Mateo Espinosa Zarlenga

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.

Katherine M. Collins, Matthew Barker, Mateo Espinosa Zarlenga et al. · cambridge

Placing a human in the loop may abate the risks of deploying AI systems in safety-critical settings (e.g., a clinician working with a medical AI system). However, mitigating risks arising from human error and uncertainty within such human-AI interactions is an important and understudied issue. In this work, we study human uncertainty in the context of concept-based models, a family of AI systems that enable human feedback via concept interventions where an expert intervenes on human-interpretable concepts relevant to the task. Prior work in this space often assumes that humans are oracles who are always certain and correct. Yet, real-world decision-making by humans is prone to occasional mistakes and uncertainty. We study how existing concept-based models deal with uncertain interventions from humans using two novel datasets: UMNIST, a visual dataset with controlled simulated uncertainty based on the MNIST dataset, and CUB-S, a relabeling of the popular CUB concept dataset with rich, densely-annotated soft labels from humans. We show that training with uncertain concept labels may help mitigate weaknesses of concept-based systems when handling uncertain interventions. These results allow us to identify several open challenges, which we argue can be tackled through future multidisciplinary research on building interactive uncertainty-aware systems. To facilitate further research, we release a new elicitation platform, UElic, to collect uncertain feedback from humans in collaborative prediction tasks.

Mateo Espinosa Zarlenga, Katherine M. Collins, Krishnamurthy Dvijotham et al. · cambridge

Concept Bottleneck Models (CBMs) tackle the opacity of neural architectures by constructing and explaining their predictions using a set of high-level concepts. A special property of these models is that they permit concept interventions, wherein users can correct mispredicted concepts and thus improve the model's performance. Recent work, however, has shown that intervention efficacy can be highly dependent on the order in which concepts are intervened on and on the model's architecture and training hyperparameters. We argue that this is rooted in a CBM's lack of train-time incentives for the model to be appropriately receptive to concept interventions. To address this, we propose Intervention-aware Concept Embedding models (IntCEMs), a novel CBM-based architecture and training paradigm that improves a model's receptiveness to test-time interventions. Our model learns a concept intervention policy in an end-to-end fashion from where it can sample meaningful intervention trajectories at train-time. This conditions IntCEMs to effectively select and receive concept interventions when deployed at test-time. Our experiments show that IntCEMs significantly outperform state-of-the-art concept-interpretable models when provided with test-time concept interventions, demonstrating the effectiveness of our approach.

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.

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.

Yael Konforti, Mateo Espinosa Zarlenga, Elaf Almahmoud et al.

Despite strong average-case performance, deep learning models often exhibit systematic errors on specific population groups, known as error slices. Identifying these groups and the root causes of their failures is critical for model debugging and bias mitigation. However, existing error Slice Discovery Methods (SDMs) typically generate explanations disconnected from the model's inference process, thus only approximating the underlying error source and may be inaccurate. We address this limitation by leveraging Concept Bottleneck Models (CBMs), whose predictions are directly dependent on human-understandable semantic concepts. Since downstream task failures in CBMs commonly arise from concept mispredictions, concept representations provide a strong candidate for error slice identification, offering fine-grained explanations directly linked to the error source. Building on this insight, we introduce CB-SLICE, a concept-based SDM that groups samples with shared concept prediction failures and identifies the keyword concepts most responsible for each slice's failure mode. Across multiple benchmarks, we show that CB-SLICE outperforms state-of-the-art methods in uncovering well-known biases while providing richer and more faithful explanations of model errors.

Mateo Espinosa Zarlenga, Swami Sankaranarayanan, Jerone T. A. Andrews et al.

Deep neural networks trained via empirical risk minimisation often exhibit significant performance disparities across groups, particularly when group and task labels are spuriously correlated (e.g., "grassy background" and "cows"). Existing bias mitigation methods that aim to address this issue often either rely on group labels for training or validation, or require an extensive hyperparameter search. Such data and computational requirements hinder the practical deployment of these methods, especially when datasets are too large to be group-annotated, computational resources are limited, and models are trained through already complex pipelines. In this paper, we propose Targeted Augmentations for Bias Mitigation (TAB), a simple hyperparameter-free framework that leverages the entire training history of a helper model to identify spurious samples, and generate a group-balanced training set from which a robust model can be trained. We show that TAB improves worst-group performance without any group information or model selection, outperforming existing methods while maintaining overall accuracy.

Oscar Hill, Mateo Espinosa Zarlenga, Mateja Jamnik

Although concept-based models promise interpretability by explaining predictions with human-understandable concepts, they typically rely on exhaustive annotations and treat concepts as flat and independent. To circumvent this, recent work has introduced Hierarchical Concept Embedding Models (HiCEMs) to explicitly model concept relationships, and Concept Splitting to discover sub-concepts using only coarse annotations. However, both HiCEMs and Concept Splitting are restricted to shallow hierarchies. We overcome this limitation with Multi-Level Concept Splitting (MLCS), which discovers multi-level concept hierarchies from only top-level supervision, and Deep-HiCEMs, an architecture that represents these discovered hierarchies and enables interventions at multiple levels of abstraction. Experiments across multiple datasets show that MLCS discovers human-interpretable concepts absent during training and that Deep-HiCEMs maintain high accuracy while supporting test-time concept interventions that can improve task performance.

Emiliano Penaloza, Tianyue H. Zhang, Laurent Charlin et al.

Concept Bottleneck Models (CBMs) propose to enhance the trustworthiness of AI systems by constraining their decisions on a set of human-understandable concepts. However, CBMs typically assume that datasets contain accurate concept labels-an assumption often violated in practice, which we show can significantly degrade performance (by 25% in some cases). To address this, we introduce the Concept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigates the negative impact of concept mislabeling on CBM performance. We provide an analysis of key properties of the CPO objective, showing it directly optimizes for the concept's posterior distribution, and contrast it against Binary Cross Entropy (BCE), demonstrating that CPO is inherently less sensitive to concept noise. We empirically confirm our analysis by finding that CPO consistently outperforms BCE on three real-world datasets, both with and without added label noise. We make our code available on Github.

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.

Mateo Espinosa Zarlenga, Zohreh Shams, Mateja Jamnik

In recent years, there has been significant work on increasing both interpretability and debuggability of a Deep Neural Network (DNN) by extracting a rule-based model that approximates its decision boundary. Nevertheless, current DNN rule extraction methods that consider a DNN's latent space when extracting rules, known as decompositional algorithms, are either restricted to single-layer DNNs or intractable as the size of the DNN or data grows. In this paper, we address these limitations by introducing ECLAIRE, a novel polynomial-time rule extraction algorithm capable of scaling to both large DNN architectures and large training datasets. We evaluate ECLAIRE on a wide variety of tasks, ranging from breast cancer prognosis to particle detection, and show that it consistently extracts more accurate and comprehensible rule sets than the current state-of-the-art methods while using orders of magnitude less computational resources. We make all of our methods available, including a rule set visualisation interface, through the open-source REMIX library (https://github.com/mateoespinosa/remix).

Haoyan Luo, Mateo Espinosa Zarlenga, Mateja Jamnik

Activation steering controls LLM behaviour towards target behaviour by intervening in internal representations, yet it often degrades reasoning and retrieval performance. We argue that a primary cause of this trade-off is attention rerouting: steering vectors alter query-key matching, shifting attention away from contextually important tokens toward less informative ones. To address this, we propose Steering via Key-Orthogonal Projections (SKOP), a steering method that constrains harmful attention rerouting without eliminating steering efficacy. SKOP achieves this by preserving attention patterns on a small set of focus tokens the model relies on for reasoning and retrieval, while allowing redistribution among less critical tail tokens. Across multiple steering benchmarks, we show that SKOP achieves the best joint steering-utility trade-off, reducing utility degradation by 5-7x while retaining over 95% of vanilla steering efficacy. Our results further suggest that, in long-context retrieval settings where vanilla steering approaches are ineffective, SKOP can maintain robust performance by avoiding attention rerouting.

Naveen Raman, Mateo Espinosa Zarlenga, Juyeon Heo et al.

Concept-based explainability methods use human-understandable intermediaries to produce explanations for machine learning models. These methods assume concept predictions can help understand a model's internal reasoning. In this work, we assess the degree to which such an assumption is true by analyzing whether concept predictors leverage "relevant" features to make predictions, a term we call locality. Concept-based models that fail to respect localities also fail to be explainable because concept predictions are based on spurious features, making the interpretation of the concept predictions vacuous. To assess whether concept-based models respect localities, we construct and use three metrics to characterize when models respect localities, complementing our analysis with theoretical results. Each of our metrics captures a different notion of perturbation and assess whether perturbing "irrelevant" features impacts the predictions made by a concept predictors. We find that many concept-based models used in practice fail to respect localities because concept predictors cannot always clearly distinguish distinct concepts. Based on these findings, we propose suggestions for alleviating this issue.

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.

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.