, and solvent accessibility.

Jianzhu Ma

Proteins are the basic building blocks of life. They usually perform functions by folding to a particular structure. Understanding the folding process could help the researchers to understand the functions of proteins and could also help to develop supplemental proteins for people with deficiencies and gain more insight into diseases associated with troublesome folding proteins. Experimental methods are both expensive and time consuming. In this thesis I introduce a new machine learning based method to predict the protein structure. The new method improves the performance from two directions: creating accurate protein alignments and predicting accurate protein contacts. First, I present an alignment framework MRFalign which goes beyond state-of-the-art methods and uses Markov Random Fields to model a protein family and align two proteins by aligning two MRFs together. Compared to other methods, that can only model local-range residue correlation, MRFs can model long-range residue interactions and thus, encodes global information in a protein. Secondly, I present a Group Graphical Lasso method for contact prediction that integrates joint multi-family Evolutionary Coupling analysis and supervised learning to improve accuracy on proteins without many sequence homologs. Different from single-family EC analysis that uses residue co-evolution information in only the target protein family, our joint EC analysis uses residue co-evolution in both the target family and its related families, which may have divergent sequences but similar folds. Our method can also integrate supervised learning methods to further improve accuracy. We evaluate the performance of both methods including each of its components on large public benchmarks. Experiments show that our methods can achieve better accuracy than existing state-of-the-art methods under all the measurements on most of the protein classes.

Jianzhu Ma, Sheng Wang, Zhiyong Wang et al.

Sequence-based protein homology detection has been extensively studied and so far the most sensitive method is based upon comparison of protein sequence profiles, which are derived from multiple sequence alignment (MSA) of sequence homologs in a protein family. A sequence profile is usually represented as a position-specific scoring matrix (PSSM) or an HMM (Hidden Markov Model) and accordingly PSSM-PSSM or HMM-HMM comparison is used for homolog detection. This paper presents a new homology detection method MRFalign, consisting of three key components: 1) a Markov Random Fields (MRF) representation of a protein family; 2) a scoring function measuring similarity of two MRFs; and 3) an efficient ADMM (Alternating Direction Method of Multipliers) algorithm aligning two MRFs. Compared to HMM that can only model very short-range residue correlation, MRFs can model long-range residue interaction pattern and thus, encode information for the global 3D structure of a protein family. Consequently, MRF-MRF comparison for remote homology detection shall be much more sensitive than HMM-HMM or PSSM-PSSM comparison. Experiments confirm that MRFalign outperforms several popular HMM or PSSM-based methods in terms of both alignment accuracy and remote homology detection and that MRFalign works particularly well for mainly beta proteins. For example, tested on the benchmark SCOP40 (8353 proteins) for homology detection, PSSM-PSSM and HMM-HMM succeed on 48% and 52% of proteins, respectively, at superfamily level, and on 15% and 27% of proteins, respectively, at fold level. In contrast, MRFalign succeeds on 57.3% and 42.5% of proteins at superfamily and fold level, respectively. This study implies that long-range residue interaction patterns are very helpful for sequence-based homology detection. The software is available for download at http://raptorx.uchicago.edu/download/.

Jianzhu Ma, Sheng Wang, Zhiyong Wang et al.

Protein contacts contain important information for protein structure and functional study, but contact prediction from sequence remains very challenging. Both evolutionary coupling (EC) analysis and supervised machine learning methods are developed to predict contacts, making use of different types of information, respectively. This paper presents a group graphical lasso (GGL) method for contact prediction that integrates joint multi-family EC analysis and supervised learning. Different from existing single-family EC analysis that uses residue co-evolution information in only the target protein family, our joint EC analysis uses residue co-evolution in both the target family and its related families, which may have divergent sequences but similar folds. To implement joint EC analysis, we model a set of related protein families using Gaussian graphical models (GGM) and then co-estimate their precision matrices by maximum-likelihood, subject to the constraint that the precision matrices shall share similar residue co-evolution patterns. To further improve the accuracy of the estimated precision matrices, we employ a supervised learning method to predict contact probability from a variety of evolutionary and non-evolutionary information and then incorporate the predicted probability as prior into our GGL framework. Experiments show that our method can predict contacts much more accurately than existing methods, and that our method performs better on both conserved and family-specific contacts.