Francesco Leofante

Junqi Jiang, Francesco Leofante, Antonio Rago et al.

The use of counterfactual explanations (CFXs) is an increasingly popular explanation strategy for machine learning models. However, recent studies have shown that these explanations may not be robust to changes in the underlying model (e.g., following retraining), which raises questions about their reliability in real-world applications. Existing attempts towards solving this problem are heuristic, and the robustness to model changes of the resulting CFXs is evaluated with only a small number of retrained models, failing to provide exhaustive guarantees. To remedy this, we propose Δ-robustness, the first notion to formally and deterministically assess the robustness (to model changes) of CFXs for neural networks. We introduce an abstraction framework based on interval neural networks to verify the Δ-robustness of CFXs against a possibly infinite set of changes to the model parameters, i.e., weights and biases. We then demonstrate the utility of this approach in two distinct ways. First, we analyse the Δ-robustness of a number of CFX generation methods from the literature and show that they unanimously host significant deficiencies in this regard. Second, we demonstrate how embedding Δ-robustness within existing methods can provide CFXs which are provably robust.

Junqi Jiang, Jianglin Lan, Francesco Leofante et al.

Counterfactual Explanations (CEs) have received increasing interest as a major methodology for explaining neural network classifiers. Usually, CEs for an input-output pair are defined as data points with minimum distance to the input that are classified with a different label than the output. To tackle the established problem that CEs are easily invalidated when model parameters are updated (e.g. retrained), studies have proposed ways to certify the robustness of CEs under model parameter changes bounded by a norm ball. However, existing methods targeting this form of robustness are not sound or complete, and they may generate implausible CEs, i.e., outliers wrt the training dataset. In fact, no existing method simultaneously optimises for closeness and plausibility while preserving robustness guarantees. In this work, we propose Provably RObust and PLAusible Counterfactual Explanations (PROPLACE), a method leveraging on robust optimisation techniques to address the aforementioned limitations in the literature. We formulate an iterative algorithm to compute provably robust CEs and prove its convergence, soundness and completeness. Through a comparative experiment involving six baselines, five of which target robustness, we show that PROPLACE achieves state-of-the-art performances against metrics on three evaluation aspects.

Francesco Leofante, Daniel Neider, Mustafa Yalçıner

Existing algorithms for generating Counterfactual Explanations (CXs) for Machine Learning (ML) typically assume fully specified inputs. However, real-world data often contains missing values, and the impact of these incomplete inputs on the performance of existing CX methods remains unexplored. To address this gap, we systematically evaluate recent CX generation methods on their ability to provide valid and plausible counterfactuals when inputs are incomplete. As part of this investigation, we hypothesize that robust CX generation methods will be better suited to address the challenge of providing valid and plausible counterfactuals when inputs are incomplete. Our findings reveal that while robust CX methods achieve higher validity than non-robust ones, all methods struggle to find valid counterfactuals. These results motivate the need for new CX methods capable of handling incomplete inputs.

Luca Marzari, Francesco Leofante, Ferdinando Cicalese et al.

We study the problem of assessing the robustness of counterfactual explanations for deep learning models. We focus on $\textit{plausible model shifts}$ altering model parameters and propose a novel framework to reason about the robustness property in this setting. To motivate our solution, we begin by showing for the first time that computing the robustness of counterfactuals with respect to plausible model shifts is NP-complete. As this (practically) rules out the existence of scalable algorithms for exactly computing robustness, we propose a novel probabilistic approach which is able to provide tight estimates of robustness with strong guarantees while preserving scalability. Remarkably, and differently from existing solutions targeting plausible model shifts, our approach does not impose requirements on the network to be analyzed, thus enabling robustness analysis on a wider range of architectures. Experiments on four binary classification datasets indicate that our method improves the state of the art in generating robust explanations, outperforming existing methods on a range of metrics.

Junqi Jiang, Luca Marzari, Aaryan Purohit et al.

The increasing use of Machine Learning (ML) models to aid decision-making in high-stakes industries demands explainability to facilitate trust. Counterfactual Explanations (CEs) are ideally suited for this, as they can offer insights into the predictions of an ML model by illustrating how changes in its input data may lead to different outcomes. However, for CEs to realise their explanatory potential, significant challenges remain in ensuring their robustness under slight changes in the scenario being explained. Despite the widespread recognition of CEs' robustness as a fundamental requirement, a lack of standardised tools and benchmarks hinders a comprehensive and effective comparison of robust CE generation methods. In this paper, we introduce RobustX, an open-source Python library implementing a collection of CE generation and evaluation methods, with a focus on the robustness property. RobustX provides interfaces to several existing methods from the literature, enabling streamlined access to state-of-the-art techniques. The library is also easily extensible, allowing fast prototyping of novel robust CE generation and evaluation methods.

Junqi Jiang, Tom Bewley, Salim I. Amoukou et al.

Test-time scaling improves large language models' (LLMs) performance by allocating more compute budget during inference. To achieve this, existing methods often require intricate modifications to prompting and sampling strategies. In this work, we introduce representation consistency (RC), a test-time scaling method for aggregating answers drawn from multiple candidate responses of an LLM regardless of how they were generated, including variations in prompt phrasing and sampling strategy. RC enhances answer aggregation by not only considering the number of occurrences of each answer in the candidate response set, but also the consistency of the model's internal activations while generating the set of responses leading to each answer. These activations can be either dense (raw model activations) or sparse (encoded via pretrained sparse autoencoders). Our rationale is that if the model's representations of multiple responses converging on the same answer are highly variable, this answer is more likely to be the result of incoherent reasoning and should be down-weighted during aggregation. Importantly, our method only uses cached activations and lightweight similarity computations and requires no additional model queries. Through experiments with four open-source LLMs and four reasoning datasets, we validate the effectiveness of RC for improving task performance during inference, with consistent accuracy improvements (up to 4%) over strong test-time scaling baselines. We also show that consistency in the sparse activation signals aligns well with the common notion of coherent reasoning.

Paul Kobialka, Andrea Pferscher, Francesco Leofante et al.

Attribution techniques explain the outcome of an AI model by assigning a numerical score to its inputs. So far, these techniques have mainly focused on attributing importance to static input features at a single point in time, and thus fail to generalize to sequential decision-making settings. This paper fills this gap by introducing techniques to generate attribution-based explanations for Markov Decision Processes (MDPs). We give a formal characterization of what attributions should represent in MDPs, focusing on explanations that assign importance scores to both individual states and execution paths. We show how importance scores can be computed by leveraging techniques for strategy synthesis, enabling the efficient computation of these scores despite the non-determinism inherent in an MDP. We evaluate our approach on five case-studies, demonstrating its utility in providing interpretable insights into the logic of sequential decision-making agents.

Junqi Jiang, Francesco Leofante, Antonio Rago et al.

Counterfactual explanations (CEs) are advocated as being ideally suited to providing algorithmic recourse for subjects affected by the predictions of machine learning models. While CEs can be beneficial to affected individuals, recent work has exposed severe issues related to the robustness of state-of-the-art methods for obtaining CEs. Since a lack of robustness may compromise the validity of CEs, techniques to mitigate this risk are in order. In this survey, we review works in the rapidly growing area of robust CEs and perform an in-depth analysis of the forms of robustness they consider. We also discuss existing solutions and their limitations, providing a solid foundation for future developments.

Junqi Jiang, Antonio Rago, Francesco Leofante et al.

Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.

Francesco Leofante, Nico Potyka

Counterfactual explanations shed light on the decisions of black-box models by explaining how an input can be altered to obtain a favourable decision from the model (e.g., when a loan application has been rejected). However, as noted recently, counterfactual explainers may lack robustness in the sense that a minor change in the input can cause a major change in the explanation. This can cause confusion on the user side and open the door for adversarial attacks. In this paper, we study some sources of non-robustness. While there are fundamental reasons for why an explainer that returns a single counterfactual cannot be robust in all instances, we show that some interesting robustness guarantees can be given by reporting multiple rather than a single counterfactual. Unfortunately, the number of counterfactuals that need to be reported for the theoretical guarantees to hold can be prohibitively large. We therefore propose an approximation algorithm that uses a diversity criterion to select a feasible number of most relevant explanations and study its robustness empirically. Our experiments indicate that our method improves the state-of-the-art in generating robust explanations, while maintaining other desirable properties and providing competitive computational performance.

Francesco Leofante, Hamed Ayoobi, Adam Dejl et al.

AI has become pervasive in recent years, but state-of-the-art approaches predominantly neglect the need for AI systems to be contestable. Instead, contestability is advocated by AI guidelines (e.g. by the OECD) and regulation of automated decision-making (e.g. GDPR). In this position paper we explore how contestability can be achieved computationally in and for AI. We argue that contestable AI requires dynamic (human-machine and/or machine-machine) explainability and decision-making processes, whereby machines can (i) interact with humans and/or other machines to progressively explain their outputs and/or their reasoning as well as assess grounds for contestation provided by these humans and/or other machines, and (ii) revise their decision-making processes to redress any issues successfully raised during contestation. Given that much of the current AI landscape is tailored to static AIs, the need to accommodate contestability will require a radical rethinking, that, we argue, computational argumentation is ideally suited to support.

Junqi Jiang, Francesco Leofante, Antonio Rago et al.

Counterfactual Explanations (CEs) have emerged as a major paradigm in explainable AI research, providing recourse recommendations for users affected by the decisions of machine learning models. However, CEs found by existing methods often become invalid when slight changes occur in the parameters of the model they were generated for. The literature lacks a way to provide exhaustive robustness guarantees for CEs under model changes, in that existing methods to improve CEs' robustness are mostly heuristic, and the robustness performances are evaluated empirically using only a limited number of retrained models. To bridge this gap, we propose a novel interval abstraction technique for parametric machine learning models, which allows us to obtain provable robustness guarantees for CEs under a possibly infinite set of plausible model changes $Δ$. Based on this idea, we formalise a robustness notion for CEs, which we call $Δ$-robustness, in both binary and multi-class classification settings. We present procedures to verify $Δ$-robustness based on Mixed Integer Linear Programming, using which we further propose algorithms to generate CEs that are $Δ$-robust. In an extensive empirical study involving neural networks and logistic regression models, we demonstrate the practical applicability of our approach. We discuss two strategies for determining the appropriate hyperparameters in our method, and we quantitatively benchmark CEs generated by eleven methods, highlighting the effectiveness of our algorithms in finding robust CEs.

Junqi Jiang, Francesco Leofante, Antonio Rago et al.

Counterfactual explanations (CEs) provide recourse recommendations for individuals affected by algorithmic decisions. A key challenge is generating CEs that are robust against various perturbation types (e.g. input and model perturbations) while simultaneously satisfying other desirable properties. These include plausibility, ensuring CEs reside on the data manifold, and diversity, providing multiple distinct recourse options for single inputs. Existing methods, however, mostly struggle to address these multifaceted requirements in a unified, model-agnostic manner. We address these limitations by proposing a novel generative framework. First, we introduce the Label-conditional Gaussian Mixture Variational Autoencoder (L-GMVAE), a model trained to learn a structured latent space where each class label is represented by a set of Gaussian components with diverse, prototypical centroids. Building on this, we present LAPACE (LAtent PAth Counterfactual Explanations), a model-agnostic algorithm that synthesises entire paths of CE points by interpolating from inputs' latent representations to those learned latent centroids. This approach inherently ensures robustness to input changes, as all paths for a given target class converge to the same fixed centroids. Furthermore, the generated paths provide a spectrum of recourse options, allowing users to navigate the trade-off between proximity and plausibility while also encouraging robustness against model changes. In addition, user-specified actionability constraints can also be easily incorporated via lightweight gradient optimisation through the L-GMVAE's decoder. Comprehensive experiments show that LAPACE is computationally efficient and achieves competitive performance across eight quantitative metrics.

Nicola Gigante, Francesco Leofante, Andrea Micheli

Counterfactual Explanations (CEs) are a powerful technique used to explain Machine Learning models by showing how the input to a model should be minimally changed for the model to produce a different output. Similar proposals have been made in the context of Automated Planning, where CEs have been characterised in terms of minimal modifications to an existing plan that would result in the satisfaction of a different goal. While such explanations may help diagnose faults and reason about the characteristics of a plan, they fail to capture higher-level properties of the problem being solved. To address this limitation, we propose a novel explanation paradigm that is based on counterfactual scenarios. In particular, given a planning problem $P$ and an \ltlf formula $ψ$ defining desired properties of a plan, counterfactual scenarios identify minimal modifications to $P$ such that it admits plans that comply with $ψ$. In this paper, we present two qualitative instantiations of counterfactual scenarios based on an explicit quantification over plans that must satisfy $ψ$. We then characterise the computational complexity of generating such counterfactual scenarios when different types of changes are allowed on $P$. We show that producing counterfactual scenarios is often only as expensive as computing a plan for $P$, thus demonstrating the practical viability of our proposal and ultimately providing a framework to construct practical algorithms in this area.

Maria Stoica, Francesco Leofante, Alessio Lomuscio

Accurate and explainable out-of-distribution (OOD) detection is required to use machine learning systems safely. Previous work has shown that feature distance to decision boundaries can be used to identify OOD data effectively. In this paper, we build on this intuition and propose a post-hoc OOD detection method that, given an input, calculates the distance to decision boundaries by leveraging counterfactual explanations. Since computing explanations can be expensive for large architectures, we also propose strategies to improve scalability by computing counterfactuals directly in embedding space. Crucially, as the method employs counterfactual explanations, we can seamlessly use them to help interpret the results of our detector. We show that our method is in line with the state of the art on CIFAR-10, achieving 93.50% AUROC and 25.80% FPR95. Our method outperforms these methods on CIFAR-100 with 97.05% AUROC and 13.79% FPR95 and on ImageNet-200 with 92.55% AUROC and 33.55% FPR95 across four OOD datasets

Junqi Jiang, Antonio Rago, Francesco Leofante et al.

In machine learning, it is common to obtain multiple equally performing models for the same prediction task, e.g., when training neural networks with different random seeds. Model multiplicity (MM) is the situation which arises when these competing models differ in their predictions for the same input, for which ensembling is often employed to determine an aggregation of the outputs. Providing recourse recommendations via counterfactual explanations (CEs) under MM thus becomes complex, since the CE may not be valid across all models, i.e., the CEs are not robust under MM. In this work, we formalise the problem of providing recourse under MM, which we name recourse-aware ensembling (RAE). We propose the idea that under MM, CEs for each individual model should be considered alongside their predictions so that the aggregated prediction and recourse are decided in tandem. Centred around this intuition, we introduce six desirable properties for solutions to this problem. For solving RAE, we propose a novel argumentative ensembling method which guarantees the robustness of CEs under MM. Specifically, our method leverages computational argumentation to explicitly represent the conflicts between models and counterfactuals regarding prediction results and CE validity. It then uses argumentation semantics to resolve the conflicts and obtain the final solution, in a manner which is parametric to the chosen semantics. Our method also allows for the specification of preferences over the models under MM, allowing further customisation of the ensemble. In a comprehensive theoretical analysis, we characterise the behaviour of argumentative ensembling with four different argumentation semantics. We then empirically demonstrate the effectiveness of our approach in satisfying desirable properties with eight instantiations of our method. (Abstract is shortened for arXiv.)

Paul Kobialka, Lina Gerlach, Francesco Leofante et al.

Counterfactuals are widely used in AI to explain how minimal changes to a model's input can lead to a different output. However, established methods for computing counterfactuals typically focus on one-step decision-making, and are not directly applicable to sequential decision-making tasks. This paper fills this gap by introducing counterfactual strategies for Markov Decision Processes (MDPs). During MDP execution, a strategy decides which of the enabled actions (with known probabilistic effects) to execute next. Given an initial strategy that reaches an undesired outcome with a probability above some limit, we identify minimal changes to the initial strategy to reduce that probability below the limit. We encode such counterfactual strategies as solutions to non-linear optimization problems, and further extend our encoding to synthesize diverse counterfactual strategies. We evaluate our approach on four real-world datasets and demonstrate its practical viability in sophisticated sequential decision-making tasks.

Dario Guidotti, Francesco Leofante, Luca Pulina et al.

Verification of deep neural networks has witnessed a recent surge of interest, fueled by success stories in diverse domains and by abreast concerns about safety and security in envisaged applications. Complexity and sheer size of such networks are challenging for automated formal verification techniques which, on the other hand, could ease the adoption of deep networks in safety- and security-critical contexts. In this paper we focus on enabling state-of-the-art verification tools to deal with neural networks of some practical interest. We propose a new training pipeline based on network pruning with the goal of striking a balance between maintaining accuracy and robustness while making the resulting networks amenable to formal analysis. The results of our experiments with a portfolio of pruning algorithms and verification tools show that our approach is successful for the kind of networks we consider and for some combinations of pruning and verification techniques, thus bringing deep neural networks closer to the reach of formally-grounded methods.

Arthur Bit-Monnot, Francesco Leofante, Luca Pulina et al.

Smart factories are on the verge of becoming the new industrial paradigm, wherein optimization permeates all aspects of production, from concept generation to sales. To fully pursue this paradigm, flexibility in the production means as well as in their timely organization is of paramount importance. AI is planning a major role in this transition, but the scenarios encountered in practice might be challenging for current tools. Task planning is one example where AI enables more efficient and flexible operation through an online automated adaptation and rescheduling of the activities to cope with new operational constraints and demands. In this paper we present SMarTplan, a task planner specifically conceived to deal with real-world scenarios in the emerging smart factory paradigm. Including both special-purpose and general-purpose algorithms, SMarTplan is based on current automated reasoning technology and it is designed to tackle complex application domains. In particular, we show its effectiveness on a logistic scenario, by comparing its specialized version with the general purpose one, and extending the comparison to other state-of-the-art task planners.

Francesco Leofante, Nina Narodytska, Luca Pulina et al.

Neural networks are one of the most investigated and widely used techniques in Machine Learning. In spite of their success, they still find limited application in safety- and security-related contexts, wherein assurance about networks' performances must be provided. In the recent past, automated reasoning techniques have been proposed by several researchers to close the gap between neural networks and applications requiring formal guarantees about their behavior. In this work, we propose a primer of such techniques and a comprehensive categorization of existing approaches for the automated verification of neural networks. A discussion about current limitations and directions for future investigation is provided to foster research on this topic at the crossroads of Machine Learning and Automated Reasoning.

Francesco Leofante, Erika Ábrahám, Tim Niemueller et al.

In manufacturing, the increasing involvement of autonomous robots in production processes poses new challenges on the production management. In this paper we report on the usage of Optimization Modulo Theories (OMT) to solve certain multi-robot scheduling problems in this area. Whereas currently existing methods are heuristic, our approach guarantees optimality for the computed solution. We do not only present our final method but also its chronological development, and draw some general observations for the development of OMT-based approaches.