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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.

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., Comment: 19 pages

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}

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., Comment: 21 pages, 8 figures

This research report introduces ElegansNet, a neural network that mimics real-world neuronal network circuitry, with the goal of better understanding the interplay between connectome topology and deep learning systems. The proposed approach utilizes the powerful representational capabilities of living beings' neuronal circuitry to design and generate improved deep learning systems with a topology similar to natural networks. The Caenorhabditis elegans connectome is used as a reference due to its completeness, reasonable size, and functional neuron classes annotations. It is demonstrated that the connectome of simple organisms exhibits specific functional relationships between neurons, and once transformed into learnable tensor networks and integrated into modern architectures, it offers bio-plausible structures that efficiently solve complex tasks. The performance of the models is demonstrated against randomly wired networks and compared to artificial networks ranked on global benchmarks. In the first case, ElegansNet outperforms randomly wired networks. Interestingly, ElegansNet models show slightly similar performance with only those based on the Watts-Strogatz small-world property. When compared to state-of-the-art artificial neural networks, such as transformers or attention-based autoencoders, ElegansNet outperforms well-known deep learning and traditional models in both supervised image classification tasks and unsupervised hand-written digits reconstruction, achieving top-1 accuracy of 99.99% on Cifar10 and 99.84% on MNIST Unsup on the validation sets., Comment: 4 pages, short report before full paper submission

In this paper we study the asymptotic behavior of sequences of stationary weak solutions to the following Liouville-type equation $-\Delta u=e^u~~~{in }~~~\Omega$, where $\Omega$ is an open set of $R^3$. By improving the partial regularity estimates obtained by the first author for the above equation, we succeed in performing a blow-up analysis without Morrey-type assumptions on the solutions $u$ and on the nonlinearity $e^u.$, Comment: 29 pages

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., Comment: 23 pages

Passive radiative cooling technologies are highly attractive in pursuing sustainable development. However, current cooling materials are often static, which makes it difficult to cope with the varying needs of all-weather thermal comfort management. Herein, a strategy is designed to obtain flexible thermoplastic polyurethane nanofiber (Es-TPU) membranes via electrospinning, realizing reversible in-situ solvent-free switching between radiative cooling and solar heating through changes in its optical reflectivity by stretching. In its radiative cooling state (0% strain), the Es-TPU membrane shows a high and angular-independent reflectance of 95.6% in the 0.25-2.5 {\mu}m wavelength range and an infrared emissivity of 93.3% in the atmospheric transparency window (8-13 {\mu}m), reaching a temperature drop of 10 {\deg}C at midday, with a corresponding cooling power of 118.25 W/m2. The excellent mechanical properties of the Es-TPU membrane allows the continuous adjustment of reflectivity by reversibly stretching it, reaching a reflectivity of 61.1% ({\Delta}R=34.5%) under an elongation strain of 80%, leading to a net temperature increase of 9.5 {\deg}C above ambient of an absorbing substrate and an equivalent power of 220.34 W/m2 in this solar heating mode. The strong haze, hydrophobicity and outstanding aging resistance exhibited by this scalable membrane hold promise for achieving uniform illumination with tunable strength and efficient thermal management in practical applications., Comment: accepted version of the manuscript published on Chemical Engineering Journal

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.

Super-resolution plays an essential role in medical imaging because it provides an alternative way to achieve high spatial resolutions and image quality with no extra acquisition costs. In the past few decades, the rapid development of deep neural networks has promoted super-resolution performance with novel network architectures, loss functions and evaluation metrics. Specifically, vision transformers dominate a broad range of computer vision tasks, but challenges still exist when applying them to low-level medical image processing tasks. This paper proposes an efficient vision transformer with residual dense connections and local feature fusion to achieve efficient single-image super-resolution (SISR) of medical modalities. Moreover, we implement a general-purpose perceptual loss with manual control for image quality improvements of desired aspects by incorporating prior knowledge of medical image segmentation. Compared with state-of-the-art methods on four public medical image datasets, the proposed method achieves the best PSNR scores of 6 modalities among seven modalities. It leads to an average improvement of $+0.09$ dB PSNR with only 38\% parameters of SwinIR. On the other hand, the segmentation-based perceptual loss increases $+0.14$ dB PSNR on average for SOTA methods, including CNNs and vision transformers. Additionally, we conduct comprehensive ablation studies to discuss potential factors for the superior performance of vision transformers over CNNs and the impacts of network and loss function components. The code will be released on GitHub with the paper published., Comment: Preprint submitted to Medical Image Analysis and under review

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., Comment: This paper is the accepted version of ACM copyrighted material published at the WWW'23 conference

Explainable AI (XAI) underwent a recent surge in research on concept extraction, focusing on extracting human-interpretable concepts from Deep Neural Networks. An important challenge facing concept extraction approaches is the difficulty of interpreting and evaluating discovered concepts, especially for complex tasks such as molecular property prediction. We address this challenge by presenting GCI: a (G)raph (C)oncept (I)nterpretation framework, used for quantitatively measuring alignment between concepts discovered from Graph Neural Networks (GNNs) and their corresponding human interpretations. GCI encodes concept interpretations as functions, which can be used to quantitatively measure the alignment between a given interpretation and concept definition. We demonstrate four applications of GCI: (i) quantitatively evaluating concept extractors, (ii) measuring alignment between concept extractors and human interpretations, (iii) measuring the completeness of interpretations with respect to an end task and (iv) a practical application of GCI to molecular property prediction, in which we demonstrate how to use chemical functional groups to explain GNNs trained on molecular property prediction tasks, and implement interpretations with a 0.76 AUCROC completeness score.

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., Comment: Accepted at ICML 2023; 21 pages

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.

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., Comment: 11th International Conference on Learning Representations (ICLR 2023) Machine Learning for Drug Discovery (MLDD) Workshop. 17 pages, 6 figures, 4 tables

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.

Quantum-dot-based single-photon sources are key assets for quantum information technology, supplying on-demand scalable quantum resources for computing and communication. However, longlasting issues such as limited long-term stability and source brightness have traditionally impeded their adoption in real-world applications. Here, we realize a quantum key distribution field trial using true single photons across an 18-km-long dark fibre, located in the Copenhagen metropolitan area, using an optimized, state-of-the-art, quantum-dot single-photon source frequency-converted to the telecom wavelength. A secret key generation rate of >2 kbits/s realized over a 9.6 dB channel loss is achieved with a polarization-encoded BB84 scheme, showing remarkable stability for more than 24 hours of continuous operation. Our results highlight the maturity of deterministic single-photon source technology while paving the way for advanced single-photon-based communication protocols, including fully device-independent quantum key distribution, towards the goal of a quantum internet., Comment: 9 pages, 4 figures. Minor edits

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}, Comment: ICML 2023

Graphs have a superior ability to represent relational data, like chemical compounds, proteins, and social networks. Hence, graph-level learning, which takes a set of graphs as input, has been applied to many tasks including comparison, regression, classification, and more. Traditional approaches to learning a set of graphs heavily rely on hand-crafted features, such as substructures. But while these methods benefit from good interpretability, they often suffer from computational bottlenecks as they cannot skirt the graph isomorphism problem. Conversely, deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and encoding graphs into low-dimensional representations. As a result, these deep graph learning methods have been responsible for many successes. Yet, there is no comprehensive survey that reviews graph-level learning starting with traditional learning and moving through to the deep learning approaches. This article fills this gap and frames the representative algorithms into a systematic taxonomy covering traditional learning, graph-level deep neural networks, graph-level graph neural networks, and graph pooling. To ensure a thoroughly comprehensive survey, the evolutions, interactions, and communications between methods from four different branches of development are also examined. This is followed by a brief review of the benchmark data sets, evaluation metrics, and common downstream applications. The survey concludes with a broad overview of 12 current and future directions in this booming field.

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.

We prove the upper-semi-continuity of the Morse index plus nullity of critical points to general conformally invariant Lagrangians in dimension 2 under weak convergence. Precisely we establish that the sum of the Morse indices and the nullity of an arbitrary sequence of weakly converging critical points to a general conformally invariant Lagrangians of maps from an arbitrary closed surface into an arbitrary closed smooth manifold passes to the limit in the following sense : it is asymptotically bounded from above by the sum of the Morse indices plus the nullity of the weak limit and the bubbles, while it was well known that the sum of the Morse index of the weak limit with the Morse indices of the bubbles is asymptotically bounded from above by the Morse indices of the weakly converging sequence. The main result is then extended to the case of sequences of maps from sequences of domains degenerating to a punctured Riemann surface assuming that the lengths of the images by the maps of the collars associated to this degeneration stay below some critical length.

Neural networks with PDEs embedded in their loss functions (physics-informed neural networks) are employed as a function approximators to find solutions to the Ricci flow (a curvature based evolution) of Riemannian metrics. A general method is developed and applied to the real torus. The validity of the solution is verified by comparing the time evolution of scalar curvature with that found using a standard PDE solver, which decreases to a constant value of 0 on the whole manifold. We also consider certain solitonic solutions to the Ricci flow equation in two real dimensions. We create visualisations of the flow by utilising an embedding into $\mathbb{R}^3$. Snapshots of highly accurate numerical evolution of the toroidal metric over time are reported. We provide guidelines on applications of this methodology to the problem of determining Ricci flat Calabi--Yau metrics in the context of String theory, a long standing problem in complex geometry.

Neural algorithmic reasoning studies the problem of learning algorithms with neural networks, especially with graph architectures. A recent proposal, XLVIN, reaps the benefits of using a graph neural network that simulates the value iteration algorithm in deep reinforcement learning agents. It allows model-free planning without access to privileged information about the environment, which is usually unavailable. However, XLVIN only supports discrete action spaces, and is hence nontrivially applicable to most tasks of real-world interest. We expand XLVIN to continuous action spaces by discretization, and evaluate several selective expansion policies to deal with the large planning graphs. Our proposal, CNAP, demonstrates how neural algorithmic reasoning can make a measurable impact in higher-dimensional continuous control settings, such as MuJoCo, bringing gains in low-data settings and outperforming model-free baselines.

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., Comment: Accepted to AAAI-2023

Kernels on graphs have had limited options for node-level problems. To address this, we present a novel, generalized kernel for graphs with node feature data for semi-supervised learning. The kernel is derived from a regularization framework by treating the graph and feature data as two Hilbert spaces. We also show how numerous kernel-based models on graphs are instances of our design. A kernel defined this way has transductive properties, and this leads to improved ability to learn on fewer training points, as well as better handling of highly non-Euclidean data. We demonstrate these advantages using synthetic data where the distribution of the whole graph can inform the pattern of the labels. Finally, by utilizing a flexible polynomial of the graph Laplacian within the kernel, the model also performed effectively in semi-supervised classification on graphs of various levels of homophily.

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.

In the wake of the growing popularity of machine learning in particle physics, this work finds a new application of geometric deep learning on Feynman diagrams to make accurate and fast matrix element predictions with the potential to be used in analysis of quantum field theory. This research uses the graph attention layer which makes matrix element predictions to 1 significant figure accuracy above 90% of the time. Peak performance was achieved in making predictions to 3 significant figure accuracy over 10% of the time with less than 200 epochs of training, serving as a proof of concept on which future works can build upon for better performance. Finally, a procedure is suggested, to use the network to make advancements in quantum field theory by constructing Feynman diagrams with effective particles that represent non-perturbative calculations.

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.

Recent work has suggested post-hoc explainers might be ineffective for detecting spurious correlations in Deep Neural Networks (DNNs). However, we show there are serious weaknesses with the existing evaluation frameworks for this setting. Previously proposed metrics are extremely difficult to interpret and are not directly comparable between explainer methods. To alleviate these constraints, we propose a new evaluation methodology, Explainer Divergence Scores (EDS), grounded in an information theory approach to evaluate explainers. EDS is easy to interpret and naturally comparable across explainers. We use our methodology to compare the detection performance of three different explainers - feature attribution methods, influential examples and concept extraction, on two different image datasets. We discover post-hoc explainers often contain substantial information about a DNN's dependence on spurious artifacts, but in ways often imperceptible to human users. This suggests the need for new techniques that can use this information to better detect a DNN's reliance on spurious correlations., Comment: Presented at the AIMLAI workshop at the 31st ACM International Conference on Information and Knowledge Management (CIKM 2022)

Reinforcement learning has seen increasing applications in real-world contexts over the past few years. However, physical environments are often imperfect and policies that perform well in simulation might not achieve the same performance when applied elsewhere. A common approach to combat this is to train agents in the presence of an adversary. An adversary acts to destabilise the agent, which learns a more robust policy and can better handle realistic conditions. Many real-world applications of reinforcement learning also make use of goal-conditioning: this is particularly useful in the context of robotics, as it allows the agent to act differently, depending on which goal is selected. Here, we focus on the problem of goal-conditioned learning in the presence of an adversary. We first present DigitFlip and CLEVR-Play, two novel goal-conditioned environments that support acting against an adversary. Next, we propose EHER and CHER -- two HER-based algorithms for goal-conditioned learning -- and evaluate their performance. Finally, we unify the two threads and introduce IGOAL: a novel framework for goal-conditioned learning in the presence of an adversary. Experimental results show that combining IGOAL with EHER allows agents to significantly outperform existing approaches, when acting against both random and competent adversaries.

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/, Comment: Accepted to CVPR 2023

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., Comment: Published in Transactions on Machine Learning Research (TMLR) 2024. Also accepted and selected for oral presentation at NeurIPS 2023 - Table Representation Learning Workshop

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., Comment: Published at NeurIPS 2022. 10 pages, 5 figures, 1 table

Recently, Logic Explained Networks (LENs) have been proposed as explainable-by-design neural models providing logic explanations for their predictions. However, these models have only been applied to vision and tabular data, and they mostly favour the generation of global explanations, while local ones tend to be noisy and verbose. For these reasons, we propose LENp, improving local explanations by perturbing input words, and we test it on text classification. Our results show that (i) LENp provides better local explanations than LIME in terms of sensitivity and faithfulness, and (ii) logic explanations are more useful and user-friendly than feature scoring provided by LIME as attested by a human survey., Comment: Accepted as short paper at the EMNLP 2022 conference

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., Comment: Accepted to NeurIPS 2022

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.

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.

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., Comment: Camera ready version for ICLR2023 publication

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., Comment: 19 pages, 5, figures, 9 tables, ICML Workshop

In this paper we study the practicality and usefulness of incorporating distributed representations of graphs into models within the context of drug pair scoring. We argue that the real world growth and update cycles of drug pair scoring datasets subvert the limitations of transductive learning associated with distributed representations. Furthermore, we argue that the vocabulary of discrete substructure patterns induced over drug sets is not dramatically large due to the limited set of atom types and constraints on bonding patterns enforced by chemistry. Under this pretext, we explore the effectiveness of distributed representations of the molecular graphs of drugs in drug pair scoring tasks such as drug synergy, polypharmacy, and drug-drug interaction prediction. To achieve this, we present a methodology for learning and incorporating distributed representations of graphs within a unified framework for drug pair scoring. Subsequently, we augment a number of recent and state-of-the-art models to utilise our embeddings. We empirically show that the incorporation of these embeddings improves downstream performance of almost every model across different drug pair scoring tasks, even those the original model was not designed for. We publicly release all of our drug embeddings for the DrugCombDB, DrugComb, DrugbankDDI, and TwoSides datasets., Comment: Updated manuscript, 9 main pages, 8 pages reference and appendix

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., Comment: To appear at NeurIPS 2022

This paper presents a study for the realization of a space mission which employs nanosatellites driven by an external laser source impinging on an optimized lightsail, as a valuable technology to launch swarms of spacecrafts into the Solar System. Nanosatellites propelled by laser can be useful for the heliosphere exploration and for planetary observation, if suitably equipped with sensors, or be adopted for the establishment of network systems when placed into specific orbits. By varying the area-to-mass ratio (i.e., the ratio between the sail area and the payload weight) and the laser power, it is ossible to insert nanosatellites into different hyperbolic orbits with respect to Earth, thus reaching the target by means of controlled trajectories in a relatively short amount of time. A mission involving nanosatellites of the order of 1 kg of mass is envisioned, by describing all the on-board subsystems and satisfying all the requirements in term of power and mass budget. Particular attention is paid to the telecommunication subsystem, which must offer all the necessary functionalities. To fabricate the lightsail, the thin films technology has been considered, by verifying the sail thermal stability during the thrust phase. Moreover, the problem of mechanical stability of the lightsail has been tackled, showing that the distance between the ligthsail structure and the payload plays a pivotal role. Some potential applications of the proposed technology are discussed, such as the mapping of the heliospheric environment.

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., Comment: 9 pages, 5 figures

Due to their unmatched entropy, complexity, and security level, optical Physical Unclonable Functions (PUFs) currently receive a lot of interest in the literature. Despite the large body of existing works, however, one of their core features has never been quantified in detail, namely their physical unclonability. This paper tackles this fundamental and yet largely unaddressed issue. In simulations and/or experiments, the sensitivity of diffraction-based optical responses is investigated with respect to various small alterations such as variation in the position, size, and number of the scatterers, as well as perturbations in the spatial alignment between the physical unclonable function (PUF) and the measurement apparatus. Our analysis focuses on 2D optical PUFs because of their relevance in integrated applications and the need to reply to security concerns that can be raised when the physical structure of the geometry is accessible. Among the results of this study, the sensitivity analysis shows that a positional perturbation of scatterers on the order of \SI{30}{\nano\meter}, i.e., far below the wavelength of the probing laser light of \SI{632}{\nano\meter} wavelength, is sufficient to invalidate the PUF response and thus detect a forgery attempt. These results support and quantify the high adversarial efforts required to clone optical PUFs, even for 2D layouts., Comment: 8 pages, 7 figures and Supporting Information

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.

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., Comment: Accepted at NeurIPS 2022

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.

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., Comment: Presented at the ICML 2022 Workshop on Topology, Algebra, and Geometry in Machine Learning

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., Comment: 17 pages, 10 figures, 30 supplementary pages