Causal discovery is a crucial initial step in establishing causality from empirical data and background knowledge. Numerous algorithms have been developed for this purpose. Among them, the score-matching method has demonstrated superior performance across various evaluation metrics, particularly for the commonly encountered Additive Nonlinear Causal Models. However, current score-matching-based algorithms are primarily designed to analyze independent and identically distributed (i.i.d.) data. More importantly, they suffer from high computational complexity due to the pruning step required for handling dense Directed Acyclic Graphs (DAGs). To enhance the scalability of score matching, we have developed a new parent-finding subroutine for leaf nodes in DAGs, significantly accelerating the most time-consuming part of the process: the pruning step. This improvement results in an efficiency-lifted score matching algorithm, termed Parent Identification-based Causal structure learning for both i.i.d. and temporal data on networKs, or PICK. The new score-matching algorithm extends the scope of existing algorithms and can handle static and temporal data on networks with weak network interference. Our proposed algorithm can efficiently cope with increasingly complex datasets that exhibit spatial and temporal dependencies, commonly encountered in academia and industry. The proposed algorithm can accelerate score-matching-based methods while maintaining high accuracy in real-world applications.

The parallels between protein sequences and natural language in their sequential structures have inspired the application of large language models (LLMs) to protein understanding. Despite the success of LLMs in NLP, their effectiveness in comprehending protein sequences remains an open question, largely due to the absence of datasets linking protein sequences to descriptive text. Researchers have then attempted to adapt LLMs for protein understanding by integrating a protein sequence encoder with a pre-trained LLM. However, this adaptation raises a fundamental question: "Can LLMs, originally designed for NLP, effectively comprehend protein sequences as a form of language?" Current datasets fall short in addressing this question due to the lack of a direct correlation between protein sequences and corresponding text descriptions, limiting the ability to train and evaluate LLMs for protein understanding effectively. To bridge this gap, we introduce ProteinLMDataset, a dataset specifically designed for further self-supervised pretraining and supervised fine-tuning (SFT) of LLMs to enhance their capability for protein sequence comprehension. Specifically, ProteinLMDataset includes 17.46 billion tokens for pretraining and 893,000 instructions for SFT. Additionally, we present ProteinLMBench, the first benchmark dataset consisting of 944 manually verified multiple-choice questions for assessing the protein understanding capabilities of LLMs. ProteinLMBench incorporates protein-related details and sequences in multiple languages, establishing a new standard for evaluating LLMs' abilities in protein comprehension. The large language model InternLM2-7B, pretrained and fine-tuned on the ProteinLMDataset, outperforms GPT-4 on ProteinLMBench, achieving the highest accuracy score.

Antibodies, crucial for immune defense, primarily rely on complementarity-determining regions (CDRs) to bind and neutralize antigens, such as viruses. The design of these CDRs determines the antibody's affinity and specificity towards its target. Generative models, particularly denoising diffusion probabilistic models (DDPMs), have shown potential to advance the structure-based design of CDR regions. However, only a limited dataset of bound antibody-antigen structures is available, and generalization to out-of-distribution interfaces remains a challenge. Physics based force-fields, which approximate atomic interactions, offer a coarse but universal source of information to better mold designs to target interfaces. Integrating this foundational information into diffusion models is, therefore, highly desirable. Here, we propose a novel approach to enhance the sampling process of diffusion models by integrating force field energy-based feedback. Our model, DiffForce, employs forces to guide the diffusion sampling process, effectively blending the two distributions. Through extensive experiments, we demonstrate that our method guides the model to sample CDRs with lower energy, enhancing both the structure and sequence of the generated antibodies.

Spectral Graph Neural Networks (GNNs), alternatively known as graph filters, have gained increasing prevalence for heterophily graphs. Optimal graph filters rely on Laplacian eigendecomposition for Fourier transform. In an attempt to avert prohibitive computations, numerous polynomial filters have been proposed. However, polynomials in the majority of these filters are predefined and remain fixed across different graphs, failing to accommodate the varying degrees of heterophily. Addressing this gap, we demystify the intrinsic correlation between the spectral property of desired polynomial bases and the heterophily degrees via thorough theoretical analyses. Subsequently, we develop a novel adaptive heterophily basis wherein the basis vectors mutually form angles reflecting the heterophily degree of the graph. We integrate this heterophily basis with the homophily basis to construct a universal polynomial basis UniBasis, which devises a polynomial filter based graph neural network - UniFilter. It optimizes the convolution and propagation in GNN, thus effectively limiting over-smoothing and alleviating over-squashing. Our extensive experiments, conducted on a diverse range of real-world and synthetic datasets with varying degrees of heterophily, support the superiority of UniFilter. These results not only demonstrate the universality of UniBasis but also highlight its proficiency in graph explanation.

Graph neural networks (GNNs) are a powerful solution for various structure learning applications due to their strong representation capabilities for graph data. However, traditional GNNs, relying on message-passing mechanisms that gather information exclusively from first-order neighbours (known as positive samples), can lead to issues such as over-smoothing and over-squashing. To mitigate these issues, we propose a layer-diverse negative sampling method for message-passing propagation. This method employs a sampling matrix within a determinantal point process, which transforms the candidate set into a space and selectively samples from this space to generate negative samples. To further enhance the diversity of the negative samples during each forward pass, we develop a space-squeezing method to achieve layer-wise diversity in multi-layer GNNs. Experiments on various real-world graph datasets demonstrate the effectiveness of our approach in improving the diversity of negative samples and overall learning performance. Moreover, adding negative samples dynamically changes the graph's topology, thus with the strong potential to improve the expressiveness of GNNs and reduce the risk of over-squashing.

Graph convolutions have been a pivotal element in learning graph representations. However, recursively aggregating neighboring information with graph convolutions leads to indistinguishable node features in deep layers, which is known as the over-smoothing issue. The performance of graph neural networks decays fast as the number of stacked layers increases, and the Dirichlet energy associated with the graph decreases to zero as well. In this work, we introduce a framelet system into the analysis of Dirichlet energy and take a multi-scale perspective to leverage the Dirichlet energy and alleviate the over-smoothing issue. Specifically, we develop a Framelet Augmentation strategy by adjusting the update rules with positive and negative increments for low-pass and high-passes respectively. Based on that, we design the Energy Enhanced Convolution (EEConv), which is an effective and practical operation that is proved to strictly enhance Dirichlet energy. From a message-passing perspective, EEConv inherits multi-hop aggregation property from the framelet transform and takes into account all hops in the multi-scale representation, which benefits the node classification tasks over heterophilous graphs. Experiments show that deep GNNs with EEConv achieve state-of-the-art performance over various node classification datasets, especially for heterophilous graphs, while also lifting the Dirichlet energy as the network goes deeper.

Inverse protein folding is challenging due to its inherent one-to-many mapping characteristic, where numerous possible amino acid sequences can fold into a single, identical protein backbone. This task involves not only identifying viable sequences but also representing the sheer diversity of potential solutions. However, existing discriminative models, such as transformer-based auto-regressive models, struggle to encapsulate the diverse range of plausible solutions. In contrast, diffusion probabilistic models, as an emerging genre of generative approaches, offer the potential to generate a diverse set of sequence candidates for determined protein backbones. We propose a novel graph denoising diffusion model for inverse protein folding, where a given protein backbone guides the diffusion process on the corresponding amino acid residue types. The model infers the joint distribution of amino acids conditioned on the nodes' physiochemical properties and local environment. Moreover, we utilize amino acid replacement matrices for the diffusion forward process, encoding the biologically meaningful prior knowledge of amino acids from their spatial and sequential neighbors as well as themselves, which reduces the sampling space of the generative process. Our model achieves state-of-the-art performance over a set of popular baseline methods in sequence recovery and exhibits great potential in generating diverse protein sequences for a determined protein backbone structure.

The performance of graph representation learning is affected by the quality of graph input. While existing research usually pursues a globally smoothed graph embedding, we believe the rarely observed anomalies are as well harmful to an accurate prediction. This work establishes a graph learning scheme that automatically detects (locally) corrupted feature attributes and recovers robust embedding for prediction tasks. The detection operation leverages a graph autoencoder, which does not make any assumptions about the distribution of the local corruptions. It pinpoints the positions of the anomalous node attributes in an unbiased mask matrix, where robust estimations are recovered with sparsity promoting regularizer. The optimizer approaches a new embedding that is sparse in the framelet domain and conditionally close to input observations. Extensive experiments are provided to validate our proposed model can recover a robust graph representation from black-box poisoning and achieve excellent performance.

Directed evolution plays an indispensable role in protein engineering that revises existing protein sequences to attain new or enhanced functions. Accurately predicting the effects of protein variants necessitates an in-depth understanding of protein structure and function. Although large self-supervised language models have demonstrated remarkable performance in zero-shot inference using only protein sequences, these models inherently do not interpret the spatial characteristics of protein structures, which are crucial for comprehending protein folding stability and internal molecular interactions. This paper introduces a novel pre-training framework that cascades sequential and geometric analyzers for protein primary and tertiary structures. It guides mutational directions toward desired traits by simulating natural selection on wild-type proteins and evaluates the effects of variants based on their fitness to perform the function. We assess the proposed approach using a public database and two new databases for a variety of variant effect prediction tasks, which encompass a diverse set of proteins and assays from different taxa. The prediction results achieve state-of-the-art performance over other zero-shot learning methods for both single-site mutations and deep mutations.

Neural message passing is a basic feature extraction unit for graph-structured data considering neighboring node features in network propagation from one layer to the next. We model such process by an interacting particle system with attractive and repulsive forces and the Allen-Cahn force arising in the modeling of phase transition. The dynamics of the system is a reaction-diffusion process which can separate particles without blowing up. This induces an Allen-Cahn message passing (ACMP) for graph neural networks where the numerical iteration for the particle system solution constitutes the message passing propagation. ACMP which has a simple implementation with a neural ODE solver can propel the network depth up to one hundred of layers with theoretically proven strictly positive lower bound of the Dirichlet energy. It thus provides a deep model of GNNs circumventing the common GNN problem of oversmoothing. GNNs with ACMP achieve state of the art performance for real-world node classification tasks on both homophilic and heterophilic datasets.