SPHINX: Structural Prediction using Hypergraph Inference Network

The importance of higher-order relations is widely recognized in a large number of real-world systems. However, annotating them is a tedious and sometimes impossible task. Consequently, current approaches for data modelling either ignore the higher-order interactions altogether or simplify them into pairwise connections. In order to facilitate higher-order processing, even when a hypergraph structure is not available, we introduce Structural Prediction using Hypergraph Inference Network (SPHINX), a model that learns to infer a latent hypergraph structure in an unsupervised way, solely from the final node-level signal. The model consists of a soft, differentiable clustering method used to sequentially predict, for each hyperedge, the probability distribution over the nodes and a sampling algorithm that converts them into an explicit hypergraph structure. We show that the recent advancement in k-subset sampling represents a suitable tool for producing discrete hypergraph structures, addressing some of the training instabilities exhibited by prior works. The resulting model can generate the higher-order structure necessary for any modern hypergraph neural network, facilitating the capture of higher-order interaction in domains where annotating them is difficult. Through extensive ablation studies and experiments conducted on two challenging datasets for trajectory prediction, we demonstrate that our model is capable of inferring suitable latent hypergraphs, that are interpretable and enhance the final performance.

Heterogeneous Sheaf Neural Networks

Heterogeneous graphs, with nodes and edges of different types, are commonly used to model relational structures in many real-world applications. Standard Graph Neural Networks (GNNs) struggle to process heterogeneous data due to oversmoothing. Instead, current approaches have focused on accounting for the heterogeneity in the model architecture, leading to increasingly complex models. Inspired by recent work, we propose using cellular sheaves to model the heterogeneity in the graph's underlying topology. Instead of modelling the data as a graph, we represent it as cellular sheaves, which allows us to encode the different data types directly in the data structure, eliminating the need to inject them into the architecture. We introduce HetSheaf, a general framework for heterogeneous sheaf neural networks, and a series of heterogeneous sheaf predictors to better encode the data's heterogeneity into the sheaf structure. Finally, we empirically evaluate HetSheaf on several standard heterogeneous graph benchmarks, achieving competitive results whilst being more parameter-efficient.

Neural Algorithmic Reasoning with Multiple Correct Solutions

Neural Algorithmic Reasoning (NAR) aims to optimize classical algorithms. However, canonical implementations of NAR train neural networks to return only a single solution, even when there are multiple correct solutions to a problem, such as single-source shortest paths. For some applications, it is desirable to recover more than one correct solution. To that end, we give the first method for NAR with multiple solutions. We demonstrate our method on two classical algorithms: Bellman-Ford (BF) and Depth-First Search (DFS), favouring deeper insight into two algorithms over a broader survey of algorithms. This method involves generating appropriate training data as well as sampling and validating solutions from model output. Each step of our method, which can serve as a framework for neural algorithmic reasoning beyond the tasks presented in this paper, might be of independent interest to the field and our results represent the first attempt at this task in the NAR literature.

Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations

We address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODE) are effective in learning node representations, they fail to quantify uncertainty. To address this, we introduce Latent Graph Neural Stochastic Differential Equations (LGNSDE), which enhance GNODE by embedding randomness through Brownian motion to quantify uncertainty. We provide theoretical guarantees for LGNSDE and empirically show better performance in uncertainty quantification.

A Survey for Large Language Models in Biomedicine

Recent breakthroughs in large language models (LLMs) offer unprecedented natural language understanding and generation capabilities. However, existing surveys on LLMs in biomedicine often focus on specific applications or model architectures, lacking a comprehensive analysis that integrates the latest advancements across various biomedical domains. This review, based on an analysis of 484 publications sourced from databases including PubMed, Web of Science, and arXiv, provides an in-depth examination of the current landscape, applications, challenges, and prospects of LLMs in biomedicine, distinguishing itself by focusing on the practical implications of these models in real-world biomedical contexts. Firstly, we explore the capabilities of LLMs in zero-shot learning across a broad spectrum of biomedical tasks, including diagnostic assistance, drug discovery, and personalized medicine, among others, with insights drawn from 137 key studies. Then, we discuss adaptation strategies of LLMs, including fine-tuning methods for both uni-modal and multi-modal LLMs to enhance their performance in specialized biomedical contexts where zero-shot fails to achieve, such as medical question answering and efficient processing of biomedical literature. Finally, we discuss the challenges that LLMs face in the biomedicine domain including data privacy concerns, limited model interpretability, issues with dataset quality, and ethics due to the sensitive nature of biomedical data, the need for highly reliable model outputs, and the ethical implications of deploying AI in healthcare. To address these challenges, we also identify future research directions of LLM in biomedicine including federated learning methods to preserve data privacy and integrating explainable AI methodologies to enhance the transparency of LLMs.

TourSynbio: A Multi-Modal Large Model and Agent Framework to Bridge Text and Protein Sequences for Protein Engineering

The structural similarities between protein sequences and natural languages have led to parallel advancements in deep learning across both domains. While large language models (LLMs) have achieved much progress in the domain of natural language processing, their potential in protein engineering remains largely unexplored. Previous approaches have equipped LLMs with protein understanding capabilities by incorporating external protein encoders, but this fails to fully leverage the inherent similarities between protein sequences and natural languages, resulting in sub-optimal performance and increased model complexity. To address this gap, we present TourSynbio-7B, the first multi-modal large model specifically designed for protein engineering tasks without external protein encoders. TourSynbio-7B demonstrates that LLMs can inherently learn to understand proteins as language. The model is post-trained and instruction fine-tuned on InternLM2-7B using ProteinLMDataset, a dataset comprising 17.46 billion tokens of text and protein sequence for self-supervised pretraining and 893K instructions for supervised fine-tuning. TourSynbio-7B outperforms GPT-4 on the ProteinLMBench, a benchmark of 944 manually verified multiple-choice questions, with 62.18% accuracy. Leveraging TourSynbio-7B's enhanced protein sequence understanding capability, we introduce TourSynbio-Agent, an innovative framework capable of performing various protein engineering tasks, including mutation analysis, inverse folding, protein folding, and visualization. TourSynbio-Agent integrates previously disconnected deep learning models in the protein engineering domain, offering a unified conversational user interface for improved usability. Finally, we demonstrate the efficacy of TourSynbio-7B and TourSynbio-Agent through two wet lab case studies on vanilla key enzyme modification and steroid compound catalysis.

Joint Diffusion Processes as an Inductive Bias in Sheaf Neural Networks

Sheaf Neural Networks (SNNs) naturally extend Graph Neural Networks (GNNs) by endowing a cellular sheaf over the graph, equipping nodes and edges with vector spaces and defining linear mappings between them. While the attached geometric structure has proven to be useful in analyzing heterophily and oversmoothing, so far the methods by which the sheaf is computed do not always guarantee a good performance in such settings. In this work, drawing inspiration from opinion dynamics concepts, we propose two novel sheaf learning approaches that (i) provide a more intuitive understanding of the involved structure maps, (ii) introduce a useful inductive bias for heterophily and oversmoothing, and (iii) infer the sheaf in a way that does not scale with the number of features, thus using fewer learnable parameters than existing methods. In our evaluation, we show the limitations of the real-world benchmarks used so far on SNNs, and design a new synthetic task -- leveraging the symmetries of n-dimensional ellipsoids -- that enables us to better assess the strengths and weaknesses of sheaf-based models. Our extensive experimentation on these novel datasets reveals valuable insights into the scenarios and contexts where SNNs in general -- and our proposed approaches in particular -- can be beneficial.

xAI-Drop: Don't Use What You Cannot Explain

Graph Neural Networks (GNNs) have emerged as the predominant paradigm for learning from graph-structured data, offering a wide range of applications from social network analysis to bioinformatics. Despite their versatility, GNNs face challenges such as oversmoothing, lack of generalization and poor interpretability, which hinder their wider adoption and reliability in critical applications. Dropping has emerged as an effective paradigm for reducing noise during training and improving robustness of GNNs. However, existing approaches often rely on random or heuristic-based selection criteria, lacking a principled method to identify and exclude nodes that contribute to noise and over-complexity in the model. In this work, we argue that explainability should be a key indicator of a model's robustness throughout its training phase. To this end, we introduce xAI-Drop, a novel topological-level dropping regularizer that leverages explainability to pinpoint noisy network elements to be excluded from the GNN propagation mechanism. An empirical evaluation on diverse real-world datasets demonstrates that our method outperforms current state-of-the-art dropping approaches in accuracy, effectively reduces over-smoothing, and improves explanation quality.

Metric Learning for Clifford Group Equivariant Neural Networks

Clifford Group Equivariant Neural Networks (CGENNs) leverage Clifford algebras and multivectors as an alternative approach to incorporating group equivariance to ensure symmetry constraints in neural representations. In principle, this formulation generalizes to orthogonal groups and preserves equivariance regardless of the metric signature. However, previous works have restricted internal network representations to Euclidean or Minkowski (pseudo-)metrics, handpicked depending on the problem at hand. In this work, we propose an alternative method that enables the metric to be learned in a data-driven fashion, allowing the CGENN network to learn more flexible representations. Specifically, we populate metric matrices fully, ensuring they are symmetric by construction, and leverage eigenvalue decomposition to integrate this additional learnable component into the original CGENN formulation in a principled manner. Additionally, we motivate our method using insights from category theory, which enables us to explain Clifford algebras as a categorical construction and guarantee the mathematical soundness of our approach. We validate our method in various tasks and showcase the advantages of learning more flexible latent metric representations. The code and data are available at https://github.com/rick-ali/Metric-Learning-for-CGENNs

G-Adaptive mesh refinement -- leveraging graph neural networks and differentiable finite element solvers

We present a novel, and effective, approach to the long-standing problem of mesh adaptivity in finite element methods (FEM). FE solvers are powerful tools for solving partial differential equations (PDEs), but their cost and accuracy are critically dependent on the choice of mesh points. To keep computational costs low, mesh relocation (r-adaptivity) seeks to optimise the position of a fixed number of mesh points to obtain the best FE solution accuracy. Classical approaches to this problem require the solution of a separate nonlinear "meshing" PDE to find the mesh point locations. This incurs significant cost at remeshing and relies on certain a-priori assumptions and guiding heuristics for optimal mesh point location. Recent machine learning approaches to r-adaptivity have mainly focused on the construction of fast surrogates for such classical methods. Our new approach combines a graph neural network (GNN) powered architecture, with training based on direct minimisation of the FE solution error with respect to the mesh point locations. The GNN employs graph neural diffusion (GRAND), closely aligning the mesh solution space to that of classical meshing methodologies, thus replacing heuristics with a learnable strategy, and providing a strong inductive bias. This allows for rapid and robust training and results in an extremely efficient and effective GNN approach to online r-adaptivity. This method outperforms classical and prior ML approaches to r-adaptive meshing on the test problems we consider, in particular achieving lower FE solution error, whilst retaining the significant speed-up over classical methods observed in prior ML work.