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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., Comment: 16 pages, 1 figure

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.

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.

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., Comment: 9 pages including appendix

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.

Sequential recommendation is a task to capture hidden user preferences from historical user item interaction data and recommend next items for the user. Significant progress has been made in this domain by leveraging classification based learning methods. Inspired by the recent paradigm of 'pretrain, prompt and predict' in NLP, we consider sequential recommendation as a sequence to sequence generation task and propose a novel model named Generative Recommendation (GenRec). Unlike classification based models that learn explicit user and item representations, GenRec utilizes the sequence modeling capability of Transformer and adopts the masked item prediction objective to effectively learn the hidden bidirectional sequential patterns. Different from existing generative sequential recommendation models, GenRec does not rely on manually designed hard prompts. The input to GenRec is textual user item sequence and the output is top ranked next items. Moreover, GenRec is lightweight and requires only a few hours to train effectively in low-resource settings, making it highly applicable to real-world scenarios and helping to democratize large language models in the sequential recommendation domain. Our extensive experiments have demonstrated that GenRec generalizes on various public real-world datasets and achieves state-of-the-art results. Our experiments also validate the effectiveness of the the proposed masked item prediction objective that improves the model performance by a large margin.

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.

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.

The existence of a cosmic background of primordial gravitational waves (PGWB) is a robust prediction of inflationary cosmology, but it has so far evaded discovery. The most promising avenue of its detection is via measurements of Cosmic Microwave Background (CMB) $B$-polarization. However, this is not straightforward due to (a) the fact that CMB maps are distorted by gravitational lensing and (b) the high-dimensional nature of CMB data, which renders likelihood-based analysis methods computationally extremely expensive. In this paper, we introduce an efficient likelihood-free, end-to-end inference method to directly infer the posterior distribution of the tensor-to-scalar ratio $r$ from lensed maps of the Stokes $Q$ and $U$ polarization parameters. Our method employs a generative model to delense the maps and utilizes the Approximate Bayesian Computation (ABC) algorithm to sample $r$. We demonstrate that our method yields unbiased estimates of $r$ with well-calibrated uncertainty quantification.

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, Comment: Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM) at the ICML 2024

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.

Omics data analysis is crucial for studying complex diseases, but its high dimensionality and heterogeneity challenge classical statistical and machine learning methods. Graph neural networks have emerged as promising alternatives, yet the optimal strategies for their design and optimization in real-world biomedical challenges remain unclear. This study evaluates various graph representation learning models for case-control classification using high-throughput biological data from Parkinson's disease and control samples. We compare topologies derived from sample similarity networks and molecular interaction networks, including protein-protein and metabolite-metabolite interactions (PPI, MMI). Graph Convolutional Network (GCNs), Chebyshev spectral graph convolution (ChebyNet), and Graph Attention Network (GAT), are evaluated alongside advanced architectures like graph transformers, the graph U-net, and simpler models like multilayer perceptron (MLP). These models are systematically applied to transcriptomics and metabolomics data independently. Our comparative analysis highlights the benefits and limitations of various architectures in extracting patterns from omics data, paving the way for more accurate and interpretable models in biomedical research., Comment: Submitted to Machine Learning in Computational Biology 2024 as an extended abstract, 2 pages + 1 appendix

We introduce ProteinWorkshop, a comprehensive benchmark suite for representation learning on protein structures with Geometric Graph Neural Networks. We consider large-scale pre-training and downstream tasks on both experimental and predicted structures to enable the systematic evaluation of the quality of the learned structural representation and their usefulness in capturing functional relationships for downstream tasks. We find that: (1) large-scale pretraining on AlphaFold structures and auxiliary tasks consistently improve the performance of both rotation-invariant and equivariant GNNs, and (2) more expressive equivariant GNNs benefit from pretraining to a greater extent compared to invariant models. We aim to establish a common ground for the machine learning and computational biology communities to rigorously compare and advance protein structure representation learning. Our open-source codebase reduces the barrier to entry for working with large protein structure datasets by providing: (1) storage-efficient dataloaders for large-scale structural databases including AlphaFoldDB and ESM Atlas, as well as (2) utilities for constructing new tasks from the entire PDB. ProteinWorkshop is available at: github.com/a-r-j/ProteinWorkshop., Comment: ICLR 2024

We introduce RNA-FrameFlow, the first generative model for 3D RNA backbone design. We build upon SE(3) flow matching for protein backbone generation and establish protocols for data preparation and evaluation to address unique challenges posed by RNA modeling. We formulate RNA structures as a set of rigid-body frames and associated loss functions which account for larger, more conformationally flexible RNA backbones (13 atoms per nucleotide) vs. proteins (4 atoms per residue). Toward tackling the lack of diversity in 3D RNA datasets, we explore training with structural clustering and cropping augmentations. Additionally, we define a suite of evaluation metrics to measure whether the generated RNA structures are globally self-consistent (via inverse folding followed by forward folding) and locally recover RNA-specific structural descriptors. The most performant version of RNA-FrameFlow generates locally realistic RNA backbones of 40-150 nucleotides, over 40% of which pass our validity criteria as measured by a self-consistency TM-score >= 0.45, at which two RNAs have the same global fold. Open-source code: https://github.com/rish-16/rna-backbone-design, Comment: To be presented as an Oral at ICML 2024 Structured Probabilistic Inference & Generative Modeling Workshop, and a Spotlight at ICML 2024 AI4Science Workshop

In this paper we study the behaviour of critical points of the Ginzburg-Landau perturbation of the Dirichlet energy into the sphere $E_\varepsilon(u):=\int_\Sigma \frac{1}{2}|du|^2_h\ \,dvol_h +\frac{1}{4\varepsilon^2}(1-|u|^2)^2\,dvol_h=\int_{\Sigma}e_{\varepsilon}(u)$. Our first main result is a precise point-wise estimate for $e_\varepsilon(u_k)$ in the regions where compactness fails, which also implies the $L^{2,1}$ quantization in the bubbling process. Our second main result consists in applying the method developed in a previous joint paper with T. Rivi\`ere to study the upper-semi-continuity of the extended Morse index to sequences of critical points of $E_{\epsilon}$: given a sequence of critical points $u_{\varepsilon_k}:\Sigma\to \mathbb{R}^{n+1}$ of $E_\varepsilon$ that converges in the bubble tree sense to a harmonic map $u_\infty\in W^{1,2}(\Sigma,{S}^{n})$ and bubbles $v^i_{\infty}:\mathbb{R}^2\to {S}^{n}$, we show that the extended Morse indices of the maps $v^i,u_\infty$ control the extended Morse index of the sequence $u_{\varepsilon_k}$ for $k$ large enough., Comment: 30 pages, internal references were broken in v1

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.

Learning computational fluid dynamics (CFD) traditionally relies on computationally intensive simulations of the Navier-Stokes equations. Recently, large language models (LLMs) have shown remarkable pattern recognition and reasoning abilities in natural language processing (NLP) and computer vision (CV). However, these models struggle with the complex geometries inherent in fluid dynamics. We introduce FLUID-LLM, a novel framework combining pre-trained LLMs with spatiotemporal-aware encoding to predict unsteady fluid dynamics. Our approach leverages the temporal autoregressive abilities of LLMs alongside spatial-aware layers, bridging the gap between previous CFD prediction methods. Evaluations on standard benchmarks reveal significant performance improvements across various fluid datasets. Our results demonstrate that FLUID-LLM effectively integrates spatiotemporal information into pre-trained LLMs, enhancing CFD task performance.

Adversarial purification is a kind of defense technique that can defend various unseen adversarial attacks without modifying the victim classifier. Existing methods often depend on external generative models or cooperation between auxiliary functions and victim classifiers. However, retraining generative models, auxiliary functions, or victim classifiers relies on the domain of the fine-tuned dataset and is computation-consuming. In this work, we suppose that adversarial images are outliers of the natural image manifold and the purification process can be considered as returning them to this manifold. Following this assumption, we present a simple adversarial purification method without further training to purify adversarial images, called ZeroPur. ZeroPur contains two steps: given an adversarial example, Guided Shift obtains the shifted embedding of the adversarial example by the guidance of its blurred counterparts; after that, Adaptive Projection constructs a directional vector by this shifted embedding to provide momentum, projecting adversarial images onto the manifold adaptively. ZeroPur is independent of external models and requires no retraining of victim classifiers or auxiliary functions, relying solely on victim classifiers themselves to achieve purification. Extensive experiments on three datasets (CIFAR-10, CIFAR-100, and ImageNet-1K) using various classifier architectures (ResNet, WideResNet) demonstrate that our method achieves state-of-the-art robust performance. The code will be publicly available., Comment: 16 pages, 5 figures, under review

This paper introduces E(n) Equivariant Message Passing Cellular Networks (EMPCNs), an extension of E(n) Equivariant Graph Neural Networks to CW-complexes. Our approach addresses two aspects of geometric message passing networks: 1) enhancing their expressiveness by incorporating arbitrary cells, and 2) achieving this in a computationally efficient way with a decoupled EMPCNs technique. We demonstrate that EMPCNs achieve close to state-of-the-art performance on multiple tasks without the need for steerability, including many-body predictions and motion capture. Moreover, ablation studies confirm that decoupled EMPCNs exhibit stronger generalization capabilities than their non-topologically informed counterparts. These findings show that EMPCNs can be used as a scalable and expressive framework for higher-order message passing in geometric and topological graphs

Tabular data is prevalent in many critical domains, yet it is often challenging to acquire in large quantities. This scarcity usually results in poor performance of machine learning models on such data. Data augmentation, a common strategy for performance improvement in vision and language tasks, typically underperforms for tabular data due to the lack of explicit symmetries in the input space. To overcome this challenge, we introduce TabMDA, a novel method for manifold data augmentation on tabular data. This method utilises a pre-trained in-context model, such as TabPFN, to map the data into an embedding space. TabMDA performs label-invariant transformations by encoding the data multiple times with varied contexts. This process explores the learned embedding space of the underlying in-context models, thereby enlarging the training dataset. TabMDA is a training-free method, making it applicable to any classifier. We evaluate TabMDA on five standard classifiers and observe significant performance improvements across various tabular datasets. Our results demonstrate that TabMDA provides an effective way to leverage information from pre-trained in-context models to enhance the performance of downstream classifiers. Code is available at https://github.com/AdrianBZG/TabMDA., Comment: Presented at 1st ICML Workshop on In-Context Learning (ICL @ ICML 2024)

Generative modelling paradigms based on denoising diffusion processes have emerged as a leading candidate for conditional sampling in inverse problems. In many real-world applications, we often have access to large, expensively trained unconditional diffusion models, which we aim to exploit for improving conditional sampling. Most recent approaches are motivated heuristically and lack a unifying framework, obscuring connections between them. Further, they often suffer from issues such as being very sensitive to hyperparameters, being expensive to train or needing access to weights hidden behind a closed API. In this work, we unify conditional training and sampling using the mathematically well-understood Doob's h-transform. This new perspective allows us to unify many existing methods under a common umbrella. Under this framework, we propose DEFT (Doob's h-transform Efficient FineTuning), a new approach for conditional generation that simply fine-tunes a very small network to quickly learn the conditional $h$-transform, while keeping the larger unconditional network unchanged. DEFT is much faster than existing baselines while achieving state-of-the-art performance across a variety of linear and non-linear benchmarks. On image reconstruction tasks, we achieve speedups of up to 1.6$\times$, while having the best perceptual quality on natural images and reconstruction performance on medical images., Comment: arXiv admin note: text overlap with arXiv:2312.09236

Explainability is often critical to the acceptable implementation of artificial intelligence (AI). Nowhere is this more important than healthcare where decision-making directly impacts patients and trust in AI systems is essential. This trust is often built on the explanations and interpretations the AI provides. Despite significant advancements in AI interpretability, there remains the need for clear guidelines on when and to what extent explanations are necessary in the medical context. We propose a novel categorization system with four distinct classes of explanation necessity, guiding the level of explanation required: patient or sample (local) level, cohort or dataset (global) level, or both levels. We introduce a mathematical formulation that distinguishes these categories and offers a practical framework for researchers to determine the necessity and depth of explanations required in medical AI applications. Three key factors are considered: the robustness of the evaluation protocol, the variability of expert observations, and the representation dimensionality of the application. In this perspective, we address the question: When does an AI medical application need to be explained, and at what level of detail?

Graph hypernetworks (GHNs), constructed by combining graph neural networks (GNNs) with hypernetworks (HNs), leverage relational data across various domains such as neural architecture search, molecular property prediction and federated learning. Despite GNNs and HNs being individually successful, we show that GHNs present problems compromising their performance, such as over-smoothing and heterophily. Moreover, we cannot apply GHNs directly to personalized federated learning (PFL) scenarios, where a priori client relation graph may be absent, private, or inaccessible. To mitigate these limitations in the context of PFL, we propose a novel class of HNs, sheaf hypernetworks (SHNs), which combine cellular sheaf theory with HNs to improve parameter sharing for PFL. We thoroughly evaluate SHNs across diverse PFL tasks, including multi-class classification, traffic and weather forecasting. Additionally, we provide a methodology for constructing client relation graphs in scenarios where such graphs are unavailable. We show that SHNs consistently outperform existing PFL solutions in complex non-IID scenarios. While the baselines' performance fluctuates depending on the task, SHNs show improvements of up to 2.7% in accuracy and 5.3% in lower mean squared error over the best-performing baseline., Comment: 25 pages, 12 figures, 7 tables, pre-print under review

In the last decade, computer vision has witnessed the establishment of various training and learning approaches. Techniques like adversarial learning, contrastive learning, diffusion denoising learning, and ordinary reconstruction learning have become standard, representing state-of-the-art methods extensively employed for fully training or pre-training networks across various vision tasks. The exploration of fine-tuning approaches has emerged as a current focal point, addressing the need for efficient model tuning with reduced GPU memory usage and time costs while enhancing overall performance, as exemplified by methodologies like low-rank adaptation (LoRA). Key questions arise: which pre-training technique yields optimal results - adversarial, contrastive, reconstruction, or diffusion denoising? How does the performance of these approaches vary as the complexity of fine-tuning is adjusted? This study aims to elucidate the advantages of pre-training techniques and fine-tuning strategies to enhance the learning process of neural networks in independent identical distribution (IID) cohorts. We underscore the significance of fine-tuning by examining various cases, including full tuning, decoder tuning, top-level tuning, and fine-tuning of linear parameters using LoRA. Systematic summaries of model performance and efficiency are presented, leveraging metrics such as accuracy, time cost, and memory efficiency. To empirically demonstrate our findings, we focus on a multi-task segmentation-classification challenge involving the paracingulate sulcus (PCS) using different 3D Convolutional Neural Network (CNN) architectures by using the TOP-OSLO cohort comprising 596 subjects.

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., Comment: arXiv admin note: substantial text overlap with arXiv:2311.18177

The accelerated progress of artificial intelligence (AI) has popularized deep learning models across domains, yet their inherent opacity poses challenges, notably in critical fields like healthcare, medicine and the geosciences. Explainable AI (XAI) has emerged to shed light on these "black box" models, helping decipher their decision making process. Nevertheless, different XAI methods yield highly different explanations. This inter-method variability increases uncertainty and lowers trust in deep networks' predictions. In this study, for the first time, we propose a novel framework designed to enhance the explainability of deep networks, by maximizing both the accuracy and the comprehensibility of the explanations. Our framework integrates various explanations from established XAI methods and employs a non-linear "explanation optimizer" to construct a unique and optimal explanation. Through experiments on multi-class and binary classification tasks in 2D object and 3D neuroscience imaging, we validate the efficacy of our approach. Our explanation optimizer achieved superior faithfulness scores, averaging 155% and 63% higher than the best performing XAI method in the 3D and 2D applications, respectively. Additionally, our approach yielded lower complexity, increasing comprehensibility. Our results suggest that optimal explanations based on specific criteria are derivable and address the issue of inter-method variability in the current XAI literature., Comment: keywords: XAI, neuroscience, brain, 3D, 2D, computer vision, classification

All fields of knowledge are being impacted by Artificial Intelligence. In particular, the Deep Learning paradigm enables the development of data analysis tools that support subject matter experts in a variety of sectors, from physics up to the recognition of ancient languages. Palaeontology is now observing this trend as well. This study explores the capability of Convolutional Neural Networks (CNNs), a particular class of Deep Learning algorithms specifically crafted for computer vision tasks, to classify images of isolated fossil shark teeth gathered from online datasets as well as from the authors$'$ experience on Peruvian Miocene and Italian Pliocene fossil assemblages. The shark taxa that are included in the final, composite dataset (which consists of more than one thousand images) are representative of both extinct and extant genera, namely, Carcharhinus, Carcharias, Carcharocles, Chlamydoselachus, Cosmopolitodus, Galeocerdo, Hemipristis, Notorynchus, Prionace and Squatina. We developed a CNN, named SharkNet-X, specifically tailored on our recognition task, reaching a 5-fold cross validated mean accuracy of 0.85 to identify images containing a single shark tooth. Furthermore, we elaborated a visualization of the features extracted from images using the last dense layer of the CNN, achieved through the application of the clustering technique t-SNE. In addition, in order to understand and explain the behaviour of the CNN while giving a paleontological point of view on the results, we introduced the explainability method SHAP. To the best of our knowledge, this is the first instance in which this method is applied to the field of palaeontology. The main goal of this work is to showcase how Deep Learning techniques can aid in identifying isolated fossil shark teeth, paving the way for developing new information tools for automating the recognition and classification of fossils., Comment: 40 pages, 8 figures

Recent breakthroughs in generative modelling have led to a number of works proposing molecular generation models for drug discovery. While these models perform well at capturing drug-like motifs, they are known to often produce synthetically inaccessible molecules. This is because they are trained to compose atoms or fragments in a way that approximates the training distribution, but they are not explicitly aware of the synthesis constraints that come with making molecules in the lab. To address this issue, we introduce SynFlowNet, a GFlowNet model whose action space uses chemically validated reactions and reactants to sequentially build new molecules. We evaluate our approach using synthetic accessibility scores and an independent retrosynthesis tool. SynFlowNet consistently samples synthetically feasible molecules, while still being able to find diverse and high-utility candidates. Furthermore, we compare molecules designed with SynFlowNet to experimentally validated actives, and find that they show comparable properties of interest, such as molecular weight, SA score and predicted protein binding affinity., Comment: Presented at ICLR 2024 GEM Workshop

Electrocardiogram (ECG) signals play a pivotal role in cardiovascular diagnostics, providing essential information on the electrical activity of the heart. However, the inherent noise and limited resolution in ECG recordings can hinder accurate interpretation and diagnosis. In this paper, we propose a novel model for ECG super resolution (SR) that uses a DNAE to enhance temporal and frequency information inside ECG signals. Our approach addresses the limitations of traditional ECG signal processing techniques. Our model takes in input 5-second length ECG windows sampled at 50 Hz (very low resolution) and it is able to reconstruct a denoised super-resolution signal with an x10 upsampling rate (sampled at 500 Hz). We trained the proposed DCAE-SR on public available myocardial infraction ECG signals. Our method demonstrates superior performance in reconstructing high-resolution ECG signals from very low-resolution signals with a sampling rate of 50 Hz. We compared our results with the current deep-learning literature approaches for ECG super-resolution and some non-deep learning reproducible methods that can perform both super-resolution and denoising. We obtained current state-of-the-art performances in super-resolution of very low resolution ECG signals frequently corrupted by ECG artifacts. We were able to obtain a signal-to-noise ratio of 12.20 dB (outperforms previous 4.68 dB), mean squared error of 0.0044 (outperforms previous 0.0154) and root mean squared error of 4.86% (outperforms previous 12.40%). In conclusion, our DCAE-SR model offers a robust (to artefact presence), versatile and explainable solution to enhance the quality of ECG signals. This advancement holds promise in advancing the field of cardiovascular diagnostics, paving the way for improved patient care and high-quality clinical decisions

The success of Large Language Models (LLMs), e.g., ChatGPT, is witnessed by their planetary popularity, their capability of human-like communication, and also by their steadily improved reasoning performance. However, it remains unclear whether LLMs reason. It is an open problem how traditional neural networks can be qualitatively extended to go beyond the statistic paradigm and achieve high-level cognition. Here, we present a novel qualitative extension by generalising computational building blocks from vectors to spheres. We propose Sphere Neural Networks (SphNNs) for human-like reasoning through model construction and inspection, and develop SphNN for syllogistic reasoning, a microcosm of human rationality. SphNN is a hierarchical neuro-symbolic Kolmogorov-Arnold geometric GNN, and uses a neuro-symbolic transition map of neighbourhood spatial relations to transform the current sphere configuration towards the target. SphNN is the first neural model that can determine the validity of long-chained syllogistic reasoning in one epoch without training data, with the worst computational complexity of O(N). SphNN can evolve into various types of reasoning, such as spatio-temporal reasoning, logical reasoning with negation and disjunction, event reasoning, neuro-symbolic unification, and humour understanding (the highest level of cognition). All these suggest a new kind of Herbert A. Simon's scissors with two neural blades. SphNNs will tremendously enhance interdisciplinary collaborations to develop the two neural blades and realise deterministic neural reasoning and human-bounded rationality and elevate LLMs to reliable psychological AI. This work suggests that the non-zero radii of spheres are the missing components that prevent traditional deep-learning systems from reaching the realm of rational reasoning and cause LLMs to be trapped in the swamp of hallucination.

In our earlier work, we introduced the concept of Gene Regulatory Neural Network (GRNN), which utilizes natural neural network-like structures inherent in biological cells to perform computing tasks using chemical inputs. We define this form of chemical-based neural network as Wet TinyML. The GRNN structures are based on the gene regulatory network and have weights associated with each link based on the estimated interactions between the genes. The GRNNs can be used for conventional computing by employing an application-based search process similar to the Network Architecture Search. This study advances this concept by incorporating cell plasticity, to further exploit natural cell's adaptability, in order to diversify the GRNN search that can match larger spectrum as well as dynamic computing tasks. As an example application, we show that through the directed cell plasticity, we can extract the mathematical regression evolution enabling it to match to dynamic system applications. We also conduct energy analysis by comparing the chemical energy of the GRNN to its silicon counterpart, where this analysis includes both artificial neural network algorithms executed on von Neumann architecture as well as neuromorphic processors. The concept of Wet TinyML can pave the way for the new emergence of chemical-based, energy-efficient and miniature Biological AI., Comment: Accepted as a full paper by the tinyML Research Symposium 2024

Graph Neural Networks (GNNs), known as spectral graph filters, find a wide range of applications in web networks. To bypass eigendecomposition, polynomial graph filters are proposed to approximate graph filters by leveraging various polynomial bases for filter training. However, no existing studies have explored the diverse polynomial graph filters from a unified perspective for optimization. In this paper, we first unify polynomial graph filters, as well as the optimal filters of identical degrees into the Krylov subspace of the same order, thus providing equivalent expressive power theoretically. Next, we investigate the asymptotic convergence property of polynomials from the unified Krylov subspace perspective, revealing their limited adaptability in graphs with varying heterophily degrees. Inspired by those facts, we design a novel adaptive Krylov subspace approach to optimize polynomial bases with provable controllability over the graph spectrum so as to adapt various heterophily graphs. Subsequently, we propose AdaptKry, an optimized polynomial graph filter utilizing bases from the adaptive Krylov subspaces. Meanwhile, in light of the diverse spectral properties of complex graphs, we extend AdaptKry by leveraging multiple adaptive Krylov bases without incurring extra training costs. As a consequence, extended AdaptKry is able to capture the intricate characteristics of graphs and provide insights into their inherent complexity. We conduct extensive experiments across a series of real-world datasets. The experimental results demonstrate the superior filtering capability of AdaptKry, as well as the optimized efficacy of the adaptive Krylov basis.

Patient triage plays a crucial role in emergency departments, ensuring timely and appropriate care based on correctly evaluating the emergency grade of patient conditions. Triage methods are generally performed by human operator based on her own experience and information that are gathered from the patient management process. Thus, it is a process that can generate errors in emergency level associations. Recently, Traditional triage methods heavily rely on human decisions, which can be subjective and prone to errors. Recently, a growing interest has been focused on leveraging artificial intelligence (AI) to develop algorithms able to maximize information gathering and minimize errors in patient triage processing. We define and implement an AI based module to manage patients emergency code assignments in emergency departments. It uses emergency department historical data to train the medical decision process. Data containing relevant patient information, such as vital signs, symptoms, and medical history, are used to accurately classify patients into triage categories. Experimental results demonstrate that the proposed algorithm achieved high accuracy outperforming traditional triage methods. By using the proposed method we claim that healthcare professionals can predict severity index to guide patient management processing and resource allocation.

Modern life sciences research is increasingly relying on artificial intelligence approaches to model biological systems, primarily centered around the use of machine learning (ML) models. Although ML is undeniably useful for identifying patterns in large, complex data sets, its widespread application in biological sciences represents a significant deviation from traditional methods of scientific inquiry. As such, the interplay between these models and scientific understanding in biology is a topic with important implications for the future of scientific research, yet it is a subject that has received little attention. Here, we draw from an epistemological toolkit to contextualize recent applications of ML in biological sciences under modern philosophical theories of understanding, identifying general principles that can guide the design and application of ML systems to model biological phenomena and advance scientific knowledge. We propose that conceptions of scientific understanding as information compression, qualitative intelligibility, and dependency relation modelling provide a useful framework for interpreting ML-mediated understanding of biological systems. Through a detailed analysis of two key application areas of ML in modern biological research - protein structure prediction and single cell RNA-sequencing - we explore how these features have thus far enabled ML systems to advance scientific understanding of their target phenomena, how they may guide the development of future ML models, and the key obstacles that remain in preventing ML from achieving its potential as a tool for biological discovery. Consideration of the epistemological features of ML applications in biology will improve the prospects of these methods to solve important problems and advance scientific understanding of living systems.

Graph augmentation methods play a crucial role in improving the performance and enhancing generalisation capabilities in Graph Neural Networks (GNNs). Existing graph augmentation methods mainly perturb the graph structures, and are usually limited to pairwise node relations. These methods cannot fully address the complexities of real-world large-scale networks, which often involve higher-order node relations beyond only being pairwise. Meanwhile, real-world graph datasets are predominantly modelled as simple graphs, due to the scarcity of data that can be used to form higher-order edges. Therefore, reconfiguring the higher-order edges as an integration into graph augmentation strategies lights up a promising research path to address the aforementioned issues. In this paper, we present Topological Augmentation (TopoAug), a novel graph augmentation method that builds a combinatorial complex from the original graph by constructing virtual hyperedges directly from the raw data. TopoAug then produces auxiliary node features by extracting information from the combinatorial complex, which are used for enhancing GNN performances on downstream tasks. We design three diverse virtual hyperedge construction strategies to accompany the construction of combinatorial complexes: (1) via graph statistics, (2) from multiple data perspectives, and (3) utilising multi-modality. Furthermore, to facilitate TopoAug evaluation, we provide 23 novel real-world graph datasets across various domains including social media, biology, and e-commerce. Our empirical study shows that TopoAug consistently and significantly outperforms GNN baselines and other graph augmentation methods, across a variety of application contexts, which clearly indicates that it can effectively incorporate higher-order node relations into the graph augmentation for real-world complex networks., Comment: In 27th European Conference on Artificial Intelligence (ECAI 2024). 13 pages, 2 figures, 13 tables

Graph neural networks (GNNs) and variations of the message passing algorithm are the predominant means for learning on graphs, largely due to their flexibility, speed, and satisfactory performance. The design of powerful and general purpose GNNs, however, requires significant research efforts and often relies on handcrafted, carefully-chosen message passing operators. Motivated by this, we propose a remarkably simple alternative for learning on graphs that relies exclusively on attention. Graphs are represented as node or edge sets and their connectivity is enforced by masking the attention weight matrix, effectively creating custom attention patterns for each graph. Despite its simplicity, masked attention for graphs (MAG) has state-of-the-art performance on long-range tasks and outperforms strong message passing baselines and much more involved attention-based methods on over 55 node and graph-level tasks. We also show significantly better transfer learning capabilities compared to GNNs and comparable or better time and memory scaling. MAG has sub-linear memory scaling in the number of nodes or edges, enabling learning on dense graphs and future-proofing the approach.

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field., Comment: Proceedings of the 41st International Conference on Machine Learning, Vienna, Austria. PMLR 235, 2024

Hypergraphs are characterized by complex topological structure, representing higher-order interactions among multiple entities through hyperedges. Lately, hypergraph-based deep learning methods to learn informative data representations for the problem of node classification on text-attributed hypergraphs have garnered increasing research attention. However, existing methods struggle to simultaneously capture the full extent of hypergraph structural information and the rich linguistic attributes inherent in the nodes attributes, which largely hampers their effectiveness and generalizability. To overcome these challenges, we explore ways to further augment a pretrained BERT model with specialized hypergraph-aware layers for the task of node classification. Such layers introduce higher-order structural inductive bias into the language model, thus improving the model's capacity to harness both higher-order context information from the hypergraph structure and semantic information present in text. In this paper, we propose a new architecture, HyperBERT, a mixed text-hypergraph model which simultaneously models hypergraph relational structure while maintaining the high-quality text encoding capabilities of a pre-trained BERT. Notably, HyperBERT presents results that achieve a new state-of-the-art on five challenging text-attributed hypergraph node classification benchmarks., Comment: EMNLP 2024

Recent work on neural algorithmic reasoning has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. Doing so, however, has always used a recurrent architecture, where each iteration of the GNN aligns with an algorithm's iteration. Since an algorithm's solution is often an equilibrium, we conjecture and empirically validate that one can train a network to solve algorithmic problems by directly finding the equilibrium. Note that this does not require matching each GNN iteration with a step of the algorithm.

Many protein design applications, such as binder or enzyme design, require scaffolding a structural motif with high precision. Generative modelling paradigms based on denoising diffusion processes emerged as a leading candidate to address this motif scaffolding problem and have shown early experimental success in some cases. In the diffusion paradigm, motif scaffolding is treated as a conditional generation task, and several conditional generation protocols were proposed or imported from the Computer Vision literature. However, most of these protocols are motivated heuristically, e.g. via analogies to Langevin dynamics, and lack a unifying framework, obscuring connections between the different approaches. In this work, we unify conditional training and conditional sampling procedures under one common framework based on the mathematically well-understood Doob's h-transform. This new perspective allows us to draw connections between existing methods and propose a new variation on existing conditional training protocols. We illustrate the effectiveness of this new protocol in both, image outpainting and motif scaffolding and find that it outperforms standard methods., Comment: 9 pages

Recent advances in computational modelling of atomic systems, spanning molecules, proteins, and materials, represent them as geometric graphs with atoms embedded as nodes in 3D Euclidean space. In these graphs, the geometric attributes transform according to the inherent physical symmetries of 3D atomic systems, including rotations and translations in Euclidean space, as well as node permutations. In recent years, Geometric Graph Neural Networks have emerged as the preferred machine learning architecture powering applications ranging from protein structure prediction to molecular simulations and material generation. Their specificity lies in the inductive biases they leverage - such as physical symmetries and chemical properties - to learn informative representations of these geometric graphs. In this opinionated paper, we provide a comprehensive and self-contained overview of the field of Geometric GNNs for 3D atomic systems. We cover fundamental background material and introduce a pedagogical taxonomy of Geometric GNN architectures: (1) invariant networks, (2) equivariant networks in Cartesian basis, (3) equivariant networks in spherical basis, and (4) unconstrained networks. Additionally, we outline key datasets and application areas and suggest future research directions. The objective of this work is to present a structured perspective on the field, making it accessible to newcomers and aiding practitioners in gaining an intuition for its mathematical abstractions.

Recent advances in the development of pre-trained Spanish language models has led to significant progress in many Natural Language Processing (NLP) tasks, such as question answering. However, the lack of efficient models imposes a barrier for the adoption of such models in resource-constrained environments. Therefore, smaller distilled models for the Spanish language could be proven to be highly scalable and facilitate their further adoption on a variety of tasks and scenarios. In this work, we take one step in this direction by developing SpanishTinyRoBERTa, a compressed language model based on RoBERTa for efficient question answering in Spanish. To achieve this, we employ knowledge distillation from a large model onto a lighter model that allows for a wider implementation, even in areas with limited computational resources, whilst attaining negligible performance sacrifice. Our experiments show that the dense distilled model can still preserve the performance of its larger counterpart, while significantly increasing inference speedup. This work serves as a starting point for further research and investigation of model compression efforts for Spanish language models across various NLP tasks., Comment: ICLR 2024 Tiny Paper (6 pages, 2 tables)