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Pietro Liò

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49 papers
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49

EAAI Journal 2026 Journal Article

Graph Neural Networks Based Analog Circuit Link Prediction

  • Guanyuan Pan
  • Tiansheng Zhou
  • Jianxiang Zhao
  • Zhi Li
  • Yugui Lin
  • Bingtao Ma
  • Yaqi Wang
  • Pietro Liò

Circuit link prediction, which identifies missing component connections from incomplete netlists, is crucial in analog circuit design automation. However, existing methods face three main challenges: (1) Insufficient use of topological patterns in circuit graphs reduces prediction accuracy; (2) Data scarcity due to the complexity of annotations hinders model generalization; (3) Limited adaptability to various netlist formats restricts model flexibility. We propose Graph Neural Networks Based Analog Circuit Link Prediction (GNN-ACLP), a graph neural networks (GNNs) based method featuring three innovations to tackle these challenges. First, we introduce the SEAL (learning from Subgraphs, Embeddings, and Attributes for Link prediction) framework and achieve port-level accuracy in circuit link prediction. Second, we propose Netlist Babel Fish, a netlist format conversion tool that leverages retrieval-augmented generation (RAG) with a large language model (LLM) to enhance the compatibility of netlist formats. Finally, we build a comprehensive dataset, SpiceNetlist, comprising 775 annotated circuits of 7 different types across 10 component classes. Experiments demonstrate accuracy improvements of 16. 08% on SpiceNetlist, 11. 38% on Image2Net, and 16. 01% on Masala-CHAI compared to the baseline in intra-dataset evaluation, while maintaining accuracy from 92. 05% to 99. 07% in cross-dataset evaluation, demonstrating robust feature transfer capabilities. However, its linear computational complexity makes processing large-scale netlists challenging and requires future addressing.

AIIM Journal 2026 Journal Article

Integrating probabilistic trees and causal networks for clinical and epidemiological data

  • Sheresh Zahoor
  • Pietro Liò
  • Gaël Dias
  • Mohammed Hasanuzzaman

Healthcare decision-making requires not only accurate predictions but also insights into how factors influence patient outcomes. While traditional machine learning (ML) models excel at predicting outcomes, such as identifying high-risk patients, they are limited in addressing "what if" questions about interventions. This study introduces the Probabilistic Causal Fusion (PCF) framework, which integrates Causal Bayesian Networks (CBNs) and Probability Trees (PTrees) to extend beyond predictions. PCF leverages causal relationships from CBNs to structure PTrees, enabling both the quantification of factor impacts and the simulation of hypothetical interventions. The framework is evaluated on three clinically diverse, real-world datasets, MIMIC-IV, Framingham Heart Study, and BRFSS (Diabetes), demonstrating consistent predictive performance comparable to conventional ML models, while offering enhanced interpretability and causal reasoning capabilities. In contrast to conventional approaches focused solely on prediction, PCF offers a unified framework for prediction, intervention modelling, and counterfactual analysis, forming a holistic toolkit for clinical decision support. To enhance interpretability, PCF incorporates sensitivity analysis and SHapley Additive exPlanations (SHAP). Sensitivity analysis quantifies the influence of causal parameters on outcomes such as Length of Stay (LOS), Coronary Heart Disease (CHD), and Diabetes, while SHAP highlights the importance of individual features in predictive modelling. This dual-layered interpretability offers both macro-level insights into causal pathways and micro-level explanations for individual predictions. By combining causal reasoning with predictive modelling, PCF bridges the gap between clinical intuition and data-driven insights. Its ability to uncover relationships between modifiable factors and simulate hypothetical scenarios provides clinicians with a clearer understanding of causal pathways. This approach supports more informed, evidence-based decision-making, offering a robust framework for addressing complex questions in diverse healthcare settings.

AIIM Journal 2025 Journal Article

A survey for large language models in biomedicine

  • Chong Wang
  • Mengyao Li
  • Junjun He
  • Zhongruo Wang
  • Erfan Darzi
  • Zan Chen
  • Jin Ye
  • Tianbin Li

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. As this field of LLM rapidly evolves, continued research and development are essential to fully harness the capabilities of LLMs in biomedicine while ensuring their responsible and effective deployment.

AAAI Conference 2025 Conference Paper

Deep Hypergraph Neural Networks with Tight Framelets

  • Ming Li
  • Yujie Fang
  • Yi Wang
  • Han Feng
  • Yongchun Gu
  • Lu Bai
  • Pietro Liò

Hypergraphs provide a flexible framework for modeling high-order (complex) interactions among multiple entities, extending beyond traditional pairwise correlations in graph structures. However, deep hypergraph neural networks (HGNNs) often face the challenge of oversmoothing with increasing depth, similar to issues in graph neural networks (GNNs). While oversmoothing in GNNs has been extensively studied, its implications in relation to hypergraphs are less explored. This paper addresses this gap by first theoretically exploring the reasons behind oversmoothing in deep HGNNs. Our novel insights suggest that a spectral-based hypergraph convolution, equipped with both low-pass and high-pass filters, can potentially mitigate these effects. Motivated by these findings, we introduce FrameHGNN, a framework that utilizes framelet-based hypergraph convolutions integrating tight framelet transforms with both low-pass and high-pass components, as well as the commonly used strategies in designing deep GNN architecture: initial residual and identity mappings. The experiment results on diverse benchmark datasets demonstrate that FrameHGNN outperforms several state-of-the-art models, effectively reducing oversmoothing while improving predictive accuracy. Our contributions not only advance the theoretical understanding of deep hypergraph learning but also provide a practical spectral-based approach for HGNNs, emphasizing the design of multifrequency channels.

AIIM Journal 2025 Journal Article

Design and use of a Denoising Convolutional Autoencoder for reconstructing electrocardiogram signals at super resolution

  • Ugo Lomoio
  • Pierangelo Veltri
  • Pietro Hiram Guzzi
  • Pietro Liò

Electrocardiogram signals play a pivotal role in cardiovascular diagnostics, providing essential information on electrical hearth activity. However, inherent noise and limited resolution can hinder an accurate interpretation of the recordings. In this paper an advanced Denoising Convolutional Autoencoder designed to process electrocardiogram signals, generating super-resolution reconstructions is proposed; this is followed by in-depth analysis of the enhanced signals. The autoencoder receives a signal window (of 5 s) sampled at 50 Hz (low resolution) as input and reconstructs a denoised super-resolution signal at 500 Hz. The proposed autoencoder is applied to publicly available datasets, demonstrating optimal performance in reconstructing high-resolution signals from very low-resolution inputs sampled at 50 Hz. The results were then compared with current state-of-the-art for electrocardiogram super-resolution, demonstrating the effectiveness of the proposed method. The method achieves a signal-to-noise ratio of 12. 20 dB, a mean squared error of 0. 0044, and a root mean squared error of 4. 86%, which significantly outperforms current state-of-the-art alternatives. This framework can effectively enhance hidden information within signals, aiding in the detection of heart-related diseases.

ICML Conference 2025 Conference Paper

EduLLM: Leveraging Large Language Models and Framelet-Based Signed Hypergraph Neural Networks for Student Performance Prediction

  • Ming Li 0065
  • Yukang Cheng
  • Lu Bai 0001
  • Feilong Cao
  • Ke Lv 0002
  • Jiye Liang
  • Pietro Liò

The growing demand for personalized learning underscores the importance of accurately predicting students’ future performance to support tailored education and optimize instructional strategies. Traditional approaches predominantly focus on temporal modeling using historical response records and learning trajectories. While effective, these methods often fall short in capturing the intricate interactions between students and learning content, as well as the subtle semantics of these interactions. To address these gaps, we present EduLLM, the first framework to leverage large language models in combination with hypergraph learning for student performance prediction. The framework incorporates FraS-HNN ($\underline{\mbox{Fra}}$melet-based $\underline{\mbox{S}}$igned $\underline{\mbox{H}}$ypergraph $\underline{\mbox{N}}$eural $\underline{\mbox{N}}$etworks), a novel spectral-based model for signed hypergraph learning, designed to model interactions between students and multiple-choice questions. In this setup, students and questions are represented as nodes, while response records are encoded as positive and negative signed hyperedges, effectively capturing both structural and semantic intricacies of personalized learning behaviors. FraS-HNN employs framelet-based low-pass and high-pass filters to extract multi-frequency features. EduLLM integrates fine-grained semantic features derived from LLMs, synergizing with signed hypergraph representations to enhance prediction accuracy. Extensive experiments conducted on multiple educational datasets demonstrate that EduLLM significantly outperforms state-of-the-art baselines, validating the novel integration of LLMs with FraS-HNN for signed hypergraph learning.

ECAI Conference 2025 Conference Paper

FAIRGAME: A Framework for AI Agents Bias Recognition Using Game Theory

  • Alessio Buscemi
  • Daniele Proverbio
  • Alessandro Di Stefano
  • Han The Anh
  • German Castignani
  • Pietro Liò

Letting AI agents interact in multi-agent applications adds a layer of complexity to the interpretability and prediction of AI outcomes, with profound implications for their trustworthy adoption in research and society. Game theory offers powerful models to capture and interpret strategic interaction among agents, but requires the support of reproducible, standardized and user-friendly IT frameworks to enable comparison and interpretation of results. To this end, we present FAIRGAME, a Framework for AI Agents Bias Recognition using Game Theory. We describe its implementation and usage, and we employ it to uncover biased outcomes in popular games among AI agents, depending on the employed Large Language Model (LLM) and used language, as well as on the personality trait or strategic knowledge of the agents. Overall, FAIRGAME allows users to reliably and easily simulate their desired games and scenarios and compare the results across simulation campaigns and with game-theoretic predictions, enabling the systematic discovery of biases, the anticipation of emerging behavior out of strategic interplays, and empowering further research into strategic decision-making using LLM agents.

ICML Conference 2025 Conference Paper

G-Adaptivity: optimised graph-based mesh relocation for finite element methods

  • James Rowbottom
  • Georg Maierhofer
  • Teo Deveney
  • Eike Hermann Müller
  • Alberto Paganini
  • Katharina Schratz
  • Pietro Liò
  • Carola Schönlieb

We present a novel, and effective, approach to achieve optimal mesh relocation in finite element methods (FEMs). The cost and accuracy of FEMs is critically dependent on the choice of mesh points. Mesh relocation (r-adaptivity) seeks to optimise the mesh geometry to obtain the best solution accuracy at given computational budget. Classical r-adaptivity relies on the solution of a separate nonlinear “meshing” PDE to determine mesh point locations. This incurs significant cost at remeshing, and relies on estimates that relate interpolation- and FEM-error. Recent machine learning approaches have focused on the construction of fast surrogates for such classical methods. Instead, our new approach trains a graph neural network (GNN) to determine mesh point locations by directly minimising the FE solution error from the PDE system Firedrake to achieve higher solution accuracy. Our GNN architecture closely aligns the mesh solution space to that of classical meshing methodologies, thus replacing classical estimates for optimality with a learnable strategy. This allows for rapid and robust training and results in an extremely efficient and effective GNN approach to online r-adaptivity. Our method outperforms both classical, and prior ML, approaches to r-adaptive meshing. In particular, it achieves lower FE solution error, whilst retaining the significant speed-up over classical methods observed in prior ML work.

ICLR Conference 2025 Conference Paper

gRNAde: Geometric Deep Learning for 3D RNA inverse design

  • Chaitanya K. Joshi
  • Arian Rokkum Jamasb
  • Ramón Viñas Torné 0001
  • Charles Harris
  • Simon V. Mathis
  • Alex Morehead
  • Rishabh Anand
  • Pietro Liò

Computational RNA design tasks are often posed as inverse problems, where sequences are designed based on adopting a single desired secondary structure without considering 3D conformational diversity. We introduce gRNAde, a geometric RNA design pipeline operating on 3D RNA backbones to design sequences that explicitly account for structure and dynamics. gRNAde uses a multi-state Graph Neural Network and autoregressive decoding to generates candidate RNA sequences conditioned on one or more 3D backbone structures where the identities of the bases are unknown. On a single-state fixed backbone re-design benchmark of 14 RNA structures from the PDB identified by Das et al. (2010), gRNAde obtains higher native sequence recovery rates (56% on average) compared to Rosetta (45% on average), taking under a second to produce designs compared to the reported hours for Rosetta. We further demonstrate the utility of gRNAde on a new benchmark of multi-state design for structurally flexible RNAs, as well as zero-shot ranking of mutational fitness landscapes in a retrospective analysis of a recent ribozyme. Experimental wet lab validation on 10 different structured RNA backbones finds that gRNAde has a success rate of 50% at designing pseudoknotted RNA structures, a significant advance over 35% for Rosetta. Open source code and tutorials are available at: github.com/chaitjo/geometric-rna-design

ICML Conference 2025 Conference Paper

Hierarchical Planning for Complex Tasks with Knowledge Graph-RAG and Symbolic Verification

  • Flavio Petruzzellis
  • Cristina Cornelio
  • Pietro Liò

Large Language Models (LLMs) have shown promise as robotic planners but often struggle with long-horizon and complex tasks, especially in specialized environments requiring external knowledge. While hierarchical planning and Retrieval-Augmented Generation (RAG) address some of these challenges, they remain insufficient on their own and a deeper integration is required for achieving more reliable systems. To this end, we propose a neuro-symbolic approach that enhances LLMs-based planners with Knowledge Graph-based RAG for hierarchical plan generation. This method decomposes complex tasks into manageable subtasks, further expanded into executable atomic action sequences. To ensure formal correctness and proper decomposition, we integrate a Symbolic Validator, which also functions as a failure detector by aligning expected and observed world states. Our evaluation against baseline methods demonstrates the consistent significant advantages of integrating hierarchical planning, symbolic verification, and RAG across tasks of varying complexity and different LLMs. Additionally, our experimental setup and novel metrics not only validate our approach for complex planning but also serve as a tool for assessing LLMs’ reasoning and compositional capabilities. Code available at https: //github. com/corneliocristina/HVR.

AAAI Conference 2025 Conference Paper

Neural Reasoning for Sure Through Constructing Explainable Models

  • Tiansi Dong
  • Mateja Jamnik
  • Pietro Liò

Neural networks remain black-box systems, unsure about their outputs, and their performance may drop unpredictably in real applications. An open question is how to qualitatively extend neural networks, so that they are sure about their reasoning results, or reasoning-for-sure. Here, we introduce set-theoretic relations explicitly and seamlessly into neural networks by extending vector embedding into sphere embedding, so that part-whole relations can explicitly encode set-theoretic relations through sphere boundaries in the vector space. A reasoning-for-sure neural network successfully constructs, within a constant number M of epochs, a sphere configuration as its semantic model for any consistent set-theoretic relation. We implement Hyperbolic Sphere Neural Network (HSphNN), the first reasoning-for-sure neural network for all types of Aristotelian syllogistic reasoning. Its construction process is realised as a sequence of neighbourhood transitions from the current towards the target configuration. We prove M=1 for HSphNN. In experiments, HSphNN achieves the symbolic level rigour of syllogistic reasoning and successfully checks both decisions and explanations of ChatGPT (gpt-3.5-turbo and gpt-4o) without errors. Through prompts, HSphNN improves the performance of gpt-3.5-turbo from 46.875% to 58.98%, and of gpt-4o from 82.42% to 84.76%. We show ways to extend HSphNN for various kinds of logical and Bayesian reasoning, and to integrate it with traditional neural networks seamlessly.

ICML Conference 2025 Conference Paper

NMA-tune: Generating Highly Designable and Dynamics Aware Protein Backbones

  • Urszula Julia Komorowska
  • Francisco Vargas 0001
  • Alessandro Rondina
  • Pietro Liò
  • Mateja Jamnik

Protein’s backbone flexibility is a crucial property that heavily influences its functionality. Recent work in the field of protein diffusion probabilistic modelling has leveraged Normal Mode Analysis (NMA) and, for the first time, introduced information about large scale protein motion into the generative process. However, obtaining molecules with both the desired dynamics and designable quality has proven challenging. In this work, we present NMA-tune, a new method that introduces the dynamics information to the protein design stage. NMA-tune uses a trainable component to condition the backbone generation on the lowest normal mode of oscillation. We implement NMA-tune as a plug-and-play extension to RFdiffusion, show that the proportion of samples with high quality structure and the desired dynamics is improved as compared to other methods without the trainable component, and we show the presence of the targeted modes in the Molecular Dynamics simulations.

ICML Conference 2025 Conference Paper

SPHINX: Structural Prediction using Hypergraph Inference Network

  • Iulia Duta
  • Pietro Liò

The importance of higher-order relations is widely recognized in numerous real-world systems. However, annotating them is a tedious and sometimes even impossible task. Consequently, current approaches for data modelling either ignore the higher-order interactions altogether or simplify them into pairwise connections. To facilitate higher-order processing, even when a hypergraph structure is not available, we introduce SPHINX, a model that learns to infer a latent hypergraph structure in an unsupervised way, solely from the final task-dependent signal. To ensure broad applicability, we design the model to be end-to-end differentiable, capable of generating a discrete hypergraph structure compatible with any modern hypergraph networks, and easily optimizable without requiring additional regularization losses. Through extensive ablation studies and experiments conducted on four challenging datasets, we demonstrate that our model is capable of inferring suitable latent hypergraphs in both transductive and inductive tasks. Moreover, the inferred latent hypergraphs are interpretable and contribute to enhancing the final performance, outperforming existing methods for hypergraph prediction.

ICML Conference 2025 Conference Paper

Stochastic Encodings for Active Feature Acquisition

  • Alexander Luke Ian Norcliffe
  • Changhee Lee
  • Fergus Imrie
  • Mihaela van der Schaar
  • Pietro Liò

Active Feature Acquisition is an instance-wise, sequential decision making problem. The aim is to dynamically select which feature to measure based on current observations, independently for each test instance. Common approaches either use Reinforcement Learning, which experiences training difficulties, or greedily maximize the conditional mutual information of the label and unobserved features, which makes myopic acquisitions. To address these shortcomings, we introduce a latent variable model, trained in a supervised manner. Acquisitions are made by reasoning about the features across many possible unobserved realizations in a stochastic latent space. Extensive evaluation on a large range of synthetic and real datasets demonstrates that our approach reliably outperforms a diverse set of baselines.

ICLR Conference 2025 Conference Paper

SynFlowNet: Design of Diverse and Novel Molecules with Synthesis Constraints

  • Miruna T. Cretu
  • Charles Harris
  • Ilia Igashov
  • Arne Schneuing
  • Marwin H. S. Segler
  • Bruno E. Correia
  • Julien Roy
  • Emmanuel Bengio

Generative models see increasing use in computer-aided drug design. However, while performing well at capturing distributions of molecular motifs, they often produce synthetically inaccessible molecules. To address this, we introduce SynFlowNet, a GFlowNet model whose action space uses chemical reactions and buyable reactants to sequentially build new molecules. By incorporating forward synthesis as an explicit constraint of the generative mechanism, we aim at bridging the gap between in silico molecular generation and real world synthesis capabilities. We evaluate our approach using synthetic accessibility scores and an independent retrosynthesis tool to assess the synthesizability of our compounds, and motivate the choice of GFlowNets through considerable improvement in sample diversity compared to baselines. Additionally, we identify challenges with reaction encodings that can complicate traversal of the MDP in the backward direction. To address this, we introduce various strategies for learning the GFlowNet backward policy and thus demonstrate how additional constraints can be integrated into the GFlowNet MDP framework. This approach enables our model to successfully identify synthesis pathways for previously unseen molecules.

ICLR Conference 2025 Conference Paper

Uncertainty Modeling in Graph Neural Networks via Stochastic Differential Equations

  • Richard Bergna
  • Sergio Calvo-Ordoñez
  • Felix L. Opolka
  • Pietro Liò
  • José Miguel Hernández-Lobato

We propose a novel Stochastic Differential Equation (SDE) framework to address the problem of learning uncertainty-aware representations for graph-structured data. While Graph Neural Ordinary Differential Equations (GNODEs) have shown promise in learning node representations, they lack the ability to quantify uncertainty. To address this, we introduce Latent Graph Neural Stochastic Differential Equations (LGNSDE), which enhance GNODE by embedding randomness through a Bayesian prior-posterior mechanism for epistemic uncertainty and Brownian motion for aleatoric uncertainty. By leveraging the existence and uniqueness of solutions to graph-based SDEs, we prove that the variance of the latent space bounds the variance of model outputs, thereby providing theoretically sensible guarantees for the uncertainty estimates. Furthermore, we show mathematically that LGNSDEs are robust to small perturbations in the input, maintaining stability over time. Empirical results across several benchmarks demonstrate that our framework is competitive in out-of-distribution detection, robustness to noise perturbations, and active learning, underscoring the ability of LGNSDEs to quantify uncertainty reliably.

AAAI Conference 2025 Conference Paper

When Hypergraph Meets Heterophily: New Benchmark Datasets and Baseline

  • Ming Li
  • Yongchun Gu
  • Yi Wang
  • Yujie Fang
  • Lu Bai
  • Xiaosheng Zhuang
  • Pietro Liò

Hypergraph neural networks (HNNs) have shown promise in handling tasks characterized by high-order correlations, achieving notable success across various applications. However, there has been limited focus on heterophilic hypergraph learning (HHL), in contrast to the increasing attention given to graph neural networks designed for graphs exhibiting heterophily. This paper aims to pave the way for HHL by addressing key gaps from multiple perspectives: measurement, dataset diversity, and baseline model development. First, we introduce metrics to quantify heterophily in hypergraphs, providing a numerical basis for assessing the homophily/heterophily ratio. Second, we develop diverse benchmark datasets across various real-world scenarios, facilitating comprehensive evaluations of existing HNNs and advancing research in HHL. Additionally, as a novel baseline model, we propose HyperUFG, a framelet-based HNN integrating both low-pass and high-pass filters. Extensive experiments conducted on synthetic and benchmark datasets highlight the challenges current HNNs face with heterophilic hypergraphs, while showcasing that HyperUFG performs competitively and often outperforms many existing models in such scenarios. Overall, our study underscores the urgent need for further exploration and development in this emerging field, with the potential to inspire and guide future research in HHL.

NeurIPS Conference 2024 Conference Paper

Deep Equilibrium Algorithmic Reasoning

  • Dobrik Georgiev
  • JJ Wilson
  • Davide Buffelli
  • Pietro Liò

Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of the GNN matches an iteration of the algorithm. In this paper we study neurally solving algorithms from a different perspective: since the algorithm’s solution is often an equilibrium, it is possible to find the solution directly by solving an equilibrium equation. Our approach requires no information on the ground-truth number of steps of the algorithm, both during train and test time. Furthermore, the proposed method improves the performance of GNNs on executing algorithms and is a step towards speeding up existing NAR models. Our empirical evidence, leveraging algorithms from the CLRS-30 benchmark, validates that one can train a network to solve algorithmic problems by directly finding the equilibrium. We discuss the practical implementation of such models and propose regularisations to improve the performance of these equilibrium reasoners.

ICLR Conference 2024 Conference Paper

Dynamics-Informed Protein Design with Structure Conditioning

  • Urszula Julia Komorowska
  • Simon V. Mathis
  • Kieran Didi
  • Francisco Vargas 0001
  • Pietro Liò
  • Mateja Jamnik

Current protein generative models are able to design novel backbones with desired shapes or functional motifs. However, despite the importance of a protein’s dynamical properties for its function, conditioning on dynamical properties remains elusive. We present a new approach to protein generative modeling by leveraging Normal Mode Analysis that enables us to capture dynamical properties too. We introduce a method for conditioning the diffusion probabilistic models on protein dynamics, specifically on the lowest non-trivial normal mode of oscillation. Our method, similar to the classifier guidance conditioning, formulates the sampling process as being driven by conditional and unconditional terms. However, unlike previous works, we approximate the conditional term with a simple analytical function rather than an external neural network, thus making the eigenvector calculations approachable. We present the corresponding SDE theory as a formal justification of our approach. We extend our framework to conditioning on structure and dynamics at the same time, enabling scaffolding of the dynamical motifs. We demonstrate the empirical effectiveness of our method by turning the open-source unconditional protein diffusion model Genie into the conditional model with no retraining. Generated proteins exhibit the desired dynamical and structural properties while still being biologically plausible. Our work represents a first step towards incorporating dynamical behaviour in protein design and may open the door to designing more flexible and functional proteins in the future.

ECAI Conference 2024 Conference Paper

Enhancing Node Representations for Real-World Complex Networks with Topological Augmentation

  • Xiangyu Zhao
  • Zehui Li
  • Mingzhu Shen
  • Guy-Bart Stan
  • Pietro Liò
  • Yiren Zhao

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.

ICLR Conference 2024 Conference Paper

Evaluating Representation Learning on the Protein Structure Universe

  • Arian Rokkum Jamasb
  • Alex Morehead
  • Chaitanya K. Joshi
  • Zuobai Zhang
  • Kieran Didi
  • Simon V. Mathis
  • Charles Harris
  • Jian Tang 0005

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.

ICML Conference 2024 Conference Paper

How Universal Polynomial Bases Enhance Spectral Graph Neural Networks: Heterophily, Over-smoothing, and Over-squashing

  • Keke Huang
  • Yu Guang Wang 0001
  • Ming Li 0065
  • Pietro Liò

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 datasets with a diverse range of heterophily, support the superiority of UniBasis in the universality but also its proficiency in graph explanation.

ICML Conference 2024 Conference Paper

Position: Topological Deep Learning is the New Frontier for Relational Learning

  • Theodore Papamarkou
  • Tolga Birdal
  • Michael M. Bronstein
  • Gunnar E. Carlsson
  • Justin Curry
  • Yue Gao
  • Mustafa Hajij
  • Roland Kwitt

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.

ICLR Conference 2024 Conference Paper

Unsupervised Pretraining for Fact Verification by Language Model Distillation

  • Adrián Bazaga
  • Pietro Liò
  • Gos Micklem

Fact verification aims to verify a claim using evidence from a trustworthy knowledge base. To address this challenge, algorithms must produce features for every claim that are both semantically meaningful, and compact enough to find a semantic alignment with the source information. In contrast to previous work, which tackled the alignment problem by learning over annotated corpora of claims and their corresponding labels, we propose SFAVEL ($\underline{S}$elf-supervised $\underline{Fa}$ct $\underline{Ve}$rification via $\underline{L}$anguage Model Distillation), a novel unsupervised pretraining framework that leverages pre-trained language models to distil self-supervised features into high-quality claim-fact alignments without the need for annotations. This is enabled by a novel contrastive loss function that encourages features to attain high-quality claim and evidence alignments whilst preserving the semantic relationships across the corpora. Notably, we present results that achieve a new state-of-the-art on FB15k-237 (+5.3\% Hits@1) and FEVER (+8\% accuracy) with linear evaluation.

AAAI Conference 2023 Conference Paper

Global Concept-Based Interpretability for Graph Neural Networks via Neuron Analysis

  • Han Xuanyuan
  • Pietro Barbiero
  • Dobrik Georgiev
  • Lucie Charlotte Magister
  • Pietro Liò

Graph neural networks (GNNs) are highly effective on a variety of graph-related tasks; however, they lack interpretability and transparency. Current explainability approaches are typically local and treat GNNs as black-boxes. They do not look inside the model, inhibiting human trust in the model and explanations. Motivated by the ability of neurons to detect high-level semantic concepts in vision models, we perform a novel analysis on the behaviour of individual GNN neurons to answer questions about GNN interpretability. We propose a novel approach for producing global explanations for GNNs using neuron-level concepts to enable practitioners to have a high-level view of the model. Specifically, (i) to the best of our knowledge, this is the first work which shows that GNN neurons act as concept detectors and have strong alignment with concepts formulated as logical compositions of node degree and neighbourhood properties; (ii) we quantitatively assess the importance of detected concepts, and identify a trade-off between training duration and neuron-level interpretability; (iii) we demonstrate that our global explainability approach has advantages over the current state-of-the-art -- we can disentangle the explanation into individual interpretable concepts backed by logical descriptions, which reduces potential for bias and improves user-friendliness.

ICLR Conference 2023 Conference Paper

Global Explainability of GNNs via Logic Combination of Learned Concepts

  • Steve Azzolin
  • Antonio Longa
  • Pietro Barbiero
  • Pietro Liò
  • Andrea Passerini

While instance-level explanation of GNN is a well-studied problem with plenty of approaches being developed, providing a global explanation for the behaviour of a GNN is much less explored, despite its potential in interpretability and debugging. Existing solutions either simply list local explanations for a given class, or generate a synthetic prototypical graph with maximal score for a given class, completely missing any combinatorial aspect that the GNN could have learned. In this work, we propose GLGExplainer (Global Logic-based GNN Explainer), the first Global Explainer capable of generating explanations as arbitrary Boolean combinations of learned graphical concepts. GLGExplainer is a fully differentiable architecture that takes local explanations as inputs and combines them into a logic formula over graphical concepts, represented as clusters of local explanations. Contrary to existing solutions, GLGExplainer provides accurate and human-interpretable global explanations that are perfectly aligned with ground-truth explanations (on synthetic data) or match existing domain knowledge (on real-world data). Extracted formulas are faithful to the model predictions, to the point of providing insights into some occasionally incorrect rules learned by the model, making GLGExplainer a promising diagnostic tool for learned GNNs.

UAI Conference 2023 Conference Paper

Graph classification Gaussian processes via spectral features

  • Felix L. Opolka
  • Yin-Cong Zhi
  • Pietro Liò
  • Xiaowen Dong 0001

Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features, which we then use to design two variants of Gaussian process models for graph classification. The first variant uses spectral features based on the distribution of energy of a node feature signal over the spectrum of the graph. We show that even such a simple approach, having no learned parameters, can yield competitive performance compared to strong neural network and graph kernel baselines. A second, more sophisticated variant is designed to capture multi-scale and localised patterns in the graph by learning spectral graph wavelet filters, obtaining improved performance on synthetic and real-world data sets. Finally, we show that both models produce well calibrated uncertainty estimates, enabling reliable decision making based on the model predictions.

NeSy Conference 2023 Conference Paper

Interpretable Neural-Symbolic Concept Reasoning

  • Pietro Barbiero
  • Gabriele Ciravegna
  • Francesco Giannini
  • Mateo Espinosa Zarlenga
  • Lucie Charlotte Magister
  • Alberto Tonda
  • Pietro Liò
  • Frédéric Precioso

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w. r. t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

ICML Conference 2023 Conference Paper

Interpretable Neural-Symbolic Concept Reasoning

  • Pietro Barbiero
  • Gabriele Ciravegna
  • Francesco Giannini
  • Mateo Espinosa Zarlenga
  • Lucie Charlotte Magister
  • Alberto Tonda
  • Pietro Liò
  • Frédéric Precioso

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w. r. t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

ICLR Conference 2023 Conference Paper

Latent Graph Inference using Product Manifolds

  • Haitz Sáez de Ocáriz Borde
  • Anees Kazi
  • Federico Barbero
  • Pietro Liò

Graph Neural Networks usually rely on the assumption that the graph topology is available to the network as well as optimal for the downstream task. Latent graph inference allows models to dynamically learn the intrinsic graph structure of problems where the connectivity patterns of data may not be directly accessible. In this work, we generalize the discrete Differentiable Graph Module (dDGM) for latent graph learning. The original dDGM architecture used the Euclidean plane to encode latent features based on which the latent graphs were generated. By incorporating Riemannian geometry into the model and generating more complex embedding spaces, we can improve the performance of the latent graph inference system. In particular, we propose a computationally tractable approach to produce product manifolds of constant curvature model spaces that can encode latent features of varying structure. The latent representations mapped onto the inferred product manifold are used to compute richer similarity measures that are leveraged by the latent graph learning model to obtain optimized latent graphs. Moreover, the curvature of the product manifold is learned during training alongside the rest of the network parameters and based on the downstream task, rather than it being a static embedding space. Our novel approach is tested on a wide range of datasets, and outperforms the original dDGM model.

NeSy Conference 2023 Conference Paper

Logic Explained Networks

  • Gabriele Ciravegna
  • Pietro Barbiero
  • Francesco Giannini
  • Marco Gori
  • Pietro Liò
  • Marco Maggini
  • Stefano Melacci

The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations in which the machine is expected to support the decision of human experts, providing a comprehensible explanation is a feature of crucial importance. The language used to communicate the explanations must be formal enough to be implementable in a machine and friendly enough to be understandable by a wide audience. In this paper, we propose a general approach to Explainable Artificial Intelligence in the case of neural architectures, showing how a mindful design of the networks leads to a family of interpretable deep learning models called Logic Explained Networks (LENs). LENs only require their inputs to be human-understandable predicates, and they provide explanations in terms of simple First-Order Logic (FOL) formulas involving such predicates. LENs are general enough to cover a large number of scenarios. Amongst them, we consider the case in which LENs are directly used as special classifiers with the capability of being explainable, or when they act as additional networks with the role of creating the conditions for making a black-box classifier explainable by FOL formulas. Despite supervised learning problems are mostly emphasized, we also show that LENs can learn and provide explanations in unsupervised learning settings. Experimental results on several datasets and tasks show that LENs may yield better classifications than established white-box models, such as decision trees and Bayesian rule lists, while providing more compact and meaningful explanations.

AIJ Journal 2023 Journal Article

Logic Explained Networks

  • Gabriele Ciravegna
  • Pietro Barbiero
  • Francesco Giannini
  • Marco Gori
  • Pietro Liò
  • Marco Maggini
  • Stefano Melacci

The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations in which the machine is expected to support the decision of human experts, providing a comprehensible explanation is a feature of crucial importance. The language used to communicate the explanations must be formal enough to be implementable in a machine and friendly enough to be understandable by a wide audience. In this paper, we propose a general approach to Explainable Artificial Intelligence in the case of neural architectures, showing how a mindful design of the networks leads to a family of interpretable deep learning models called Logic Explained Networks (LENs). LENs only require their inputs to be human-understandable predicates, and they provide explanations in terms of simple First-Order Logic (FOL) formulas involving such predicates. LENs are general enough to cover a large number of scenarios. Amongst them, we consider the case in which LENs are directly used as special classifiers with the capability of being explainable, or when they act as additional networks with the role of creating the conditions for making a black-box classifier explainable by FOL formulas. Despite supervised learning problems are mostly emphasized, we also show that LENs can learn and provide explanations in unsupervised learning settings. Experimental results on several datasets and tasks show that LENs may yield better classifications than established white-box models, such as decision trees and Bayesian rule lists, while providing more compact and meaningful explanations.

ICML Conference 2023 Conference Paper

On Over-Squashing in Message Passing Neural Networks: The Impact of Width, Depth, and Topology

  • Francesco Di Giovanni
  • Lorenzo Giusti
  • Federico Barbero
  • Giulia Luise
  • Pietro Liò
  • Michael M. Bronstein

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

ICML Conference 2023 Conference Paper

On the Expressive Power of Geometric Graph Neural Networks

  • Chaitanya K. Joshi
  • Cristian Bodnar
  • Simon V. Mathis
  • Taco Cohen
  • Pietro Liò

The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in Euclidean space, such as biomolecules, materials, and other physical systems. In this work, we propose a geometric version of the WL test (GWL) for discriminating geometric graphs while respecting the underlying physical symmetries: permutations, rotation, reflection, and translation. We use GWL to characterise the expressive power of geometric GNNs that are invariant or equivariant to physical symmetries in terms of distinguishing geometric graphs. GWL unpacks how key design choices influence geometric GNN expressivity: (1) Invariant layers have limited expressivity as they cannot distinguish one-hop identical geometric graphs; (2) Equivariant layers distinguish a larger class of graphs by propagating geometric information beyond local neighbourhoods; (3) Higher order tensors and scalarisation enable maximally powerful geometric GNNs; and (4) GWL’s discrimination-based perspective is equivalent to universal approximation. Synthetic experiments supplementing our results are available at https: //github. com/chaitjo/geometric-gnn-dojo

AAAI Conference 2023 Conference Paper

Weight Predictor Network with Feature Selection for Small Sample Tabular Biomedical Data

  • Andrei Margeloiu
  • Nikola Simidjievski
  • Pietro Liò
  • Mateja Jamnik

Tabular biomedical data is often high-dimensional but with a very small number of samples. Although recent work showed that well-regularised simple neural networks could outperform more sophisticated architectures on tabular data, they are still prone to overfitting on tiny datasets with many potentially irrelevant features. To combat these issues, we propose Weight Predictor Network with Feature Selection (WPFS) for learning neural networks from high-dimensional and small sample data by reducing the number of learnable parameters and simultaneously performing feature selection. In addition to the classification network, WPFS uses two small auxiliary networks that together output the weights of the first layer of the classification model. We evaluate on nine real-world biomedical datasets and demonstrate that WPFS outperforms other standard as well as more recent methods typically applied to tabular data. Furthermore, we investigate the proposed feature selection mechanism and show that it improves performance while providing useful insights into the learning task.

ICML Conference 2022 Conference Paper

3D Infomax improves GNNs for Molecular Property Prediction

  • Hannes Stärk
  • Dominique Beaini
  • Gabriele Corso
  • Prudencio Tossou
  • Christian Dallago
  • Stephan Günnemann
  • Pietro Liò

Molecular property prediction is one of the fastest-growing applications of deep learning with critical real-world impacts. Although the 3D molecular graph structure is necessary for models to achieve strong performance on many tasks, it is infeasible to obtain 3D structures at the scale required by many real-world applications. To tackle this issue, we propose to use existing 3D molecular datasets to pre-train a model to reason about the geometry of molecules given only their 2D molecular graphs. Our method, called 3D Infomax, maximizes the mutual information between learned 3D summary vectors and the representations of a graph neural network (GNN). During fine-tuning on molecules with unknown geometry, the GNN is still able to produce implicit 3D information and uses it for downstream tasks. We show that 3D Infomax provides significant improvements for a wide range of properties, including a 22% average MAE reduction on QM9 quantum mechanical properties. Moreover, the learned representations can be effectively transferred between datasets in different molecular spaces.

ICML Conference 2022 Conference Paper

Attentional Meta-learners for Few-shot Polythetic Classification

  • Ben J. Day
  • Ramón Viñas Torné 0001
  • Nikola Simidjievski
  • Pietro Liò

Polythetic classifications, based on shared patterns of features that need neither be universal nor constant among members of a class, are common in the natural world and greatly outnumber monothetic classifications over a set of features. We show that threshold meta-learners, such as Prototypical Networks, require an embedding dimension that is exponential in the number of task-relevant features to emulate these functions. In contrast, attentional classifiers, such as Matching Networks, are polythetic by default and able to solve these problems with a linear embedding dimension. However, we find that in the presence of task-irrelevant features, inherent to meta-learning problems, attentional models are susceptible to misclassification. To address this challenge, we propose a self-attention feature-selection mechanism that adaptively dilutes non-discriminative features. We demonstrate the effectiveness of our approach in meta-learning Boolean functions, and synthetic and real-world few-shot learning tasks.

ICLR Conference 2022 Conference Paper

Do We Need Anisotropic Graph Neural Networks?

  • Shyam A. Tailor
  • Felix L. Opolka
  • Pietro Liò
  • Nicholas Donald Lane

Common wisdom in the graph neural network (GNN) community dictates that anisotropic models---in which messages sent between nodes are a function of both the source and target node---are required to achieve state-of-the-art performance. Benchmarks to date have demonstrated that these models perform better than comparable isotropic models---where messages are a function of the source node only. In this work we provide empirical evidence challenging this narrative: we propose an isotropic GNN, which we call Efficient Graph Convolution (EGC), that consistently outperforms comparable anisotropic models, including the popular GAT or PNA architectures by using spatially-varying adaptive filters. In addition to raising important questions for the GNN community, our work has significant real-world implications for efficiency. EGC achieves higher model accuracy, with lower memory consumption and latency, along with characteristics suited to accelerator implementation, while being a drop-in replacement for existing architectures. As an isotropic model, it requires memory proportional to the number of vertices in the graph ($\mathcal{O}(V)$); in contrast, anisotropic models require memory proportional to the number of edges ($\mathcal{O}(E)$). We demonstrate that EGC outperforms existing approaches across 6 large and diverse benchmark datasets, and conclude by discussing questions that our work raise for the community going forward. Code and pretrained models for our experiments are provided at https://github.com/shyam196/egc.

NeurIPS Conference 2022 Conference Paper

Graph Neural Networks with Adaptive Readouts

  • David Buterez
  • Jon Paul Janet
  • Steven J Kiddle
  • Dino Oglic
  • Pietro Liò

An effective aggregation of node features into a graph-level representation via readout functions is an essential step in numerous learning tasks involving graph neural networks. Typically, readouts are simple and non-adaptive functions designed such that the resulting hypothesis space is permutation invariant. Prior work on deep sets indicates that such readouts might require complex node embeddings that can be difficult to learn via standard neighborhood aggregation schemes. Motivated by this, we investigate the potential of adaptive readouts given by neural networks that do not necessarily give rise to permutation invariant hypothesis spaces. We argue that in some problems such as binding affinity prediction where molecules are typically presented in a canonical form it might be possible to relax the constraints on permutation invariance of the hypothesis space and learn a more effective model of the affinity by employing an adaptive readout function. Our empirical results demonstrate the effectiveness of neural readouts on more than 40 datasets spanning different domains and graph characteristics. Moreover, we observe a consistent improvement over standard readouts (i. e. , sum, max, and mean) relative to the number of neighborhood aggregation iterations and different convolutional operators.

ICML Conference 2021 Conference Paper

Directional Graph Networks

  • Dominique Beaini
  • Saro Passaro
  • Vincent Létourneau
  • William L. Hamilton
  • Gabriele Corso
  • Pietro Liò

The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then, we propose the use of the Laplacian eigenvectors as such vector field. We show that the method generalizes CNNs on an $n$-dimensional grid and is provably more discriminative than standard GNNs regarding the Weisfeiler-Lehman 1-WL test. We evaluate our method on different standard benchmarks and see a relative error reduction of 8% on the CIFAR10 graph dataset and 11% to 32% on the molecular ZINC dataset, and a relative increase in precision of 1.6% on the MolPCBA dataset. An important outcome of this work is that it enables graph networks to embed directions in an unsupervised way, thus allowing a better representation of the anisotropic features in different physical or biological problems.

ICML Conference 2021 Conference Paper

How Framelets Enhance Graph Neural Networks

  • Xuebin Zheng
  • Bingxin Zhou
  • Junbin Gao
  • Yu Guang Wang 0001
  • Pietro Liò
  • Ming Li 0065
  • Guido Montúfar

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. We decompose an input graph into low-pass and high-pass frequencies coefficients for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds high-frequency information at different scales. Compared to ReLU, shrinkage activation improves model performance on denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with well-preserved prediction performance.

NeurIPS Conference 2021 Conference Paper

Neural Distance Embeddings for Biological Sequences

  • Gabriele Corso
  • Zhitao Ying
  • Michal Pándy
  • Petar Veličković
  • Jure Leskovec
  • Pietro Liò

The development of data-dependent heuristics and representations for biological sequences that reflect their evolutionary distance is critical for large-scale biological research. However, popular machine learning approaches, based on continuous Euclidean spaces, have struggled with the discrete combinatorial formulation of the edit distance that models evolution and the hierarchical relationship that characterises real-world datasets. We present Neural Distance Embeddings (NeuroSEED), a general framework to embed sequences in geometric vector spaces, and illustrate the effectiveness of the hyperbolic space that captures the hierarchical structure and provides an average 38% reduction in embedding RMSE against the best competing geometry. The capacity of the framework and the significance of these improvements are then demonstrated devising supervised and unsupervised NeuroSEED approaches to multiple core tasks in bioinformatics. Benchmarked with common baselines, the proposed approaches display significant accuracy and/or runtime improvements on real-world datasets. As an example for hierarchical clustering, the proposed pretrained and from-scratch methods match the quality of competing baselines with 30x and 15x runtime reduction, respectively.

ICLR Conference 2021 Conference Paper

Neural ODE Processes

  • Alexander Luke Ian Norcliffe
  • Cristian Bodnar
  • Ben J. Day
  • Jacob Moss
  • Pietro Liò

Neural Ordinary Differential Equations (NODEs) use a neural network to model the instantaneous rate of change in the state of a system. However, despite their apparent suitability for dynamics-governed time-series, NODEs present a few disadvantages. First, they are unable to adapt to incoming data-points, a fundamental requirement for real-time applications imposed by the natural direction of time. Second, time-series are often composed of a sparse set of measurements that could be explained by many possible underlying dynamics. NODEs do not capture this uncertainty. In contrast, Neural Processes (NPs) are a new class of stochastic processes providing uncertainty estimation and fast data-adaptation, but lack an explicit treatment of the flow of time. To address these problems, we introduce Neural ODE Processes (NDPs), a new class of stochastic processes determined by a distribution over Neural ODEs. By maintaining an adaptive data-dependent distribution over the underlying ODE, we show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points. At the same time, we demonstrate that NDPs scale up to challenging high-dimensional time-series with unknown latent dynamics such as rotating MNIST digits.

NeurIPS Conference 2021 Conference Paper

Weisfeiler and Lehman Go Cellular: CW Networks

  • Cristian Bodnar
  • Fabrizio Frasca
  • Nina Otter
  • Yuguang Wang
  • Pietro Liò
  • Guido F. Montufar
  • Michael Bronstein

Graph Neural Networks (GNNs) are limited in their expressive power, struggle with long-range interactions and lack a principled way to model higher-order structures. These problems can be attributed to the strong coupling between the computational graph and the input graph structure. The recently proposed Message Passing Simplicial Networks naturally decouple these elements by performing message passing on the clique complex of the graph. Nevertheless, these models can be severely constrained by the rigid combinatorial structure of Simplicial Complexes (SCs). In this work, we extend recent theoretical results on SCs to regular Cell Complexes, topological objects that flexibly subsume SCs and graphs. We show that this generalisation provides a powerful set of graph "lifting" transformations, each leading to a unique hierarchical message passing procedure. The resulting methods, which we collectively call CW Networks (CWNs), are strictly more powerful than the WL test and not less powerful than the 3-WL test. In particular, we demonstrate the effectiveness of one such scheme, based on rings, when applied to molecular graph problems. The proposed architecture benefits from provably larger expressivity than commonly used GNNs, principled modelling of higher-order signals and from compressing the distances between nodes. We demonstrate that our model achieves state-of-the-art results on a variety of molecular datasets.

ICML Conference 2021 Conference Paper

Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networks

  • Cristian Bodnar
  • Fabrizio Frasca
  • Yu Guang Wang 0001
  • Nina Otter
  • Guido Montúfar
  • Pietro Liò
  • Michael M. Bronstein

The pairwise interaction paradigm of graph machine learning has predominantly governed the modelling of relational systems. However, graphs alone cannot capture the multi-level interactions present in many complex systems and the expressive power of such schemes was proven to be limited. To overcome these limitations, we propose Message Passing Simplicial Networks (MPSNs), a class of models that perform message passing on simplicial complexes (SCs). To theoretically analyse the expressivity of our model we introduce a Simplicial Weisfeiler-Lehman (SWL) colouring procedure for distinguishing non-isomorphic SCs. We relate the power of SWL to the problem of distinguishing non-isomorphic graphs and show that SWL and MPSNs are strictly more powerful than the WL test and not less powerful than the 3-WL test. We deepen the analysis by comparing our model with traditional graph neural networks (GNNs) with ReLU activations in terms of the number of linear regions of the functions they can represent. We empirically support our theoretical claims by showing that MPSNs can distinguish challenging strongly regular graphs for which GNNs fail and, when equipped with orientation equivariant layers, they can improve classification accuracy in oriented SCs compared to a GNN baseline.

ICLR Conference 2020 Conference Paper

Abstract Diagrammatic Reasoning with Multiplex Graph Networks

  • Duo Wang
  • Mateja Jamnik
  • Pietro Liò

Abstract reasoning, particularly in the visual domain, is a complex human ability, but it remains a challenging problem for artificial neural learning systems. In this work we propose MXGNet, a multilayer graph neural network for multi-panel diagrammatic reasoning tasks. MXGNet combines three powerful concepts, namely, object-level representation, graph neural networks and multiplex graphs, for solving visual reasoning tasks. MXGNet first extracts object-level representations for each element in all panels of the diagrams, and then forms a multi-layer multiplex graph capturing multiple relations between objects across different diagram panels. MXGNet summarises the multiple graphs extracted from the diagrams of the task, and uses this summarisation to pick the most probable answer from the given candidates. We have tested MXGNet on two types of diagrammatic reasoning tasks, namely Diagram Syllogisms and Raven Progressive Matrices (RPM). For an Euler Diagram Syllogism task MXGNet achieves state-of-the-art accuracy of 99.8%. For PGM and RAVEN, two comprehensive datasets for RPM reasoning, MXGNet outperforms the state-of-the-art models by a considerable margin.

NeurIPS Conference 2020 Conference Paper

Path Integral Based Convolution and Pooling for Graph Neural Networks

  • Zheng Ma
  • Junyu Xuan
  • Yu Guang Wang
  • Ming Li
  • Pietro Liò

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call \emph{maximal entropy transition} (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus lead to a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.

NeurIPS Conference 2020 Conference Paper

Principal Neighbourhood Aggregation for Graph Nets

  • Gabriele Corso
  • Luca Cavalleri
  • Dominique Beaini
  • Pietro Liò
  • Petar Veličković

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features---which occur regularly in real-world input domains and within the hidden layers of GNNs---and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

YNIMG Journal 2019 Journal Article

A parameter-efficient deep learning approach to predict conversion from mild cognitive impairment to Alzheimer's disease

  • Simeon Spasov
  • Luca Passamonti
  • Andrea Duggento
  • Pietro Liò
  • Nicola Toschi

Some forms of mild cognitive impairment (MCI) are the clinical precursors of Alzheimer's disease (AD), while other MCI types tend to remain stable over-time and do not progress to AD. To identify and choose effective and personalized strategies to prevent or slow the progression of AD, we need to develop objective measures that are able to discriminate the MCI patients who are at risk of AD from those MCI patients who have less risk to develop AD. Here, we present a novel deep learning architecture, based on dual learning and an ad hoc layer for 3D separable convolutions, which aims at identifying MCI patients who have a high likelihood of developing AD within 3 years. Our deep learning procedures combine structural magnetic resonance imaging (MRI), demographic, neuropsychological, and APOe4 genetic data as input measures. The most novel characteristics of our machine learning model compared to previous ones are the following: 1) our deep learning model is multi-tasking, in the sense that it jointly learns to simultaneously predict both MCI to AD conversion as well as AD vs. healthy controls classification, which facilitates relevant feature extraction for AD prognostication; 2) the neural network classifier employs fewer parameters than other deep learning architectures which significantly limits data-overfitting (we use ∼550, 000 network parameters, which is orders of magnitude lower than other network designs); 3) both structural MRI images and their warp field characteristics, which quantify local volumetric changes in relation to the MRI template, were used as separate input streams to extract as much information as possible from the MRI data. All analyses were performed on a subset of the database made publicly available via the Alzheimer's Disease Neuroimaging Initiative (ADNI), (n = 785 participants, n = 192 AD patients, n = 409 MCI patients (including both MCI patients who convert to AD and MCI patients who do not covert to AD), and n = 184 healthy controls). The most predictive combination of inputs were the structural MRI images and the demographic, neuropsychological, and APOe4 data. In contrast, the warp field metrics were of little added predictive value. The algorithm was able to distinguish the MCI patients developing AD within 3 years from those patients with stable MCI over the same time-period with an area under the curve (AUC) of 0. 925 and a 10-fold cross-validated accuracy of 86%, a sensitivity of 87. 5%, and specificity of 85%. To our knowledge, this is the highest performance achieved so far using similar datasets. The same network provided an AUC of 1 and 100% accuracy, sensitivity, and specificity when classifying patients with AD from healthy controls. Our classification framework was also robust to the use of different co-registration templates and potentially irrelevant features/image portions. Our approach is flexible and can in principle integrate other imaging modalities, such as PET, and diverse other sets of clinical data. The convolutional framework is potentially applicable to any 3D image dataset and gives the flexibility to design a computer-aided diagnosis system targeting the prediction of several medical conditions and neuropsychiatric disorders via multi-modal imaging and tabular clinical data.

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