Shahaf Bassan

Shahaf Bassan, Guy Katz

With the rapid growth of machine learning, deep neural networks (DNNs) are now being used in numerous domains. Unfortunately, DNNs are "black-boxes", and cannot be interpreted by humans, which is a substantial concern in safety-critical systems. To mitigate this issue, researchers have begun working on explainable AI (XAI) methods, which can identify a subset of input features that are the cause of a DNN's decision for a given input. Most existing techniques are heuristic, and cannot guarantee the correctness of the explanation provided. In contrast, recent and exciting attempts have shown that formal methods can be used to generate provably correct explanations. Although these methods are sound, the computational complexity of the underlying verification problem limits their scalability; and the explanations they produce might sometimes be overly complex. Here, we propose a novel approach to tackle these limitations. We (1) suggest an efficient, verification-based method for finding minimal explanations, which constitute a provable approximation of the global, minimum explanation; (2) show how DNN verification can assist in calculating lower and upper bounds on the optimal explanation; (3) propose heuristics that significantly improve the scalability of the verification process; and (4) suggest the use of bundles, which allows us to arrive at more succinct and interpretable explanations. Our evaluation shows that our approach significantly outperforms state-of-the-art techniques, and produces explanations that are more useful to humans. We thus regard this work as a step toward leveraging verification technology in producing DNNs that are more reliable and comprehensible.

Shahaf Bassan, Guy Amir, Davide Corsi et al.

Deep neural networks (DNNs) are increasingly being used as controllers in reactive systems. However, DNNs are highly opaque, which renders it difficult to explain and justify their actions. To mitigate this issue, there has been a surge of interest in explainable AI (XAI) techniques, capable of pinpointing the input features that caused the DNN to act as it did. Existing XAI techniques typically face two limitations: (i) they are heuristic, and do not provide formal guarantees that the explanations are correct; and (ii) they often apply to ``one-shot'' systems, where the DNN is invoked independently of past invocations, as opposed to reactive systems. Here, we begin bridging this gap, and propose a formal DNN-verification-based XAI technique for reasoning about multi-step, reactive systems. We suggest methods for efficiently calculating succinct explanations, by exploiting the system's transition constraints in order to curtail the search space explored by the underlying verifier. We evaluate our approach on two popular benchmarks from the domain of automated navigation; and observe that our methods allow the efficient computation of minimal and minimum explanations, significantly outperforming the state of the art. We also demonstrate that our methods produce formal explanations that are more reliable than competing, non-verification-based XAI techniques.

Guy Amir, Shahaf Bassan, Guy Katz

The ability to interpret Machine Learning (ML) models is becoming increasingly essential. However, despite significant progress in the field, there remains a lack of rigorous characterization regarding the innate interpretability of different models. In an attempt to bridge this gap, recent work has demonstrated that it is possible to formally assess interpretability by studying the computational complexity of explaining the decisions of various models. In this setting, if explanations for a particular model can be obtained efficiently, the model is considered interpretable (since it can be explained ``easily''). However, if generating explanations over an ML model is computationally intractable, it is considered uninterpretable. Prior research identified two key factors that influence the complexity of interpreting an ML model: (i) the type of the model (e.g., neural networks, decision trees, etc.); and (ii) the form of explanation (e.g., contrastive explanations, Shapley values, etc.). In this work, we claim that a third, important factor must also be considered for this analysis -- the underlying distribution over which the explanation is obtained. Considering the underlying distribution is key in avoiding explanations that are socially misaligned, i.e., convey information that is biased and unhelpful to users. We demonstrate the significant influence of the underlying distribution on the resulting overall interpretation complexity, in two settings: (i) prediction models paired with an external out-of-distribution (OOD) detector; and (ii) prediction models designed to inherently generate socially aligned explanations. Our findings prove that the expressiveness of the distribution can significantly influence the overall complexity of interpretation, and identify essential prerequisites that a model must possess to generate socially aligned explanations.

Itamar Hadad, Guy Katz, Shahaf Bassan

*Automated circuit discovery* is a central tool in mechanistic interpretability for identifying the internal components of neural networks responsible for specific behaviors. While prior methods have made significant progress, they typically depend on heuristics or approximations and do not offer provable guarantees over continuous input domains for the resulting circuits. In this work, we leverage recent advances in neural network verification to propose a suite of automated algorithms that yield circuits with *provable guarantees*. We focus on three types of guarantees: (1) *input domain robustness*, ensuring the circuit agrees with the model across a continuous input region; (2) *robust patching*, certifying circuit alignment under continuous patching perturbations; and (3) *minimality*, formalizing and capturing a wide array of various notions of succinctness. Interestingly, we uncover a diverse set of novel theoretical connections among these three families of guarantees, with critical implications for the convergence of our algorithms. Finally, we conduct experiments with state-of-the-art verifiers on various vision models, showing that our algorithms yield circuits with substantially stronger robustness guarantees than standard circuit discovery methods, establishing a principled foundation for provable circuit discovery.

Shahaf Bassan, Yizhak Yisrael Elboher, Tobias Ladner et al.

Despite significant progress in post-hoc explanation methods for neural networks, many remain heuristic and lack provable guarantees. A key approach for obtaining explanations with provable guarantees is by identifying a cardinally-minimal subset of input features which by itself is provably sufficient to determine the prediction. However, for standard neural networks, this task is often computationally infeasible, as it demands a worst-case exponential number of verification queries in the number of input features, each of which is NP-hard. In this work, we show that for Neural Additive Models (NAMs), a recent and more interpretable neural network family, we can efficiently generate explanations with such guarantees. We present a new model-specific algorithm for NAMs that generates provably cardinally-minimal explanations using only a logarithmic number of verification queries in the number of input features, after a parallelized preprocessing step with logarithmic runtime in the required precision is applied to each small univariate NAM component. Our algorithm not only makes the task of obtaining cardinally-minimal explanations feasible, but even outperforms existing algorithms designed to find the relaxed variant of subset-minimal explanations - which may be larger and less informative but easier to compute - despite our algorithm solving a much more difficult task. Our experiments demonstrate that, compared to previous algorithms, our approach provides provably smaller explanations than existing works and substantially reduces the computation time. Moreover, we show that our generated provable explanations offer benefits that are unattainable by standard sampling-based techniques typically used to interpret NAMs.

Shahaf Bassan, Ron Eliav, Shlomit Gur

*Minimal sufficient reasons* represent a prevalent form of explanation - the smallest subset of input features which, when held constant at their corresponding values, ensure that the prediction remains unchanged. Previous *post-hoc* methods attempt to obtain such explanations but face two main limitations: (1) Obtaining these subsets poses a computational challenge, leading most scalable methods to converge towards suboptimal, less meaningful subsets; (2) These methods heavily rely on sampling out-of-distribution input assignments, potentially resulting in counterintuitive behaviors. To tackle these limitations, we propose in this work a self-supervised training approach, which we term *sufficient subset training* (SST). Using SST, we train models to generate concise sufficient reasons for their predictions as an integral part of their output. Our results indicate that our framework produces succinct and faithful subsets substantially more efficiently than competing post-hoc methods, while maintaining comparable predictive performance.

Shahaf Bassan, Guy Amir, Meirav Zehavi et al.

Ensemble models are widely recognized in the ML community for their limited interpretability. For instance, while a single decision tree is considered interpretable, ensembles of trees (e.g., boosted trees) are often treated as black-boxes. Despite this folklore recognition, there remains a lack of rigorous mathematical understanding of what particularly makes an ensemble (un)-interpretable, including how fundamental factors like the (1) *number*, (2) *size*, and (3) *type* of base models influence its interpretability. In this work, we seek to bridge this gap by applying concepts from computational complexity theory to study the challenges of generating explanations for various ensemble configurations. Our analysis uncovers nuanced complexity patterns influenced by various factors. For example, we demonstrate that under standard complexity assumptions like P$\neq$NP, interpreting ensembles remains intractable even when base models are of constant size. Surprisingly, the complexity changes drastically with the number of base models: small ensembles of decision trees are efficiently interpretable, whereas interpreting ensembles with even a constant number of linear models remains intractable. We believe that our findings provide a more robust foundation for understanding the interpretability of ensembles, emphasizing the benefits of examining it through a computational complexity lens.

Shahaf Bassan, Yizhak Yisrael Elboher, Tobias Ladner et al.

Despite significant advancements in post-hoc explainability techniques for neural networks, many current methods rely on heuristics and do not provide formally provable guarantees over the explanations provided. Recent work has shown that it is possible to obtain explanations with formal guarantees by identifying subsets of input features that are sufficient to determine that predictions remain unchanged using neural network verification techniques. Despite the appeal of these explanations, their computation faces significant scalability challenges. In this work, we address this gap by proposing a novel abstraction-refinement technique for efficiently computing provably sufficient explanations of neural network predictions. Our method abstracts the original large neural network by constructing a substantially reduced network, where a sufficient explanation of the reduced network is also provably sufficient for the original network, hence significantly speeding up the verification process. If the explanation is in sufficient on the reduced network, we iteratively refine the network size by gradually increasing it until convergence. Our experiments demonstrate that our approach enhances the efficiency of obtaining provably sufficient explanations for neural network predictions while additionally providing a fine-grained interpretation of the network's predictions across different abstraction levels.

Shahaf Bassan, Xuanxiang Huang, Guy Katz

Previous work has explored the computational complexity of deriving two fundamental types of explanations for ML model predictions: (1) *sufficient reasons*, which are subsets of input features that, when fixed, determine a prediction, and (2) *contrastive reasons*, which are subsets of input features that, when modified, alter a prediction. Prior studies have examined these explanations in different contexts, such as non-probabilistic versus probabilistic frameworks and local versus global settings. In this study, we introduce a unified framework for analyzing these explanations, demonstrating that they can all be characterized through the minimization of a unified probabilistic value function. We then prove that the complexity of these computations is influenced by three key properties of the value function: (1) *monotonicity*, (2) *submodularity*, and (3) *supermodularity* - which are three fundamental properties in *combinatorial optimization*. Our findings uncover some counterintuitive results regarding the nature of these properties within the explanation settings examined. For instance, although the *local* value functions do not exhibit monotonicity or submodularity/supermodularity whatsoever, we demonstrate that the *global* value functions do possess these properties. This distinction enables us to prove a series of novel polynomial-time results for computing various explanations with provable guarantees in the global explainability setting, across a range of ML models that span the interpretability spectrum, such as neural networks, decision trees, and tree ensembles. In contrast, we show that even highly simplified versions of these explanations become NP-hard to compute in the corresponding local explainability setting.

Haoze Wu, Omri Isac, Aleksandar Zeljić et al.

This paper serves as a comprehensive system description of version 2.0 of the Marabou framework for formal analysis of neural networks. We discuss the tool's architectural design and highlight the major features and components introduced since its initial release.