Píetro Lió

Xuan Zhang, Limei Wang, Jacob Helwig et al. · cambridge, mit

Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.

Chaitanya K. Joshi, Cristian Bodnar, Simon V. Mathis et al. · cambridge

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 \url{https://github.com/chaitjo/geometric-gnn-dojo}

Andrei Margeloiu, Nikola Simidjievski, Pietro Lio et al. · cambridge

Neural networks often struggle with high-dimensional but small sample-size tabular datasets. One reason is that current weight initialisation methods assume independence between weights, which can be problematic when there are insufficient samples to estimate the model's parameters accurately. In such small data scenarios, leveraging additional structures can improve the model's performance and training stability. To address this, we propose GCondNet, a general approach to enhance neural networks by leveraging implicit structures present in tabular data. We create a graph between samples for each data dimension, and utilise Graph Neural Networks (GNNs) to extract this implicit structure, and for conditioning the parameters of the first layer of an underlying predictor network. By creating many small graphs, GCondNet exploits the data's high-dimensionality, and thus improves the performance of an underlying predictor network. We demonstrate GCondNet's effectiveness on 12 real-world datasets, where it outperforms 14 standard and state-of-the-art methods. The results show that GCondNet is a versatile framework for injecting graph-regularisation into various types of neural networks, including MLPs and tabular Transformers. Code is available at https://github.com/andreimargeloiu/GCondNet.

Arne Schneuing, Charles Harris, Yuanqi Du et al.

Structure-based drug design (SBDD) aims to design small-molecule ligands that bind with high affinity and specificity to pre-determined protein targets. Generative SBDD methods leverage structural data of drugs in complex with their protein targets to propose new drug candidates. These approaches typically place one atom at a time in an autoregressive fashion using the binding pocket as well as previously added ligand atoms as context in each step. Recently a surge of diffusion generative models has entered this domain which hold promise to capture the statistical properties of natural ligands more faithfully. However, most existing methods focus exclusively on bottom-up de novo design of compounds or tackle other drug development challenges with task-specific models. The latter requires curation of suitable datasets, careful engineering of the models and retraining from scratch for each task. Here we show how a single pre-trained diffusion model can be applied to a broader range of problems, such as off-the-shelf property optimization, explicit negative design, and partial molecular design with inpainting. We formulate SBDD as a 3D-conditional generation problem and present DiffSBDD, an SE(3)-equivariant diffusion model that generates novel ligands conditioned on protein pockets. Our in silico experiments demonstrate that DiffSBDD captures the statistics of the ground truth data effectively. Furthermore, we show how additional constraints can be used to improve the generated drug candidates according to a variety of computational metrics. These results support the assumption that diffusion models represent the complex distribution of structural data more accurately than previous methods, and are able to incorporate additional design objectives and constraints changing nothing but the sampling strategy.

Niccolò Grillo, James Rowbottom, Pietro Liò et al.

Adaptive mesh refinement is central to the efficient solution of partial differential equations (PDEs) via the finite element method (FEM). Classical $r$-adaptivity optimizes vertex positions but requires solving expensive auxiliary PDEs such as the Monge-Ampère equation, while classical $h$-adaptivity modifies topology through element subdivision but suffers from expensive error indicator computation and is constrained by isotropic refinement patterns that impose accuracy ceilings. Combined $hr$-adaptive techniques naturally outperform single-modality approaches, yet inherit both computational bottlenecks and the restricted cost-accuracy trade-off. Emerging machine learning methods for adaptive mesh refinement seek to overcome these limitations, but existing approaches address $h$-adaptivity or $r$-adaptivity in isolation. We present HypeR, a deep reinforcement learning framework that jointly optimizes mesh relocation and refinement. HypeR casts the joint adaptation problem using tools from hypergraph neural networks and multi-agent reinforcement learning. Refinement is formulated as a heterogeneous multi-agent Markov decision process (MDP) where element agents decide discrete refinement actions, while relocation follows an anisotropic diffusion-based policy on vertex agents with provable prevention of mesh tangling. The reward function combines local and global error reduction to promote general accuracy. Across benchmark PDEs, HypeR reduces approximation error by up to 6--10$\times$ versus state-of-art $h$-adaptive baselines at comparable element counts, breaking through the uniform refinement accuracy ceiling that constrains subdivision-only methods. The framework produces meshes with improved shape metrics and alignment to solution anisotropy, demonstrating that jointly learned $hr$-adaptivity strategies can substantially enhance the capabilities of automated mesh generation.

Mehedi Hasan, Moloud Abdar, Abbas Khosravi et al.

Although neural networks (especially deep neural networks) have achieved \textit{better-than-human} performance in many fields, their real-world deployment is still questionable due to the lack of awareness about the limitation in their knowledge. To incorporate such awareness in the machine learning model, prediction with reject option (also known as selective classification or classification with abstention) has been proposed in literature. In this paper, we present a systematic review of the prediction with the reject option in the context of various neural networks. To the best of our knowledge, this is the first study focusing on this aspect of neural networks. Moreover, we discuss different novel loss functions related to the reject option and post-training processing (if any) of network output for generating suitable measurements for knowledge awareness of the model. Finally, we address the application of the rejection option in reducing the prediction time for the real-time problems and present a comprehensive summary of the techniques related to the reject option in the context of extensive variety of neural networks. Our code is available on GitHub: \url{https://github.com/MehediHasanTutul/Reject_option}

Lihao Liu, Jean Prost, Lei Zhu et al.

Shadows in videos are difficult to detect because of the large shadow deformation between frames. In this work, we argue that accounting for shadow deformation is essential when designing a video shadow detection method. To this end, we introduce the shadow deformation attention trajectory (SODA), a new type of video self-attention module, specially designed to handle the large shadow deformations in videos. Moreover, we present a new shadow contrastive learning mechanism (SCOTCH) which aims at guiding the network to learn a unified shadow representation from massive positive shadow pairs across different videos. We demonstrate empirically the effectiveness of our two contributions in an ablation study. Furthermore, we show that SCOTCH and SODA significantly outperforms existing techniques for video shadow detection. Code is available at the project page: https://lihaoliu-cambridge.github.io/scotch_and_soda/

Mateo Espinosa Zarlenga, Pietro Barbiero, Gabriele Ciravegna et al. · cambridge

Deploying AI-powered systems requires trustworthy models supporting effective human interactions, going beyond raw prediction accuracy. Concept bottleneck models promote trustworthiness by conditioning classification tasks on an intermediate level of human-like concepts. This enables human interventions which can correct mispredicted concepts to improve the model's performance. However, existing concept bottleneck models are unable to find optimal compromises between high task accuracy, robust concept-based explanations, and effective interventions on concepts -- particularly in real-world conditions where complete and accurate concept supervisions are scarce. To address this, we propose Concept Embedding Models, a novel family of concept bottleneck models which goes beyond the current accuracy-vs-interpretability trade-off by learning interpretable high-dimensional concept representations. Our experiments demonstrate that Concept Embedding Models (1) attain better or competitive task accuracy w.r.t. standard neural models without concepts, (2) provide concept representations capturing meaningful semantics including and beyond their ground truth labels, (3) support test-time concept interventions whose effect in test accuracy surpasses that in standard concept bottleneck models, and (4) scale to real-world conditions where complete concept supervisions are scarce.

Antonio Purificato, Giulia Cassarà, Federico Siciliano et al.

Recent advancements in Graph Neural Networks (GNN) have facilitated their widespread adoption in various applications, including recommendation systems. GNNs have proven to be effective in addressing the challenges posed by recommendation systems by efficiently modeling graphs in which nodes represent users or items and edges denote preference relationships. However, current GNN techniques represent nodes by means of a single static vector, which may inadequately capture the intricate complexities of users and items. To overcome these limitations, we propose a solution integrating a cutting-edge model inspired by category theory: Sheaf4Rec. Unlike single vector representations, Sheaf Neural Networks and their corresponding Laplacians represent each node (and edge) using a vector space. Our approach takes advantage from this theory and results in a more comprehensive representation that can be effectively exploited during inference, providing a versatile method applicable to a wide range of graph-related tasks and demonstrating unparalleled performance. Our proposed model exhibits a noteworthy relative improvement of up to 8.53% on F1-Score@10 and an impressive increase of up to 11.29% on NDCG@10, outperforming existing state-of-the-art models such as Neural Graph Collaborative Filtering (NGCF), KGTORe and other recently developed GNN-based models. In addition to its superior predictive capabilities, Sheaf4Rec shows remarkable improvements in terms of efficiency: we observe substantial runtime improvements ranging from 2.5% up to 37% when compared to other GNN-based competitor models, indicating a more efficient way of handling information while achieving better performance. Code is available at https://github.com/antoniopurificato/Sheaf4Rec.

Tolou Shadbahr, Michael Roberts, Jan Stanczuk et al.

Classifying samples in incomplete datasets is a common aim for machine learning practitioners, but is non-trivial. Missing data is found in most real-world datasets and these missing values are typically imputed using established methods, followed by classification of the now complete, imputed, samples. The focus of the machine learning researcher is then to optimise the downstream classification performance. In this study, we highlight that it is imperative to consider the quality of the imputation. We demonstrate how the commonly used measures for assessing quality are flawed and propose a new class of discrepancy scores which focus on how well the method recreates the overall distribution of the data. To conclude, we highlight the compromised interpretability of classifier models trained using poorly imputed data.

Md Shofiqul Islam, Khondokar Fida Hasan, Sunjida Sultana et al.

In this paper have developed a novel hybrid hierarchical attention-based bidirectional recurrent neural network with dilated CNN (HARDC) method for arrhythmia classification. This solves problems that arise when traditional dilated convolutional neural network (CNN) models disregard the correlation between contexts and gradient dispersion. The proposed HARDC fully exploits the dilated CNN and bidirectional recurrent neural network unit (BiGRU-BiLSTM) architecture to generate fusion features. As a result of incorporating both local and global feature information and an attention mechanism, the model's performance for prediction is improved.By combining the fusion features with a dilated CNN and a hierarchical attention mechanism, the trained HARDC model showed significantly improved classification results and interpretability of feature extraction on the PhysioNet 2017 challenge dataset. Sequential Z-Score normalization, filtering, denoising, and segmentation are used to prepare the raw data for analysis. CGAN (Conditional Generative Adversarial Network) is then used to generate synthetic signals from the processed data. The experimental results demonstrate that the proposed HARDC model significantly outperforms other existing models, achieving an accuracy of 99.60\%, F1 score of 98.21\%, a precision of 97.66\%, and recall of 99.60\% using MIT-BIH generated ECG. In addition, this approach substantially reduces run time when using dilated CNN compared to normal convolution. Overall, this hybrid model demonstrates an innovative and cost-effective strategy for ECG signal compression and high-performance ECG recognition. Our results indicate that an automated and highly computed method to classify multiple types of arrhythmia signals holds considerable promise.

Federico Barbero, Cristian Bodnar, Haitz Sáez de Ocáriz Borde et al. · cambridge

A Sheaf Neural Network (SNN) is a type of Graph Neural Network (GNN) that operates on a sheaf, an object that equips a graph with vector spaces over its nodes and edges and linear maps between these spaces. SNNs have been shown to have useful theoretical properties that help tackle issues arising from heterophily and over-smoothing. One complication intrinsic to these models is finding a good sheaf for the task to be solved. Previous works proposed two diametrically opposed approaches: manually constructing the sheaf based on domain knowledge and learning the sheaf end-to-end using gradient-based methods. However, domain knowledge is often insufficient, while learning a sheaf could lead to overfitting and significant computational overhead. In this work, we propose a novel way of computing sheaves drawing inspiration from Riemannian geometry: we leverage the manifold assumption to compute manifold-and-graph-aware orthogonal maps, which optimally align the tangent spaces of neighbouring data points. We show that this approach achieves promising results with less computational overhead when compared to previous SNN models. Overall, this work provides an interesting connection between algebraic topology and differential geometry, and we hope that it will spark future research in this direction.

Michal Pándy, Weikang Qiu, Gabriele Corso et al.

Searching for a path between two nodes in a graph is one of the most well-studied and fundamental problems in computer science. In numerous domains such as robotics, AI, or biology, practitioners develop search heuristics to accelerate their pathfinding algorithms. However, it is a laborious and complex process to hand-design heuristics based on the problem and the structure of a given use case. Here we present PHIL (Path Heuristic with Imitation Learning), a novel neural architecture and a training algorithm for discovering graph search and navigation heuristics from data by leveraging recent advances in imitation learning and graph representation learning. At training time, we aggregate datasets of search trajectories and ground-truth shortest path distances, which we use to train a specialized graph neural network-based heuristic function using backpropagation through steps of the pathfinding process. Our heuristic function learns graph embeddings useful for inferring node distances, runs in constant time independent of graph sizes, and can be easily incorporated in an algorithm such as A* at test time. Experiments show that PHIL reduces the number of explored nodes compared to state-of-the-art methods on benchmark datasets by 58.5\% on average, can be directly applied in diverse graphs ranging from biological networks to road networks, and allows for fast planning in time-critical robotics domains.

Aleksa Bisercic, Mladen Nikolic, Mihaela van der Schaar et al.

Tabular data is often hidden in text, particularly in medical diagnostic reports. Traditional machine learning (ML) models designed to work with tabular data, cannot effectively process information in such form. On the other hand, large language models (LLMs) which excel at textual tasks, are probably not the best tool for modeling tabular data. Therefore, we propose a novel, simple, and effective methodology for extracting structured tabular data from textual medical reports, called TEMED-LLM. Drawing upon the reasoning capabilities of LLMs, TEMED-LLM goes beyond traditional extraction techniques, accurately inferring tabular features, even when their names are not explicitly mentioned in the text. This is achieved by combining domain-specific reasoning guidelines with a proposed data validation and reasoning correction feedback loop. By applying interpretable ML models such as decision trees and logistic regression over the extracted and validated data, we obtain end-to-end interpretable predictions. We demonstrate that our approach significantly outperforms state-of-the-art text classification models in medical diagnostics. Given its predictive performance, simplicity, and interpretability, TEMED-LLM underscores the potential of leveraging LLMs to improve the performance and trustworthiness of ML models in medical applications.

Alexander Norcliffe, Bogdan Cebere, Fergus Imrie et al.

Synthetic data is becoming an increasingly promising technology, and successful applications can improve privacy, fairness, and data democratization. While there are many methods for generating synthetic tabular data, the task remains non-trivial and unexplored for specific scenarios. One such scenario is survival data. Here, the key difficulty is censoring: for some instances, we are not aware of the time of event, or if one even occurred. Imbalances in censoring and time horizons cause generative models to experience three new failure modes specific to survival analysis: (1) generating too few at-risk members; (2) generating too many at-risk members; and (3) censoring too early. We formalize these failure modes and provide three new generative metrics to quantify them. Following this, we propose SurvivalGAN, a generative model that handles survival data firstly by addressing the imbalance in the censoring and event horizons, and secondly by using a dedicated mechanism for approximating time-to-event/censoring. We evaluate this method via extensive experiments on medical datasets. SurvivalGAN outperforms multiple baselines at generating survival data, and in particular addresses the failure modes as measured by the new metrics, in addition to improving downstream performance of survival models trained on the synthetic data.

Andrei Margeloiu, Nikola Simidjievski, Pietro Lio et al. · cambridge

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.

Jiahao Huang, Yingying Fang, Yang Nan et al.

Research studies have shown no qualms about using data driven deep learning models for downstream tasks in medical image analysis, e.g., anatomy segmentation and lesion detection, disease diagnosis and prognosis, and treatment planning. However, deep learning models are not the sovereign remedy for medical image analysis when the upstream imaging is not being conducted properly (with artefacts). This has been manifested in MRI studies, where the scanning is typically slow, prone to motion artefacts, with a relatively low signal to noise ratio, and poor spatial and/or temporal resolution. Recent studies have witnessed substantial growth in the development of deep learning techniques for propelling fast MRI. This article aims to (1) introduce the deep learning based data driven techniques for fast MRI including convolutional neural network and generative adversarial network based methods, (2) survey the attention and transformer based models for speeding up MRI reconstruction, and (3) detail the research in coupling physics and data driven models for MRI acceleration. Finally, we will demonstrate through a few clinical applications, explain the importance of data harmonisation and explainable models for such fast MRI techniques in multicentre and multi-scanner studies, and discuss common pitfalls in current research and recommendations for future research directions.

Fergus Imrie, Alexander Norcliffe, Pietro Lio et al.

In many real world problems, features do not act alone but in combination with each other. For example, in genomics, diseases might not be caused by any single mutation but require the presence of multiple mutations. Prior work on feature selection either seeks to identify individual features or can only determine relevant groups from a predefined set. We investigate the problem of discovering groups of predictive features without predefined grouping. To do so, we define predictive groups in terms of linear and non-linear interactions between features. We introduce a novel deep learning architecture that uses an ensemble of feature selection models to find predictive groups, without requiring candidate groups to be provided. The selected groups are sparse and exhibit minimum overlap. Furthermore, we propose a new metric to measure similarity between discovered groups and the ground truth. We demonstrate the utility of our model on multiple synthetic tasks and semi-synthetic chemistry datasets, where the ground truth structure is known, as well as an image dataset and a real-world cancer dataset.

Christopher Wei Jin Goh, Cristian Bodnar, Pietro Liò · cambridge

Graph representation learning methods have mostly been limited to the modelling of node-wise interactions. Recently, there has been an increased interest in understanding how higher-order structures can be utilised to further enhance the learning abilities of graph neural networks (GNNs) in combinatorial spaces. Simplicial Neural Networks (SNNs) naturally model these interactions by performing message passing on simplicial complexes, higher-dimensional generalisations of graphs. Nonetheless, the computations performed by most existent SNNs are strictly tied to the combinatorial structure of the complex. Leveraging the success of attention mechanisms in structured domains, we propose Simplicial Attention Networks (SAT), a new type of simplicial network that dynamically weighs the interactions between neighbouring simplicies and can readily adapt to novel structures. Additionally, we propose a signed attention mechanism that makes SAT orientation equivariant, a desirable property for models operating on (co)chain complexes. We demonstrate that SAT outperforms existent convolutional SNNs and GNNs in two image and trajectory classification tasks.

Antonio Longa, Veronica Lachi, Gabriele Santin et al.

Graph Neural Networks (GNNs) have become the leading paradigm for learning on (static) graph-structured data. However, many real-world systems are dynamic in nature, since the graph and node/edge attributes change over time. In recent years, GNN-based models for temporal graphs have emerged as a promising area of research to extend the capabilities of GNNs. In this work, we provide the first comprehensive overview of the current state-of-the-art of temporal GNN, introducing a rigorous formalization of learning settings and tasks and a novel taxonomy categorizing existing approaches in terms of how the temporal aspect is represented and processed. We conclude the survey with a discussion of the most relevant open challenges for the field, from both research and application perspectives.

Xiaoyong Mei, Yi Yang, Ming Li et al.

Reference-based super-resolution (RefSR) has gained considerable success in the field of super-resolution with the addition of high-resolution reference images to reconstruct low-resolution (LR) inputs with more high-frequency details, thereby overcoming some limitations of single image super-resolution (SISR). Previous research in the field of RefSR has mostly focused on two crucial aspects. The first is accurate correspondence matching between the LR and the reference (Ref) image. The second is the effective transfer and aggregation of similar texture information from the Ref images. Nonetheless, an important detail of perceptual loss and adversarial loss has been underestimated, which has a certain adverse effect on texture transfer and reconstruction. In this study, we propose a feature reuse framework that guides the step-by-step texture reconstruction process through different stages, reducing the negative impacts of perceptual and adversarial loss. The feature reuse framework can be used for any RefSR model, and several RefSR approaches have improved their performance after being retrained using our framework. Additionally, we introduce a single image feature embedding module and a texture-adaptive aggregation module. The single image feature embedding module assists in reconstructing the features of the LR inputs itself and effectively lowers the possibility of including irrelevant textures. The texture-adaptive aggregation module dynamically perceives and aggregates texture information between the LR inputs and the Ref images using dynamic filters. This enhances the utilization of the reference texture while reducing reference misuse. The source code is available at https://github.com/Yi-Yang355/FRFSR.

Francesco Di Giovanni, Lorenzo Giusti, Federico Barbero et al.

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 (access) 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.

Steve Azzolin, Antonio Longa, Pietro Barbiero et al.

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.

Han Xuanyuan, Pietro Barbiero, Dobrik Georgiev et al. · cambridge

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, and propose new metrics for evaluating the interpretability of GNN neurons. 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.

David Buterez, Jon Paul Janet, Steven J. Kiddle et al.

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.

Lucie Charlotte Magister, Pietro Barbiero, Dmitry Kazhdan et al.

The opaque reasoning of Graph Neural Networks induces a lack of human trust. Existing graph network explainers attempt to address this issue by providing post-hoc explanations, however, they fail to make the model itself more interpretable. To fill this gap, we introduce the Concept Encoder Module, the first differentiable concept-discovery approach for graph networks. The proposed approach makes graph networks explainable by design by first discovering graph concepts and then using these to solve the task. Our results demonstrate that this approach allows graph networks to: (i) attain model accuracy comparable with their equivalent vanilla versions, (ii) discover meaningful concepts that achieve high concept completeness and purity scores, (iii) provide high-quality concept-based logic explanations for their prediction, and (iv) support effective interventions at test time: these can increase human trust as well as significantly improve model performance.

Pietro Barbiero, Stefano Fioravanti, Francesco Giannini et al. · ibm-research

Explainable AI (XAI) aims to address the human need for safe and reliable AI systems. However, numerous surveys emphasize the absence of a sound mathematical formalization of key XAI notions -- remarkably including the term "explanation" which still lacks a precise definition. To bridge this gap, this paper presents the first mathematically rigorous definitions of key XAI notions and processes, using the well-funded formalism of Category theory. We show that our categorical framework allows to: (i) model existing learning schemes and architectures, (ii) formally define the term "explanation", (iii) establish a theoretical basis for XAI taxonomies, and (iv) analyze commonly overlooked aspects of explaining methods. As a consequence, our categorical framework promotes the ethical and secure deployment of AI technologies as it represents a significant step towards a sound theoretical foundation of explainable AI.

Antonio Longa, Steve Azzolin, Gabriele Santin et al.

Following a fast initial breakthrough in graph based learning, Graph Neural Networks (GNNs) have reached a widespread application in many science and engineering fields, prompting the need for methods to understand their decision process. GNN explainers have started to emerge in recent years, with a multitude of methods both novel or adapted from other domains. To sort out this plethora of alternative approaches, several studies have benchmarked the performance of different explainers in terms of various explainability metrics. However, these earlier works make no attempts at providing insights into why different GNN architectures are more or less explainable, or which explainer should be preferred in a given setting. In this survey, we fill these gaps by devising a systematic experimental study, which tests ten explainers on eight representative architectures trained on six carefully designed graph and node classification datasets. With our results we provide key insights on the choice and applicability of GNN explainers, we isolate key components that make them usable and successful and provide recommendations on how to avoid common interpretation pitfalls. We conclude by highlighting open questions and directions of possible future research.

Jialin Chen, Yuelin Wang, Cristian Bodnar et al. · cambridge

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

Richard Bergna, Sergio Calvo-Ordoñez, Felix L. Opolka et al.

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, and active learning, underscoring the ability of LGNSDEs to quantify uncertainty reliably. Code is available at \href{https://github.com/Richard-Bergna/GraphNeuralSDE}{\texttt{github.com/Richard-Bergna/GraphNeuralSDE}}.

Pietro Barbiero, Gabriele Ciravegna, Francesco Giannini et al.

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.

Davide Buffelli, Pietro Liò, Fabio Vandin

In the past few years, graph neural networks (GNNs) have become the de facto model of choice for graph classification. While, from the theoretical viewpoint, most GNNs can operate on graphs of any size, it is empirically observed that their classification performance degrades when they are applied on graphs with sizes that differ from those in the training data. Previous works have tried to tackle this issue in graph classification by providing the model with inductive biases derived from assumptions on the generative process of the graphs, or by requiring access to graphs from the test domain. The first strategy is tied to the quality of the assumptions made for the generative process, and requires the use of specific models designed after the explicit definition of the generative process of the data, leaving open the question of how to improve the performance of generic GNN models in general settings. On the other hand, the second strategy can be applied to any GNN, but requires access to information that is not always easy to obtain. In this work we consider the scenario in which we only have access to the training data, and we propose a regularization strategy that can be applied to any GNN to improve its generalization capabilities from smaller to larger graphs without requiring access to the test data. Our regularization is based on the idea of simulating a shift in the size of the training graphs using coarsening techniques, and enforcing the model to be robust to such a shift. Experimental results on standard datasets show that popular GNN models, trained on the 50% smallest graphs in the dataset and tested on the 10% largest graphs, obtain performance improvements of up to 30% when trained with our regularization strategy.

Alexander Campbell, Antonio Giuliano Zippo, Luca Passamonti et al.

Graph neural networks (GNNs) have demonstrated success in learning representations of brain graphs derived from functional magnetic resonance imaging (fMRI) data. However, existing GNN methods assume brain graphs are static over time and the graph adjacency matrix is known prior to model training. These assumptions contradict evidence that brain graphs are time-varying with a connectivity structure that depends on the choice of functional connectivity measure. Incorrectly representing fMRI data with noisy brain graphs can adversely affect GNN performance. To address this, we propose DynDepNet, a novel method for learning the optimal time-varying dependency structure of fMRI data induced by downstream prediction tasks. Experiments on real-world fMRI datasets, for the task of sex classification, demonstrate that DynDepNet achieves state-of-the-art results, outperforming the best baseline in terms of accuracy by approximately 8 and 6 percentage points, respectively. Furthermore, analysis of the learned dynamic graphs reveals prediction-related brain regions consistent with existing neuroscience literature.

Lorenzo Giusti, Teodora Reu, Francesco Ceccarelli et al. · cambridge

Graph Neural Networks (GNNs) have demonstrated remarkable success in learning from graph-structured data. However, they face significant limitations in expressive power, struggling with long-range interactions and lacking a principled approach to modeling higher-order structures and group interactions. Cellular Isomorphism Networks (CINs) recently addressed most of these challenges with a message passing scheme based on cell complexes. Despite their advantages, CINs make use only of boundary and upper messages which do not consider a direct interaction between the rings present in the underlying complex. Accounting for these interactions might be crucial for learning representations of many real-world complex phenomena such as the dynamics of supramolecular assemblies, neural activity within the brain, and gene regulation processes. In this work, we propose CIN++, an enhancement of the topological message passing scheme introduced in CINs. Our message passing scheme accounts for the aforementioned limitations by letting the cells to receive also lower messages within each layer. By providing a more comprehensive representation of higher-order and long-range interactions, our enhanced topological message passing scheme achieves state-of-the-art results on large-scale and long-range chemistry benchmarks.

Donato Crisostomi, Irene Cannistraci, Luca Moschella et al. · eth-zurich

Models trained on semantically related datasets and tasks exhibit comparable inter-sample relations within their latent spaces. We investigate in this study the aggregation of such latent spaces to create a unified space encompassing the combined information. To this end, we introduce Relative Latent Space Aggregation, a two-step approach that first renders the spaces comparable using relative representations, and then aggregates them via a simple mean. We carefully divide a classification problem into a series of learning tasks under three different settings: sharing samples, classes, or neither. We then train a model on each task and aggregate the resulting latent spaces. We compare the aggregated space with that derived from an end-to-end model trained over all tasks and show that the two spaces are similar. We then observe that the aggregated space is better suited for classification, and empirically demonstrate that it is due to the unique imprints left by task-specific embedders within the representations. We finally test our framework in scenarios where no shared region exists and show that it can still be used to merge the spaces, albeit with diminished benefits over naive merging.

Lucie Charlotte Magister, Alexander Norcliffe, Iulia Duta et al.

The reasoning process of Graph Neural Networks is complex and considered opaque, limiting trust in their predictions. To alleviate this issue, prior work has proposed concept-based explanations, extracted from clusters in the model's node embeddings. However, a limitation of concept-based explanations is that they only explain the node embedding space and are obscured by pooling in graph classification. To mitigate this issue and provide a deeper level of understanding, we propose the Subgraph Concept Network. The Subgraph Concept Network is the first graph neural network architecture that distils subgraph and graph-level concepts. It achieves this by performing soft clustering on node concept embeddings to derive subgraph and graph-level concepts. Our results show that the Subgraph Concept Network allows to obtain competitive model accuracy, while discovering meaningful concepts at different levels of the network.

Xiangyu Zhao, Hannes Stärk, Dominique Beaini et al. · mit

It has been increasingly demanding to develop reliable methods to evaluate the progress of Graph Neural Network (GNN) research for molecular representation learning. Existing GNN benchmarking methods for molecular representation learning focus on comparing the GNNs' performances on some node/graph classification/regression tasks on certain datasets. However, there lacks a principled, task-agnostic method to directly compare two GNNs. Additionally, most of the existing self-supervised learning works incorporate handcrafted augmentations to the data, which has several severe difficulties to be applied on graphs due to their unique characteristics. To address the aforementioned issues, we propose GraphAC (Graph Adversarial Collaboration) -- a conceptually novel, principled, task-agnostic, and stable framework for evaluating GNNs through contrastive self-supervision. We introduce a novel objective function: the Competitive Barlow Twins, that allow two GNNs to jointly update themselves from direct competitions against each other. GraphAC succeeds in distinguishing GNNs of different expressiveness across various aspects, and has demonstrated to be a principled and reliable GNN evaluation method, without necessitating any augmentations.

Zhenda Shen, Yanqi Cheng, Raymond H. Chan et al.

Implicit neural representations (INRs) have garnered significant interest recently for their ability to model complex, high-dimensional data without explicit parameterisation. In this work, we introduce TRIDENT, a novel function for implicit neural representations characterised by a trilogy of nonlinearities. Firstly, it is designed to represent high-order features through order compactness. Secondly, TRIDENT efficiently captures frequency information, a feature called frequency compactness. Thirdly, it has the capability to represent signals or images such that most of its energy is concentrated in a limited spatial region, denoting spatial compactness. We demonstrated through extensive experiments on various inverse problems that our proposed function outperforms existing implicit neural representation functions.

Lev Telyatnikov, Maria Sofia Bucarelli, Guillermo Bernardez et al.

Most of the current hypergraph learning methodologies and benchmarking datasets in the hypergraph realm are obtained by lifting procedures from their graph analogs, leading to overshadowing specific characteristics of hypergraphs. This paper attempts to confront some pending questions in that regard: Q1 Can the concept of homophily play a crucial role in Hypergraph Neural Networks (HNNs)? Q2 Is there room for improving current HNN architectures by carefully addressing specific characteristics of higher-order networks? Q3 Do existing datasets provide a meaningful benchmark for HNNs? To address them, we first introduce a novel conceptualization of homophily in higher-order networks based on a Message Passing (MP) scheme, unifying both the analytical examination and the modeling of higher-order networks. Further, we investigate some natural, yet mostly unexplored, strategies for processing higher-order structures within HNNs such as keeping hyperedge-dependent node representations, or performing node/hyperedge stochastic samplings, leading us to the most general MP formulation up to date -MultiSet-, as well as to an original architecture design, MultiSetMixer. Finally, we conduct an extensive set of experiments that contextualize our proposals and successfully provide insights about our inquiries.

Kai Yi, Bingxin Zhou, Yiqing Shen et al.

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

James Rowbottom, Georg Maierhofer, Teo Deveney et al.

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.

Kai Yi, Jialin Chen, Yu Guang Wang et al.

This paper develops a rotation-invariant needlet convolution for rotation group SO(3) to distill multiscale information of spherical signals. The spherical needlet transform is generalized from $\mathbb{S}^2$ onto the SO(3) group, which decomposes a spherical signal to approximate and detailed spectral coefficients by a set of tight framelet operators. The spherical signal during the decomposition and reconstruction achieves rotation invariance. Based on needlet transforms, we form a Needlet approximate Equivariance Spherical CNN (NES) with multiple SO(3) needlet convolutional layers. The network establishes a powerful tool to extract geometric-invariant features of spherical signals. The model allows sufficient network scalability with multi-resolution representation. A robust signal embedding is learned with wavelet shrinkage activation function, which filters out redundant high-pass representation while maintaining approximate rotation invariance. The NES achieves state-of-the-art performance for quantum chemistry regression and Cosmic Microwave Background (CMB) delensing reconstruction, which shows great potential for solving scientific challenges with high-resolution and multi-scale spherical signal representation.

Alexander Campbell, Simeon Spasov, Nicola Toschi et al.

Graphs are a natural representation of brain activity derived from functional magnetic imaging (fMRI) data. It is well known that clusters of anatomical brain regions, known as functional connectivity networks (FCNs), encode temporal relationships which can serve as useful biomarkers for understanding brain function and dysfunction. Previous works, however, ignore the temporal dynamics of the brain and focus on static graphs. In this paper, we propose a dynamic brain graph deep generative model (DBGDGM) which simultaneously clusters brain regions into temporally evolving communities and learns dynamic unsupervised node embeddings. Specifically, DBGDGM represents brain graph nodes as embeddings sampled from a distribution over communities that evolve over time. We parameterise this community distribution using neural networks that learn from subject and node embeddings as well as past community assignments. Experiments demonstrate DBGDGM outperforms baselines in graph generation, dynamic link prediction, and is comparable for graph classification. Finally, an analysis of the learnt community distributions reveals overlap with known FCNs reported in neuroscience literature.

Adrián Bazaga, Pietro Liò, Gos Micklem

In recent years, the task of text-to-SQL translation, which converts natural language questions into executable SQL queries, has gained significant attention for its potential to democratize data access. Despite its promise, challenges such as adapting to unseen databases and aligning natural language with SQL syntax have hindered widespread adoption. To overcome these issues, we introduce SQLformer, a novel Transformer architecture specifically crafted to perform text-to-SQL translation tasks. Our model predicts SQL queries as abstract syntax trees (ASTs) in an autoregressive way, incorporating structural inductive bias in the encoder and decoder layers. This bias, guided by database table and column selection, aids the decoder in generating SQL query ASTs represented as graphs in a Breadth-First Search canonical order. Our experiments demonstrate that SQLformer achieves state-of-the-art performance across six prominent text-to-SQL benchmarks.

Lihao Liu, Zhening Huang, Pietro Liò et al.

Medical image registration and segmentation are critical tasks for several clinical procedures. Manual realisation of those tasks is time-consuming and the quality is highly dependent on the level of expertise of the physician. To mitigate that laborious task, automatic tools have been developed where the majority of solutions are supervised techniques. However, in medical domain, the strong assumption of having a well-representative ground truth is far from being realistic. To overcome this challenge, unsupervised techniques have been investigated. However, they are still limited in performance and they fail to produce plausible results. In this work, we propose a novel unified unsupervised framework for image registration and segmentation that we called PC-SwinMorph. The core of our framework is two patch-based strategies, where we demonstrate that patch representation is key for performance gain. We first introduce a patch-based contrastive strategy that enforces locality conditions and richer feature representation. Secondly, we utilise a 3D window/shifted-window multi-head self-attention module as a patch stitching strategy to eliminate artifacts from the patch splitting. We demonstrate, through a set of numerical and visual results, that our technique outperforms current state-of-the-art unsupervised techniques.

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 (Self-supervised Fact Verification via Language 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.

Emma L. Ambags, Giulia Capitoli, Vincenzo L' Imperio et al.

The need for fully human-understandable models is increasingly being recognised as a central theme in AI research. The acceptance of AI models to assist in decision making in sensitive domains will grow when these models are interpretable, and this trend towards interpretable models will be amplified by upcoming regulations. One of the killer applications of interpretable AI is medical practice, which can benefit from accurate decision support methodologies that inherently generate trust. In this work, we propose FPT, (MedFP), a novel method that combines probabilistic trees and fuzzy logic to assist clinical practice. This approach is fully interpretable as it allows clinicians to generate, control and verify the entire diagnosis procedure; one of the methodology's strength is the capability to decrease the frequency of misdiagnoses by providing an estimate of uncertainties and counterfactuals. Our approach is applied as a proof-of-concept to two real medical scenarios: classifying malignant thyroid nodules and predicting the risk of progression in chronic kidney disease patients. Our results show that probabilistic fuzzy decision trees can provide interpretable support to clinicians, furthermore, introducing fuzzy variables into the probabilistic model brings significant nuances that are lost when using the crisp thresholds set by traditional probabilistic decision trees. We show that FPT and its predictions can assist clinical practice in an intuitive manner, with the use of a user-friendly interface specifically designed for this purpose. Moreover, we discuss the interpretability of the FPT model.

Yana Lishkova, Paul Scherer, Steffen Ridderbusch et al.

By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behave in time. If the dynamics exhibit additional symmetries, then the motion fulfils additional conservation laws, such as conservation of energy (time invariance), momentum (translation invariance), or angular momentum (rotational invariance). To learn a system representation, one could learn the discrete Euler-Lagrange equations, or alternatively, learn the discrete Lagrangian function $\mathcal{L}_d$ which defines them. Based on ideas from Lie group theory, in this work we introduce a framework to learn a discrete Lagrangian along with its symmetry group from discrete observations of motions and, therefore, identify conserved quantities. The learning process does not restrict the form of the Lagrangian, does not require velocity or momentum observations or predictions and incorporates a cost term which safeguards against unwanted solutions and against potential numerical issues in forward simulations. The learnt discrete quantities are related to their continuous analogues using variational backward error analysis and numerical results demonstrate the improvement such models can have both qualitatively and quantitatively even in the presence of noise.

Gianluca Mittone, Filip Svoboda, Marco Aldinucci et al.

Aggregating pharmaceutical data in the drug-target interaction (DTI) domain has the potential to deliver life-saving breakthroughs. It is, however, notoriously difficult due to regulatory constraints and commercial interests. This work proposes the application of federated learning, which we argue to be reconcilable with the industry's constraints, as it does not require sharing of any information that would reveal the entities' data or any other high-level summary of it. When used on a representative GraphDTA model and the KIBA dataset it achieves up to 15% improved performance relative to the best available non-privacy preserving alternative. Our extensive battery of experiments shows that, unlike in other domains, the non-IID data distribution in the DTI datasets does not deteriorate FL performance. Additionally, we identify a material trade-off between the benefits of adding new data, and the cost of adding more clients.

Riccardo Ali, Paulina Kulytė, Haitz Sáez de Ocáriz Borde et al.

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