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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 ``\textit{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.

Recent work on interpretability has focused on concept-based explanations, where deep learning models are explained in terms of high-level units of information, referred to as concepts. Concept learning models, however, have been shown to be prone to encoding impurities in their representations, failing to fully capture meaningful features of their inputs. While concept learning lacks metrics to measure such phenomena, the field of disentanglement learning has explored the related notion of underlying factors of variation in the data, with plenty of metrics to measure the purity of such factors. In this paper, we show that such metrics are not appropriate for concept learning and propose novel metrics for evaluating the purity of concept representations in both approaches. We show the advantage of these metrics over existing ones and demonstrate their utility in evaluating the robustness of concept representations and interventions performed on them. In addition, we show their utility for benchmarking state-of-the-art methods from both families and find that, contrary to common assumptions, supervision alone may not be sufficient for pure concept representations., Comment: To appear at AAAI 2023

International audience; 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 highdimensional 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.

The COVID-19 pandemic has led to unprecedented strain on intensive care unit (ICU) admission in parts of the world. Strategies to create surge ICU capacity requires complex local and national service reconfiguration and reduction or cancellation of elective activity. Theses measures require time to implement and have an inevitable lag before additional capacity comes on-line. An accurate short-range forecast would be helpful in guiding such difficult, costly and ethically challenging decisions. At the time this work began, cases in England were starting to increase. Here we present an attempt at an agile short-range forecast based on published real-time COVID-19 case data from the seven National Health Service commissioning regions in England (East of England, London, Midlands, North East and Yorkshire, North West, South East and South West). We use a Monte Carlo approach to model the likely impact of current diagnoses on regional ICU capacity over a 14 day horizon. Our model is designed to be parsimonious and based on plausible epidemiological data from the literature available. On the basis of the modelling assumptions made, ICU occupancy is likely to increase dramatically in the the days following the time of modelling. If the current exponential growth continues, 5 out of 7 commissioning regions will have more critically ill COVID-19 patients than there are ICU beds within two weeks\todo{last thing to do}. Despite variable growth in absolute patients, all commissioning regions are forecast to be heavily burdened under the assumptions used. Whilst, like any forecast model, there remain uncertainties both in terms of model specification and robust epidemiological data in this early prospective phase, it would seem that surge capacity will be required in the very near future. We hope that our model will help policy decision makers with their preparations. The uncertainties in the data highlight the urgent need for ongoing real-time surveillance to allow forecasts to be constantly updated using high quality local patient-facing data as it emerges.

Clustering in high dimensional spaces is a very difficult task. Dealing with DNA microarrays is even more difficult because gene subsets are coregulated and coexpressed only under specific conditions. Biclusterng addresses the problem of finding such submanifolds by exploiting both gene and condition (tissue) clustering. The paper proposes a self-organizing neural network, GH EXIN, which builds a hierarchical tree by adapting its architecture to data. It is integrated in a framework in which gene and tissue clustering are alternated and controlled by the quality of the bicluster. Examples of the approach and a biological validation of results are also given

ObjectiveModern medicine needs to shift from a wait and react, curative discipline to a preventative, interdisciplinary science aiming at providing personalised, systemic and precise treatment plans to patients. The aim of this work is to present how the integration of machine learning approaches with mechanistic computational modelling could yield a reliable infrastructure to run probabilistic simulations where the entire organism is considered as a whole.MethodsWe propose a general framework that composes advanced AI approaches and integrates mathematical modelling in order to provide a panoramic view over current and future physiological conditions. The proposed architecture is based on a graph neural network (GNNs) forecasting clinically relevant endpoints (such as blood pressure) and a generative adversarial network (GANs) providing a proof of concept of transcriptomic integrability.ResultsWe show the results of the investigation of pathological effects of overexpression of ACE2 across different signalling pathways in multiple tissues on cardiovascular functions. We provide a proof of concept of integrating a large set of composable clinical models using molecular data to drive local and global clinical parameters and derive future trajectories representing the evolution of the physiological state of the patient.SignificanceWe argue that the graph representation of a computational patient has potential to solve important technological challenges in integrating multiscale computational modelling with AI. We believe that this work represents a step forward towards a healthcare digital twin.

Objective: Modern medicine needs to shift from a wait and react, curative discipline to a preventative, interdisciplinary science aiming at providing personalized, systemic, and precise treatment plans to patients. To this purpose, we propose a “digital twin” of patients modeling the human body as a whole and providing a panoramic view over individuals' conditions.Methods: We propose a general framework that composes advanced artificial intelligence (AI) approaches and integrates mathematical modeling in order to provide a panoramic view over current and future pathophysiological conditions. Our modular architecture is based on a graph neural network (GNN) forecasting clinically relevant endpoints (such as blood pressure) and a generative adversarial network (GAN) providing a proof of concept of transcriptomic integrability.Results: We tested our digital twin model on two simulated clinical case studies combining information at organ, tissue, and cellular level. We provided a panoramic overview over current and future patient's conditions by monitoring and forecasting clinically relevant endpoints representing the evolution of patient's vital parameters using the GNN model. We showed how to use the GAN to generate multi-tissue expression data for blood and lung to find associations between cytokines conditioned on the expression of genes in the renin–angiotensin pathway. Our approach was to detect inflammatory cytokines, which are known to have effects on blood pressure and have previously been associated with SARS-CoV-2 infection (e.g., CXCR6, XCL1, and others).Significance: The graph representation of a computational patient has potential to solve important technological challenges in integrating multiscale computational modeling with AI. We believe that this work represents a step forward toward next-generation devices for precision and predictive medicine.