Crystal Structure Prediction (CSP), which aims to generate stable crystal structures from compositions, represents a critical pathway for discovering novel materials. While structure prediction tasks in other domains, such as proteins, have seen remarkable progress, CSP remains a relatively underexplored area due to the more complex geometries inherent in crystal structures. In this paper, we propose Siamese foundation models specifically designed to address CSP. Our pretrain-finetune framework, named DAO, comprises two complementary foundation models: DAO-G for structure generation and DAO-P for energy prediction. Experiments on CSP benchmarks (MP-20 and MPTS-52) demonstrate that our DAO-G significantly surpasses state-of-the-art (SOTA) methods across all metrics. Extensive ablation studies further confirm that DAO-G excels in generating diverse polymorphic structures, and the dataset relaxation and energy guidance provided by DAO-P are essential for enhancing DAO-G's performance. When applied to three real-world superconductors ($\text{CsV}_3\text{Sb}_5$, $ \text{Zr}_{16}\text{Rh}_8\text{O}_4$ and $\text{Zr}_{16}\text{Pd}_8\text{O}_4$) that are known to be challenging to analyze, our foundation models achieve accurate critical temperature predictions and structure generations. For instance, on $\text{CsV}_3\text{Sb}_5$, DAO-G generates a structure close to the experimental one with an RMSE of 0.0085; DAO-P predicts the $T_c$ value with high accuracy (2.26 K vs. the ground-truth value of 2.30 K). In contrast, conventional DFT calculators like Quantum Espresso only successfully derive the structure of the first superconductor within an acceptable time, while the RMSE is nearly 8 times larger, and the computation speed is more than 1000 times slower. These compelling results collectively highlight the potential of our approach for advancing materials science research and development.

Graph Transformers (GTs) have demonstrated a strong capability in modeling graph structures by addressing the intrinsic limitations of graph neural networks (GNNs), such as over-smoothing and over-squashing. Recent studies have proposed diverse architectures, enhanced explainability, and practical applications for Graph Transformers. In light of these rapid developments, we conduct a comprehensive review of Graph Transformers, covering aspects such as their architectures, theoretical foundations, and applications within this survey. We categorize the architecture of Graph Transformers according to their strategies for processing structural information, including graph tokenization, positional encoding, structure-aware attention and model ensemble. Furthermore, from the theoretical perspective, we examine the expressivity of Graph Transformers in various discussed architectures and contrast them with other advanced graph learning algorithms to discover the connections. Furthermore, we provide a summary of the practical applications where Graph Transformers have been utilized, such as molecule, protein, language, vision, traffic, brain and material data. At the end of this survey, we will discuss the current challenges and prospective directions in Graph Transformers for potential future research.

Targeted protein degradation (TPD) induced by small molecules has emerged as a rapidly evolving modality in drug discovery, targeting proteins traditionally considered "undruggable". Proteolysis-targeting chimeras (PROTACs) and molecular glue degraders (MGDs) are the primary small molecules that induce TPD. Both types of molecules form a ternary complex linking an E3 ligase with a target protein, a crucial step for drug discovery. While significant advances have been made in binary structure prediction for proteins and small molecules, ternary structure prediction remains challenging due to obscure interaction mechanisms and insufficient training data. Traditional methods relying on manually assigned rules perform poorly and are computationally demanding due to extensive random sampling. In this work, we introduce DeepTernary, a novel deep learning-based approach that directly predicts ternary structures in an end-to-end manner using an encoder-decoder architecture. DeepTernary leverages an SE(3)-equivariant graph neural network (GNN) with both intra-graph and ternary inter-graph attention mechanisms to capture intricate ternary interactions from our collected high-quality training dataset, TernaryDB. The proposed query-based Pocket Points Decoder extracts the 3D structure of the final binding ternary complex from learned ternary embeddings, demonstrating state-of-the-art accuracy and speed in existing PROTAC benchmarks without prior knowledge from known PROTACs. It also achieves notable accuracy on the more challenging MGD benchmark under the blind docking protocol. Remarkably, our experiments reveal that the buried surface area calculated from predicted structures correlates with experimentally obtained degradation potency-related metrics. Consequently, DeepTernary shows potential in effectively assisting and accelerating the development of TPDs for previously undruggable targets.

Wenhui T an, Boyuan Li, Chuhao Jin, Wenbing Huang, Xiting Wang & Ruihua Song Gaoling School of Artificial Intelligence Renmin University of China Beijing, China {tanwenhui404,liboyuan,jinchuhao,hwenbing,xitingwang,rsong } @ruc.edu.cn Figure 1: Given a human action as input, our Think-Then-React model first thinks by generating an action description and reasons out a reaction prompt. It then reacts to the action based on the results of this thinking process. TTR reacts in a real-time manner at every timestep and periodically re-thinks at specific interval (every two timesteps in the illustration) to mitigate accumulated errors. Modeling human-like action-to-reaction generation has significant real-world applications, like human-robot interaction and games. Despite recent advancements in single-person motion generation, it is still challenging to well handle action-to-reaction generation, due to the difficulty of directly predicting reaction from action sequence without prompts, and the absence of a unified representation that effectively encodes multi-person motion. To address these challenges, we introduce Think-Then-React (TTR), a large language-model-based framework designed to generate human-like reactions. First, with our fine-grained multimodal training strategy, TTR is capable to unify two processes during inference: a thinking process that explicitly infers action intentions and reasons corresponding reaction description, which serve as semantic prompts, and a reacting process that predicts reactions based on input action and the inferred semantic prompts. Second, to effectively represent multi-person motion in language models, we propose a unified motion tokenizer by decoupling egocentric pose and absolute space features, which effectively represents action and reaction motion with same encoding. Extensive experiments demonstrate that TTR outperforms existing baselines, achieving significant improvements in evaluation metrics, such as reducing FID from 3.988 to 1.942. Predicting human reaction to human action in real world scenario is an online and unconstrained task, i.e., future states and text prompts are inaccessible, and it has board applications in virtual reality, human-robot interaction and gaming. Furthermore, Large Language Models (LLMs) have been applied to human motion generation, demonstrating superior performance (Jiang et al., 2023; Zhang et al., 2024).

Accurately predicting 3D structures and dynamics of physical systems is crucial in scientific applications. Existing approaches that rely on geometric Graph Neural Networks (GNNs) effectively enforce $\mathrm{E}(3)$-equivariance, but they often fall in leveraging extensive broader information. While direct application of Large Language Models (LLMs) can incorporate external knowledge, they lack the capability for spatial reasoning with guaranteed equivariance. In this paper, we propose EquiLLM, a novel framework for representing 3D physical systems that seamlessly integrates E(3)-equivariance with LLM capabilities. Specifically, EquiLLM comprises four key components: geometry-aware prompting, an equivariant encoder, an LLM, and an equivariant adaptor. Essentially, the LLM guided by the instructive prompt serves as a sophisticated invariant feature processor, while 3D directional information is exclusively handled by the equivariant encoder and adaptor modules. Experimental results demonstrate that EquiLLM delivers significant improvements over previous methods across molecular dynamics simulation, human motion simulation, and antibody design, highlighting its promising generalizability.

Equivariant Graph Neural Networks (GNNs) that incorporate E(3) symmetry have achieved significant success in various scientific applications. As one of the most successful models, EGNN leverages a simple scalarization technique to perform equivariant message passing over only Cartesian vectors (i.e., 1st-degree steerable vectors), enjoying greater efficiency and efficacy compared to equivariant GNNs using higher-degree steerable vectors. This success suggests that higher-degree representations might be unnecessary. In this paper, we disprove this hypothesis by exploring the expressivity of equivariant GNNs on symmetric structures, including $k$-fold rotations and regular polyhedra. We theoretically demonstrate that equivariant GNNs will always degenerate to a zero function if the degree of the output representations is fixed to 1 or other specific values. Based on this theoretical insight, we propose HEGNN, a high-degree version of EGNN to increase the expressivity by incorporating high-degree steerable vectors while maintaining EGNN's efficiency through the scalarization trick. Our extensive experiments demonstrate that HEGNN not only aligns with our theoretical analyses on toy datasets consisting of symmetric structures, but also shows substantial improvements on more complicated datasets such as $N$-body and MD17. Our theoretical findings and empirical results potentially open up new possibilities for the research of equivariant GNNs.

Learning policies for multi-entity systems in 3D environments is far more complicated against single-entity scenarios, due to the exponential expansion of the global state space as the number of entities increases. One potential solution of alleviating the exponential complexity is dividing the global space into independent local views that are invariant to transformations including translations and rotations. To this end, this paper proposes Subequivariant Hierarchical Neural Networks (SHNN) to facilitate multi-entity policy learning. In particular, SHNN first dynamically decouples the global space into local entity-level graphs via task assignment. Second, it leverages subequivariant message passing over the local entity-level graphs to devise local reference frames, remarkably compressing the representation redundancy, particularly in gravity-affected environments. Furthermore, to overcome the limitations of existing benchmarks in capturing the subtleties of multi-entity systems under the Euclidean symmetry, we propose the Multi-entity Benchmark (MEBEN), a new suite of environments tailored for exploring a wide range of multi-entity reinforcement learning. Extensive experiments demonstrate significant advancements of SHNN on the proposed benchmarks compared to existing methods. Comprehensive ablations are conducted to verify the indispensability of task assignment and subequivariance.

The core challenge of de novo protein design lies in creating proteins with specific functions or properties, guided by certain conditions. Current models explore to generate protein using structural and evolutionary guidance, which only provide indirect conditions concerning functions and properties. However, textual annotations of proteins, especially the annotations for protein domains, which directly describe the protein's high-level functionalities, properties, and their correlation with target amino acid sequences, remain unexplored in the context of protein design tasks. In this paper, we propose Protein-Annotation Alignment Generation (PAAG), a multimodality protein design framework that integrates the textual annotations extracted from protein database for controllable generation in sequence space. Specifically, within a multi-level alignment module, PAAG can explicitly generate proteins containing specific domains conditioned on the corresponding domain annotations, and can even design novel proteins with flexible combinations of different kinds of annotations. Our experimental results underscore the superiority of the aligned protein representations from PAAG over 7 prediction tasks. Furthermore, PAAG demonstrates a nearly sixfold increase in generation success rate (24.7% vs 4.7% in zinc finger, and 54.3% vs 8.7% in the immunoglobulin domain) in comparison to the existing model. We anticipate that PAAG will broaden the horizons of protein design by leveraging the knowledge from between textual annotation and proteins.

Learning to represent and simulate the dynamics of physical systems is a crucial yet challenging task. Existing equivariant Graph Neural Network (GNN) based methods have encapsulated the symmetry of physics, \emph{e.g.}, translations, rotations, etc, leading to better generalization ability. Nevertheless, their frame-to-frame formulation of the task overlooks the non-Markov property mainly incurred by unobserved dynamics in the environment. In this paper, we reformulate dynamics simulation as a spatio-temporal prediction task, by employing the trajectory in the past period to recover the Non-Markovian interactions. We propose Equivariant Spatio-Temporal Attentive Graph Networks (ESTAG), an equivariant version of spatio-temporal GNNs, to fulfill our purpose. At its core, we design a novel Equivariant Discrete Fourier Transform (EDFT) to extract periodic patterns from the history frames, and then construct an Equivariant Spatial Module (ESM) to accomplish spatial message passing, and an Equivariant Temporal Module (ETM) with the forward attention and equivariant pooling mechanisms to aggregate temporal message. We evaluate our model on three real datasets corresponding to the molecular-, protein- and macro-level. Experimental results verify the effectiveness of ESTAG compared to typical spatio-temporal GNNs and equivariant GNNs.

Understanding and leveraging the 3D structures of proteins is central to a variety of biological and drug discovery tasks. While deep learning has been applied successfully for structure-based protein function prediction tasks, current methods usually employ distinct training for each task. However, each of the tasks is of small size, and such a single-task strategy hinders the models' performance and generalization ability. As some labeled 3D protein datasets are biologically related, combining multi-source datasets for larger-scale multi-task learning is one way to overcome this problem. In this paper, we propose a neural network model to address multiple tasks jointly upon the input of 3D protein structures. In particular, we first construct a standard structure-based multi-task benchmark called Protein-MT, consisting of 6 biologically relevant tasks, including affinity prediction and property prediction, integrated from 4 public datasets. Then, we develop a novel graph neural network for multi-task learning, dubbed Heterogeneous Multichannel Equivariant Network (HeMeNet), which is E(3) equivariant and able to capture heterogeneous relationships between different atoms. Besides, HeMeNet can achieve task-specific learning via the task-aware readout mechanism. Extensive evaluations on our benchmark verify the effectiveness of multi-task learning, and our model generally surpasses state-of-the-art models.