Pietro Barbiero

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.

Mateo Espinosa Zarlenga, Pietro Barbiero, Zohreh Shams et al. · cambridge

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.

David Debot, Pietro Barbiero, Francesco Giannini et al. · ibm-research

The lack of transparency in the decision-making processes of deep learning systems presents a significant challenge in modern artificial intelligence (AI), as it impairs users' ability to rely on and verify these systems. To address this challenge, Concept Bottleneck Models (CBMs) have made significant progress by incorporating human-interpretable concepts into deep learning architectures. This approach allows predictions to be traced back to specific concept patterns that users can understand and potentially intervene on. However, existing CBMs' task predictors are not fully interpretable, preventing a thorough analysis and any form of formal verification of their decision-making process prior to deployment, thereby raising significant reliability concerns. To bridge this gap, we introduce Concept-based Memory Reasoner (CMR), a novel CBM designed to provide a human-understandable and provably-verifiable task prediction process. Our approach is to model each task prediction as a neural selection mechanism over a memory of learnable logic rules, followed by a symbolic evaluation of the selected rule. The presence of an explicit memory and the symbolic evaluation allow domain experts to inspect and formally verify the validity of certain global properties of interest for the task prediction process. Experimental results demonstrate that CMR achieves better accuracy-interpretability trade-offs to state-of-the-art CBMs, discovers logic rules consistent with ground truths, allows for rule interventions, and allows pre-deployment verification.

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.

Giacomo Camposampiero, Pietro Barbiero, Michael Hersche et al.

Compositional generalization-a key open challenge in modern machine learning-requires models to predict unknown combinations of known concepts. However, assessing compositional generalization remains a fundamental challenge due to the lack of standardized evaluation protocols and the limitations of current benchmarks, which often favor efficiency over rigor. At the same time, general-purpose vision architectures lack the necessary inductive biases, and existing approaches to endow them compromise scalability. As a remedy, this paper introduces: 1) a rigorous evaluation framework that unifies and extends previous approaches while reducing computational requirements from combinatorial to constant; 2) an extensive and modern evaluation on the status of compositional generalization in supervised vision backbones, training more than 5000 models; 3) Attribute Invariant Networks, a class of models establishing a new Pareto frontier in compositional generalization, achieving a 23.43% accuracy improvement over baselines while reducing parameter overhead from 600% to 16% compared to fully disentangled counterparts. Our code is available at https://github.com/IBM/scalable-compositional-generalization.

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.

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.

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.

Dmitry Kazhdan, Botty Dimanov, Lucie Charlotte Magister et al.

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.

Pietro Barbiero, Francesco Giannini, Gabriele Ciravegna et al.

The design of interpretable deep learning models working in relational domains poses an open challenge: interpretable deep learning methods, such as Concept Bottleneck Models (CBMs), are not designed to solve relational problems, while relational deep learning models, such as Graph Neural Networks (GNNs), are not as interpretable as CBMs. To overcome these limitations, we propose Relational Concept Bottleneck Models (R-CBMs), a family of relational deep learning methods providing interpretable task predictions. As special cases, we show that R-CBMs are capable of both representing standard CBMs and message-passing GNNs. To evaluate the effectiveness and versatility of these models, we designed a class of experimental problems, ranging from image classification to link prediction in knowledge graphs. In particular we show that R-CBMs (i) match generalization performance of existing relational black-boxes, (ii) support the generation of quantified concept-based explanations, (iii) effectively respond to test-time interventions, and (iv) withstand demanding settings including out-of-distribution scenarios, limited training data regimes, and scarce concept supervisions.

Rishabh Jain, Gabriele Ciravegna, Pietro Barbiero et al.

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.

Aurora Spagnol, Kacper Sokol, Pietro Barbiero et al.

Clustering algorithms rely on complex optimisation processes that may be difficult to comprehend, especially for individuals who lack technical expertise. While many explainable artificial intelligence techniques exist for supervised machine learning, unsupervised learning -- and clustering in particular -- has been largely neglected. To complicate matters further, the notion of a ``true'' cluster is inherently challenging to define. These facets of unsupervised learning and its explainability make it difficult to foster trust in such methods and curtail their adoption. To address these challenges, we propose a new, model-agnostic technique for explaining clustering algorithms with counterfactual statements. Our approach relies on a novel soft-scoring method that captures the spatial information utilised by clustering models. It builds upon a state-of-the-art Bayesian counterfactual generator for supervised learning to deliver high-quality explanations. We evaluate its performance on five datasets and two clustering algorithms, and demonstrate that introducing soft scores to guide counterfactual search significantly improves the results.

Gabriele Dominici, Pietro Barbiero, Lucie Charlotte Magister et al.

Multimodal learning is an essential paradigm for addressing complex real-world problems, where individual data modalities are typically insufficient to accurately solve a given modelling task. While various deep learning approaches have successfully addressed these challenges, their reasoning process is often opaque; limiting the capabilities for a principled explainable cross-modal analysis and any domain-expert intervention. In this paper, we introduce SHARCS (SHARed Concept Space) -- a novel concept-based approach for explainable multimodal learning. SHARCS learns and maps interpretable concepts from different heterogeneous modalities into a single unified concept-manifold, which leads to an intuitive projection of semantically similar cross-modal concepts. We demonstrate that such an approach can lead to inherently explainable task predictions while also improving downstream predictive performance. Moreover, we show that SHARCS can operate and significantly outperform other approaches in practically significant scenarios, such as retrieval of missing modalities and cross-modal explanations. Our approach is model-agnostic and easily applicable to different types (and number) of modalities, thus advancing the development of effective, interpretable, and trustworthy multimodal approaches.

Dario Fenoglio, Arianna Casanova, Francesco De Santis et al.

Concept-based models (CMs) enhance interpretability in deep learning by grounding predictions in human-understandable concepts. However, concept annotations are expensive to obtain and rarely available at scale within a single data source. Federated learning (FL) could alleviate this limitation by enabling cross-institutional training that leverages concept annotations distributed across multiple data owners. Yet, FL lacks interpretable modeling paradigms. Integrating CMs with FL is non-trivial: CMs assume a fixed concept space and a predefined model architecture, whereas real-world FL is heterogeneous and non-stationary, with institutions joining over time and bringing new supervision. In this work, we propose Federated Concept-based Models (F-CMs), a new methodology for deploying CMs in evolving FL settings. F-CMs aggregate concept-level information across institutions and efficiently adapt the model architecture in response to changes in the available concept supervision, while preserving institutional privacy. Empirically, F-CMs preserve the accuracy and intervention effectiveness of training settings with full concept supervision, while outperforming non-adaptive federated baselines. Notably, F-CMs enable interpretable inference on concepts not available to a given institution, a key novelty with respect to existing approaches.

Stefano Colamonaco, David Debot, Pietro Barbiero et al.

Concept Bottleneck Models (CBMs) aim to improve interpretability in Deep Learning by structuring predictions through human-understandable concepts, but they provide no way to verify whether learned concepts align with the human's intended meaning, hurting interpretability. We introduce Prototype-Grounded Concept Models (PGCMs), which ground concepts in learned visual prototypes: image parts that serve as explicit evidence for the concepts. This grounding enables direct inspection of concept semantics and supports targeted human intervention at the prototype level to correct misalignments. Empirically, PGCMs match the predictive performance of state-of-the-art CBMs while substantially improving transparency, interpretability, and intervenability.

Jonas Jürß, Lucie Charlotte Magister, Pietro Barbiero et al.

Graph neural networks (GNNs) have led to major breakthroughs in a variety of domains such as drug discovery, social network analysis, and travel time estimation. However, they lack interpretability which hinders human trust and thereby deployment to settings with high-stakes decisions. A line of interpretable methods approach this by discovering a small set of relevant concepts as subgraphs in the last GNN layer that together explain the prediction. This can yield oversimplified explanations, failing to explain the interaction between GNN layers. To address this oversight, we provide HELP (Hierarchical Explainable Latent Pooling), a novel, inherently interpretable graph pooling approach that reveals how concepts from different GNN layers compose to new ones in later steps. HELP is more than 1-WL expressive and is the first non-spectral, end-to-end-learnable, hierarchical graph pooling method that can learn to pool a variable number of arbitrary connected components. We empirically demonstrate that it performs on-par with standard GCNs and popular pooling methods in terms of accuracy while yielding explanations that are aligned with expert knowledge in the domains of chemistry and social networks. In addition to a qualitative analysis, we employ concept completeness scores as well as concept conformity, a novel metric to measure the noise in discovered concepts, quantitatively verifying that the discovered concepts are significantly easier to fully understand than those from previous work. Our work represents a first step towards an understanding of graph neural networks that goes beyond a set of concepts from the final layer and instead explains the complex interplay of concepts on different levels.

Nicola Debole, Pietro Barbiero, Francesco Giannini et al.

Concept Bottleneck Models (CBMs) are neural networks designed to conjoin high performance with ante-hoc interpretability. CBMs work by first mapping inputs (e.g., images) to high-level concepts (e.g., visible objects and their properties) and then use these to solve a downstream task (e.g., tagging or scoring an image) in an interpretable manner. Their performance and interpretability, however, hinge on the quality of the concepts they learn. The go-to strategy for ensuring good quality concepts is to leverage expert annotations, which are expensive to collect and seldom available in applications. Researchers have recently addressed this issue by introducing "VLM-CBM" architectures that replace manual annotations with weak supervision from foundation models. It is however unclear what is the impact of doing so on the quality of the learned concepts. To answer this question, we put state-of-the-art VLM-CBMs to the test, analyzing their learned concepts empirically using a selection of significant metrics. Our results show that, depending on the task, VLM supervision can sensibly differ from expert annotations, and that concept accuracy and quality are not strongly correlated. Our code is available at https://github.com/debryu/CQA.

Giovanni De Felice, Riccardo D'Elia, Alberto Termine et al.

Deep time series models continue to improve predictive performance, yet their deployment remains limited by their black-box nature. In response, existing interpretability approaches in the field keep focusing on explaining the internal model computations, without addressing whether they align or not with how a human would reason about the studied phenomenon. Instead, we state interpretability in deep time series models should pursue semantic alignment: predictions should be expressed in terms of variables that are meaningful to the end user, mediated by spatial and temporal mechanisms that admit user-dependent constraints. In this paper, we formalize this requirement and require that, once established, semantic alignment must be preserved under temporal evolution: a constraint with no analog in static settings. Provided with this definition, we outline a blueprint for semantically aligned deep time series models, identify properties that support trust, and discuss implications for model design.

Pietro Barbiero, Mateo Espinosa Zarlenga, Alberto Termine et al.

We argue that existing definitions of interpretability are not actionable in that they fail to inform users about general, sound, and robust interpretable model design. This makes current interpretability research fundamentally ill-posed. To address this issue, we propose a definition of interpretability that is general, simple, and subsumes existing informal notions within the interpretable AI community. We show that our definition is actionable, as it directly reveals the foundational properties, underlying assumptions, principles, data structures, and architectural features necessary for designing interpretable models. Building on this, we propose a general blueprint for designing interpretable models and introduce the first open-sourced library with native support for interpretable data structures and processes.

Pietro Barbiero, Gabriele Ciravegna, Dobrik Georgiev et al.

"PyTorch, Explain!" is a Python module integrating a variety of state-of-the-art approaches to provide logic explanations from neural networks. This package focuses on bringing these methods to non-specialists. It has minimal dependencies and it is distributed under the Apache 2.0 licence allowing both academic and commercial use. Source code and documentation can be downloaded from the github repository: https://github.com/pietrobarbiero/pytorch_explain.

Gabriele Dominici, Pietro Barbiero, Francesco Giannini et al. · ibm-research

Current deep learning models are not designed to simultaneously address three fundamental questions: predict class labels to solve a given classification task (the "What?"), simulate changes in the situation to evaluate how this impacts class predictions (the "How?"), and imagine how the scenario should change to result in different class predictions (the "Why not?"). The inability to answer these questions represents a crucial gap in deploying reliable AI agents, calibrating human trust, and improving human-machine interaction. To bridge this gap, we introduce CounterFactual Concept Bottleneck Models (CF-CBMs), a class of models designed to efficiently address the above queries all at once without the need to run post-hoc searches. Our experimental results demonstrate that CF-CBMs: achieve classification accuracy comparable to black-box models and existing CBMs ("What?"), rely on fewer important concepts leading to simpler explanations ("How?"), and produce interpretable, concept-based counterfactuals ("Why not?"). Additionally, we show that training the counterfactual generator jointly with the CBM leads to two key improvements: (i) it alters the model's decision-making process, making the model rely on fewer important concepts (leading to simpler explanations), and (ii) it significantly increases the causal effect of concept interventions on class predictions, making the model more responsive to these changes.

Giovanni De Felice, Arianna Casanova Flores, Francesco De Santis et al.

Concept-based models are an emerging paradigm in deep learning that constrains the inference process to operate through human-interpretable variables, facilitating explainability and human interaction. However, these architectures, on par with popular opaque neural models, fail to account for the true causal mechanisms underlying the target phenomena represented in the data. This hampers their ability to support causal reasoning tasks, limits out-of-distribution generalization, and hinders the implementation of fairness constraints. To overcome these issues, we propose Causally reliable Concept Bottleneck Models (C$^2$BMs), a class of concept-based architectures that enforce reasoning through a bottleneck of concepts structured according to a model of the real-world causal mechanisms. We also introduce a pipeline to automatically learn this structure from observational data and unstructured background knowledge (e.g., scientific literature). Experimental evidence suggests that C$^2$BMs are more interpretable, causally reliable, and improve responsiveness to interventions w.r.t. standard opaque and concept-based models, while maintaining their accuracy.

Mohan Li, Martin Gjoreski, Pietro Barbiero et al.

Human Sensing, a field that leverages technology to monitor human activities, psycho-physiological states, and interactions with the environment, enhances our understanding of human behavior and drives the development of advanced services that improve overall quality of life. However, its reliance on detailed and often privacy-sensitive data as the basis for its machine learning (ML) models raises significant legal and ethical concerns. The recently proposed ML approach of Federated Learning (FL) promises to alleviate many of these concerns, as it is able to create accurate ML models without sending raw user data to a central server. While FL has demonstrated its usefulness across a variety of areas, such as text prediction and cyber security, its benefits in Human Sensing are under-explored, given the particular challenges in this domain. This survey conducts a comprehensive analysis of the current state-of-the-art studies on FL in Human Sensing, and proposes a taxonomy and an eight-dimensional assessment for FL approaches. Through the eight-dimensional assessment, we then evaluate whether the surveyed studies consider a specific FL-in-Human-Sensing challenge or not. Finally, based on the overall analysis, we discuss open challenges and highlight five research aspects related to FL in Human Sensing that require urgent research attention. Our work provides a comprehensive corpus of FL studies and aims to assist FL practitioners in developing and evaluating solutions that effectively address the real-world complexities of Human Sensing.

David Debot, Pietro Barbiero, Gabriele Dominici et al.

Concept-Based Models (CBMs) are a class of deep learning models that provide interpretability by explaining predictions through high-level concepts. These models first predict concepts and then use them to perform a downstream task. However, current CBMs offer interpretability only for the final task prediction, while the concept predictions themselves are typically made via black-box neural networks. To address this limitation, we propose Hierarchical Concept Memory Reasoner (H-CMR), a new CBM that provides interpretability for both concept and task predictions. H-CMR models relationships between concepts using a learned directed acyclic graph, where edges represent logic rules that define concepts in terms of other concepts. During inference, H-CMR employs a neural attention mechanism to select a subset of these rules, which are then applied hierarchically to predict all concepts and the final task. Experimental results demonstrate that H-CMR matches state-of-the-art performance while enabling strong human interaction through concept and model interventions. The former can significantly improve accuracy at inference time, while the latter can enhance data efficiency during training when background knowledge is available.

Pietro Barbiero, Giuseppe Marra, Gabriele Ciravegna et al.

We formalize a novel modeling framework for achieving interpretability in deep learning, anchored in the principle of inference equivariance. While the direct verification of interpretability scales exponentially with the number of variables of the system, we show that this complexity can be mitigated by treating interpretability as a Markovian property and employing neural re-parametrization techniques. Building on these insights, we propose a new modeling paradigm -- neural generation and interpretable execution -- that enables scalable verification of equivariance. This paradigm provides a general approach for designing Neural Interpretable Reasoners that are not only expressive but also transparent.

Mateo Espinosa Zarlenga, Gabriele Dominici, Pietro Barbiero et al.

In this paper, we investigate how concept-based models (CMs) respond to out-of-distribution (OOD) inputs. CMs are interpretable neural architectures that first predict a set of high-level concepts (e.g., stripes, black) and then predict a task label from those concepts. In particular, we study the impact of concept interventions (i.e., operations where a human expert corrects a CM's mispredicted concepts at test time) on CMs' task predictions when inputs are OOD. Our analysis reveals a weakness in current state-of-the-art CMs, which we term leakage poisoning, that prevents them from properly improving their accuracy when intervened on for OOD inputs. To address this, we introduce MixCEM, a new CM that learns to dynamically exploit leaked information missing from its concepts only when this information is in-distribution. Our results across tasks with and without complete sets of concept annotations demonstrate that MixCEMs outperform strong baselines by significantly improving their accuracy for both in-distribution and OOD samples in the presence and absence of concept interventions.

Andrea Pugnana, Riccardo Massidda, Francesco Giannini et al.

Concept Bottleneck Models (CBMs) are machine learning models that improve interpretability by grounding their predictions on human-understandable concepts, allowing for targeted interventions in their decision-making process. However, when intervened on, CBMs assume the availability of humans that can identify the need to intervene and always provide correct interventions. Both assumptions are unrealistic and impractical, considering labor costs and human error-proneness. In contrast, Learning to Defer (L2D) extends supervised learning by allowing machine learning models to identify cases where a human is more likely to be correct than the model, thus leading to deferring systems with improved performance. In this work, we gain inspiration from L2D and propose Deferring CBMs (DCBMs), a novel framework that allows CBMs to learn when an intervention is needed. To this end, we model DCBMs as a composition of deferring systems and derive a consistent L2D loss to train them. Moreover, by relying on a CBM architecture, DCBMs can explain why defer occurs on the final task. Our results show that DCBMs achieve high predictive performance and interpretability at the cost of deferring more to humans.

Alessandro Farace di Villaforesta, Lucie Charlotte Magister, Pietro Barbiero et al.

To address the challenge of the ``black-box" nature of deep learning in medical settings, we combine GCExplainer - an automated concept discovery solution - along with Logic Explained Networks to provide global explanations for Graph Neural Networks. We demonstrate this using a generally applicable graph construction and classification pipeline, involving panoptic segmentation with HoVer-Net and cancer prediction with Graph Convolution Networks. By training on H&E slides of breast cancer, we show promising results in offering explainable and trustworthy AI tools for clinicians.

Pietro Barbiero, Mateo Espinosa Zarlenga, Francesco Giannini et al.

This paper argues that interpretability research in Artificial Intelligence is fundamentally ill-posed as existing definitions of interpretability are not *actionable*: they fail to provide formal principles from which concrete modelling and inferential rules can be derived. We posit that for a definition of interpretability to be actionable, it must be given in terms of *symmetries*. We hypothesise that four symmetries suffice to (i) motivate core interpretability properties, (ii) characterize the class of interpretable models, and (iii) derive a unified formulation of interpretable inference (e.g., alignment, interventions, and counterfactuals) as a form of Bayesian inversion.

Francesco De Santis, Gabriele Ciravegna, Giovanni De Felice et al.

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically fix their task predictor to a single linear or Boolean expression, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of experts and the functional form of each expert, exposing an underexplored region of the design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data under user-specified operator vocabularies. Empirical evaluation demonstrates that varying the mixture size and functional form provides a robust framework for navigating the accuracy-interpretability trade-off, adapting to different user and task needs.

Dario Fenoglio, Mohan Li, Pietro Barbiero et al.

Federated Learning (FL) enables collaborative model training across multiple clients while preserving data privacy. Traditional FL methods often use a global model to fit all clients, assuming that clients' data are independent and identically distributed (IID). However, when this assumption does not hold, the global model accuracy may drop significantly, limiting FL applicability in real-world scenarios. To address this gap, we propose FLUX, a novel clustering-based FL (CFL) framework that addresses the four most common types of distribution shifts during both training and test time. To this end, FLUX leverages privacy-preserving client-side descriptor extraction and unsupervised clustering to ensure robust performance and scalability across varying levels and types of distribution shifts. Unlike existing CFL methods addressing non-IID client distribution shifts, FLUX i) does not require any prior knowledge of the types of distribution shifts or the number of client clusters, and ii) supports test-time adaptation, enabling unseen and unlabeled clients to benefit from the most suitable cluster-specific models. Extensive experiments across four standard benchmarks, two real-world datasets and ten state-of-the-art baselines show that FLUX improves performance and stability under diverse distribution shifts, achieving an average accuracy gain of up to 23 percentage points over the best-performing baselines, while maintaining computational and communication overhead comparable to FedAvg.

Francesco De Santis, Philippe Bich, Gabriele Ciravegna et al.

To increase the trustworthiness of deep neural networks, it is critical to improve the understanding of how they make decisions. This paper introduces a novel unsupervised concept-based model for image classification, named Learnable Concept-Based Model (LCBM) which models concepts as random variables within a Bernoulli latent space. Unlike traditional methods that either require extensive human supervision or suffer from limited scalability, our approach employs a reduced number of concepts without sacrificing performance. We demonstrate that LCBM surpasses existing unsupervised concept-based models in generalization capability and nearly matches the performance of black-box models. The proposed concept representation enhances information retention and aligns more closely with human understanding. A user study demonstrates the discovered concepts are also more intuitive for humans to interpret. Finally, despite the use of concept embeddings, we maintain model interpretability by means of a local linear combination of concepts.

Stefano Fioravanti, Francesco Giannini, Paolo Frazzetto et al.

The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that account for the mutual interactions of input features in the form of logic rules. However, these methods frequently fail to guarantee the consistency of the extracted explanations with the model's underlying reasoning. To bridge this gap, we propose a theoretically grounded approach to ensure coherence and fidelity of the extracted explanations, moving beyond the limitations of current heuristic-based approaches. To this end, drawing from category theory, we introduce an explaining functor which structurally preserves logical entailment between the explanation and the opaque model's reasoning. As a proof of concept, we validate the proposed theoretical constructions on a synthetic benchmark verifying how the proposed approach significantly mitigates the generation of contradictory or unfaithful explanations.

Francesco De Santis, Philippe Bich, Gabriele Ciravegna et al.

Despite their success, Large-Language Models (LLMs) still face criticism due to their lack of interpretability. Traditional post-hoc interpretation methods, based on attention and gradient-based analysis, offer limited insights as they only approximate the model's decision-making processes and have been proved to be unreliable. For this reason, Concept-Bottleneck Models (CBMs) have been lately proposed in the textual field to provide interpretable predictions based on human-understandable concepts. However, CBMs still exhibit several limitations due to their architectural constraints limiting their expressivity, to the absence of task-interpretability when employing non-linear task predictors and for requiring extensive annotations that are impractical for real-world text data. In this paper, we address these challenges by proposing a novel Linearly Interpretable Concept Embedding Model (LICEM) going beyond the current accuracy-interpretability trade-off. LICEMs classification accuracy is better than existing interpretable models and matches black-box ones. We show that the explanations provided by our models are more interveneable and causally consistent with respect to existing solutions. Finally, we show that LICEMs can be trained without requiring any concept supervision, as concepts can be automatically predicted when using an LLM backbone.

Dario Fenoglio, Gabriele Dominici, Pietro Barbiero et al. · ibm-research

Federated Learning (FL), a privacy-aware approach in distributed deep learning environments, enables many clients to collaboratively train a model without sharing sensitive data, thereby reducing privacy risks. However, enabling human trust and control over FL systems requires understanding the evolving behaviour of clients, whether beneficial or detrimental for the training, which still represents a key challenge in the current literature. To address this challenge, we introduce Federated Behavioural Planes (FBPs), a novel method to analyse, visualise, and explain the dynamics of FL systems, showing how clients behave under two different lenses: predictive performance (error behavioural space) and decision-making processes (counterfactual behavioural space). Our experiments demonstrate that FBPs provide informative trajectories describing the evolving states of clients and their contributions to the global model, thereby enabling the identification of clusters of clients with similar behaviours. Leveraging the patterns identified by FBPs, we propose a robust aggregation technique named Federated Behavioural Shields to detect malicious or noisy client models, thereby enhancing security and surpassing the efficacy of existing state-of-the-art FL defense mechanisms. Our code is publicly available on GitHub.

Francesco Giannini, Stefano Fioravanti, Oguzhan Keskin et al.

The rise of Artificial Intelligence (AI) recently empowered researchers to investigate hard mathematical problems which eluded traditional approaches for decades. Yet, the use of AI in Universal Algebra (UA) -- one of the fields laying the foundations of modern mathematics -- is still completely unexplored. This work proposes the first use of AI to investigate UA's conjectures with an equivalent equational and topological characterization. While topological representations would enable the analysis of such properties using graph neural networks, the limited transparency and brittle explainability of these models hinder their straightforward use to empirically validate existing conjectures or to formulate new ones. To bridge these gaps, we propose a general algorithm generating AI-ready datasets based on UA's conjectures, and introduce a novel neural layer to build fully interpretable graph networks. The results of our experiments demonstrate that interpretable graph networks: (i) enhance interpretability without sacrificing task accuracy, (ii) strongly generalize when predicting universal algebra's properties, (iii) generate simple explanations that empirically validate existing conjectures, and (iv) identify subgraphs suggesting the formulation of novel conjectures.

Gabriele Ciravegna, Pietro Barbiero, Francesco Giannini et al.

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

Dobrik Georgiev, Pietro Barbiero, Dmitry Kazhdan et al.

Recent research on graph neural network (GNN) models successfully applied GNNs to classical graph algorithms and combinatorial optimisation problems. This has numerous benefits, such as allowing applications of algorithms when preconditions are not satisfied, or reusing learned models when sufficient training data is not available or can't be generated. Unfortunately, a key hindrance of these approaches is their lack of explainability, since GNNs are black-box models that cannot be interpreted directly. In this work, we address this limitation by applying existing work on concept-based explanations to GNN models. We introduce concept-bottleneck GNNs, which rely on a modification to the GNN readout mechanism. Using three case studies we demonstrate that: (i) our proposed model is capable of accurately learning concepts and extracting propositional formulas based on the learned concepts for each target class; (ii) our concept-based GNN models achieve comparative performance with state-of-the-art models; (iii) we can derive global graph concepts, without explicitly providing any supervision on graph-level concepts.

Pietro Barbiero, Gabriele Ciravegna, Francesco Giannini et al.

Explainable artificial intelligence has rapidly emerged since lawmakers have started requiring interpretable models for safety-critical domains. Concept-based neural networks have arisen as explainable-by-design methods as they leverage human-understandable symbols (i.e. concepts) to predict class memberships. However, most of these approaches focus on the identification of the most relevant concepts but do not provide concise, formal explanations of how such concepts are leveraged by the classifier to make predictions. In this paper, we propose a novel end-to-end differentiable approach enabling the extraction of logic explanations from neural networks using the formalism of First-Order Logic. The method relies on an entropy-based criterion which automatically identifies the most relevant concepts. We consider four different case studies to demonstrate that: (i) this entropy-based criterion enables the distillation of concise logic explanations in safety-critical domains from clinical data to computer vision; (ii) the proposed approach outperforms state-of-the-art white-box models in terms of classification accuracy and matches black box performances.

Pietro Barbiero, Ramon Viñas Torné, Pietro Lió

Objective: Modern 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. Methods: We 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. Results: We 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. Significance: We 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.

Giansalvo Cirrincione, Pietro Barbiero, Gabriele Ciravegna et al.

Deep learning has been widely used for supervised learning and classification/regression problems. Recently, a novel area of research has applied this paradigm to unsupervised tasks; indeed, a gradient-based approach extracts, efficiently and autonomously, the relevant features for handling input data. However, state-of-the-art techniques focus mostly on algorithmic efficiency and accuracy rather than mimic the input manifold. On the contrary, competitive learning is a powerful tool for replicating the input distribution topology. This paper introduces a novel perspective in this area by combining these two techniques: unsupervised gradient-based and competitive learning. The theory is based on the intuition that neural networks are able to learn topological structures by working directly on the transpose of the input matrix. At this purpose, the vanilla competitive layer and its dual are presented. The former is just an adaptation of a standard competitive layer for deep clustering, while the latter is trained on the transposed matrix. Their equivalence is extensively proven both theoretically and experimentally. However, the dual layer is better suited for handling very high-dimensional datasets. The proposed approach has a great potential as it can be generalized to a vast selection of topological learning tasks, such as non-stationary and hierarchical clustering; furthermore, it can also be integrated within more complex architectures such as autoencoders and generative adversarial networks.

Pietro Barbiero, Gabriele Ciravegna, Vincenzo Randazzo et al.

Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks. However, these methods are not based on gradient optimization which has been proven to provide striking results in feature extraction also in unsupervised learning. Unfortunately, by focusing mostly on algorithmic efficiency and accuracy, deep clustering techniques are composed of overly complex feature extractors, while using trivial algorithms in their top layer. The aim of this work is to present a novel comprehensive theory aspiring at bridging competitive learning with gradient-based learning, thus allowing the use of extremely powerful deep neural networks for feature extraction and projection combined with the remarkable flexibility and expressiveness of competitive learning. In this paper we fully demonstrate the theoretical equivalence of two novel gradient-based competitive layers. Preliminary experiments show how the dual approach, trained on the transpose of the input matrix i.e. $X^T$, lead to faster convergence rate and higher training accuracy both in low and high-dimensional scenarios.

Pietro Barbiero, Giovanni Squillero, Alberto Tonda

As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine learning predictions. In many real-world cases, it is of utmost importance to estimate the capabilities of a machine learning algorithm to generalize, i.e., to provide accurate predictions on unseen data, depending on the characteristics of the target problem. In this work, we perform a meta-analysis of 109 publicly-available classification data sets, modeling machine learning generalization as a function of a variety of data set characteristics, ranging from number of samples to intrinsic dimensionality, from class-wise feature skewness to $F1$ evaluated on test samples falling outside the convex hull of the training set. Experimental results demonstrate the relevance of using the concept of the convex hull of the training data in assessing machine learning generalization, by emphasizing the difference between interpolated and extrapolated predictions. Besides several predictable correlations, we observe unexpectedly weak associations between the generalization ability of machine learning models and all metrics related to dimensionality, thus challenging the common assumption that the \textit{curse of dimensionality} might impair generalization in machine learning.

Pietro Barbiero, Giovanni Squillero, Alberto Tonda

A coreset is a subset of the training set, using which a machine learning algorithm obtains performances similar to what it would deliver if trained over the whole original data. Coreset discovery is an active and open line of research as it allows improving training speed for the algorithms and may help human understanding the results. Building on previous works, a novel approach is presented: candidate corsets are iteratively optimized, adding and removing samples. As there is an obvious trade-off between limiting training size and quality of the results, a multi-objective evolutionary algorithm is used to minimize simultaneously the number of points in the set and the classification error. Experimental results on non-trivial benchmarks show that the proposed approach is able to deliver results that allow a classifier to obtain lower error and better ability of generalizing on unseen data than state-of-the-art coreset discovery techniques.