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, Yossi Adi, Jeffrey S. Rosenschein

Symbolic music segmentation is the process of dividing symbolic melodies into smaller meaningful groups, such as melodic phrases. We proposed an unsupervised method for segmenting symbolic music. The proposed model is based on an ensemble of temporal prediction error models. During training, each model predicts the next token to identify musical phrase changes. While at test time, we perform a peak detection algorithm to select segment candidates. Finally, we aggregate the predictions of each of the models participating in the ensemble to predict the final segmentation. Results suggest the proposed method reaches state-of-the-art performance on the Essen Folksong dataset under the unsupervised setting when considering F-Score and R-value. We additionally provide an ablation study to better assess the contribution of each of the model components to the final results. As expected, the proposed method is inferior to the supervised setting, which leaves room for improvement in future research considering closing the gap between unsupervised and supervised methods.

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.

David Boetius, Shahaf Bassan, Guy Katz et al.

Shapley additive explanations (SHAP) are widely recognised as computationally intractable for neural networks, since they induce an exponential search space over the input features. In this work, we take a first step towards scaling exact SHAP computation to larger search spaces by introducing an algorithm that leverages recent advances in neural network verification to compute arbitrarily tight exact lower and upper bounds on SHAP values for neural networks, ultimately recovering the exact SHAP values. We demonstrate that our approach scales to orders of magnitude larger search spaces than state-of-the-art exact methods. This provides an important first step towards exact SHAP computation and establishes a principled cornerstone for evaluating statistical approximation methods on larger search spaces.

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.

Ryma Boumazouza, Raya Elsaleh, Melanie Ducoffe et al.

We propose FAME (Formal Abstract Minimal Explanations), a new class of abductive explanations grounded in abstract interpretation. FAME is the first method to scale to large neural networks while reducing explanation size. Our main contribution is the design of dedicated perturbation domains that eliminate the need for traversal order. FAME progressively shrinks these domains and leverages LiRPA-based bounds to discard irrelevant features, ultimately converging to a formal abstract minimal explanation. To assess explanation quality, we introduce a procedure that measures the worst-case distance between an abstract minimal explanation and a true minimal explanation. This procedure combines adversarial attacks with an optional VERIX+ refinement step. We benchmark FAME against VERIX+ and demonstrate consistent gains in both explanation size and runtime on medium- to large-scale neural networks.

Reda Marzouk, Shahaf Bassan, Guy Katz et al.

Recent studies have examined the computational complexity of computing Shapley additive explanations (also known as SHAP) across various models and distributions, revealing their tractability or intractability in different settings. However, these studies primarily focused on a specific variant called Conditional SHAP, though many other variants exist and address different limitations. In this work, we analyze the complexity of computing a much broader range of such variants, including Conditional, Interventional, and Baseline SHAP, while exploring both local and global computations. We show that both local and global Interventional and Baseline SHAP can be computed in polynomial time for various ML models under Hidden Markov Model distributions, extending popular algorithms such as TreeSHAP beyond empirical distributions. On the downside, we prove intractability results for these variants over a wide range of neural networks and tree ensembles. We believe that our results emphasize the intricate diversity of computing Shapley values, demonstrating how their complexity is substantially shaped by both the specific SHAP variant, the model type, and the distribution.

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.

Ron Eliav, Arie Cattan, Eran Hirsch et al.

A common approach to hallucination detection casts it as a natural language inference (NLI) task, often using LLMs to classify whether the generated text is entailed by corresponding reference texts. Since entailment classification is a complex reasoning task, one would expect that LLMs could benefit from generating an explicit reasoning process, as in CoT reasoning or the explicit ``thinking'' of recent reasoning models. In this work, we propose that guiding such models to perform a systematic and comprehensive reasoning process -- one that both decomposes the text into smaller facts and also finds evidence in the source for each fact -- allows models to execute much finer-grained and accurate entailment decisions, leading to increased performance. To that end, we define a 3-step reasoning process, consisting of (i) claim decomposition, (ii) sub-claim attribution and entailment classification, and (iii) aggregated classification, showing that such guided reasoning indeed yields improved hallucination detection. Following this reasoning framework, we introduce an analysis scheme, consisting of several metrics that measure the quality of the intermediate reasoning steps, which provided additional empirical evidence for the improved quality of our guided reasoning scheme.

Shahaf Bassan, Shlomit Gur, Sergey Zeltyn et al.

Tasks in Predictive Business Process Monitoring (PBPM), such as Next Activity Prediction, focus on generating useful business predictions from historical case logs. Recently, Deep Learning methods, particularly sequence-to-sequence models like Long Short-Term Memory (LSTM), have become a dominant approach for tackling these tasks. However, to enhance model transparency, build trust in the predictions, and gain a deeper understanding of business processes, it is crucial to explain the decisions made by these models. Existing explainability methods for PBPM decisions are typically *post-hoc*, meaning they provide explanations only after the model has been trained. Unfortunately, these post-hoc approaches have shown to face various challenges, including lack of faithfulness, high computational costs and a significant sensitivity to out-of-distribution samples. In this work, we introduce, to the best of our knowledge, the first *self-explaining neural network* architecture for predictive process monitoring. Our framework trains an LSTM model that not only provides predictions but also outputs a concise explanation for each prediction, while adapting the optimization objective to improve the reliability of the explanation. We first demonstrate that incorporating explainability into the training process does not hurt model performance, and in some cases, actually improves it. Additionally, we show that our method outperforms post-hoc approaches in terms of both the faithfulness of the generated explanations and substantial improvements in efficiency.

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.

Reda Marzouk, Shahaf Bassan, Guy Katz

Although Shapley additive explanations (SHAP) can be computed in polynomial time for simple models like decision trees, they unfortunately become NP-hard to compute for more expressive black-box models like neural networks - where generating explanations is often most critical. In this work, we analyze the problem of computing SHAP explanations for *Tensor Networks (TNs)*, a broader and more expressive class of models than those for which current exact SHAP algorithms are known to hold, and which is widely used for neural network abstraction and compression. First, we introduce a general framework for computing provably exact SHAP explanations for general TNs with arbitrary structures. Interestingly, we show that, when TNs are restricted to a *Tensor Train (TT)* structure, SHAP computation can be performed in *poly-logarithmic* time using *parallel* computation. Thanks to the expressiveness power of TTs, this complexity result can be generalized to many other popular ML models such as decision trees, tree ensembles, linear models, and linear RNNs, therefore tightening previously reported complexity results for these families of models. Finally, by leveraging reductions of binarized neural networks to Tensor Network representations, we demonstrate that SHAP computation can become *efficiently tractable* when the network's *width* is fixed, while it remains computationally hard even with constant *depth*. This highlights an important insight: for this class of models, width - rather than depth - emerges as the primary computational bottleneck in SHAP computation.

Shahaf Bassan, Michal Moshkovitz, Guy Katz

Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to hypothesize that obtaining meaningful explanations for GAMs could be performed efficiently and would not be computationally infeasible. In this work, we challenge this hypothesis by analyzing the *computational complexity* of generating different explanations for various forms of GAMs across multiple contexts. Our analysis reveals a surprisingly diverse landscape of both positive and negative complexity outcomes. Particularly, under standard complexity assumptions such as P!=NP, we establish several key findings: (1) in stark contrast to many other common ML models, the complexity of generating explanations for GAMs is heavily influenced by the structure of the input space; (2) the complexity of explaining GAMs varies significantly with the types of component models used - but interestingly, these differences only emerge under specific input domain settings; (3) significant complexity distinctions appear for obtaining explanations in regression tasks versus classification tasks in GAMs; and (4) expressing complex models like neural networks additively (e.g., as neural additive models) can make them easier to explain, though interestingly, this benefit appears only for certain explanation methods and input domains. Collectively, these results shed light on the feasibility of computing diverse explanations for GAMs, offering a rigorous theoretical picture of the conditions under which such computations are possible or provably hard.

Shahaf Bassan, Guy Amir, Guy Katz

The local and global interpretability of various ML models has been studied extensively in recent years. However, despite significant progress in the field, many known results remain informal or lack sufficient mathematical rigor. We propose a framework for bridging this gap, by using computational complexity theory to assess local and global perspectives of interpreting ML models. We begin by proposing proofs for two novel insights that are essential for our analysis: (1) a duality between local and global forms of explanations; and (2) the inherent uniqueness of certain global explanation forms. We then use these insights to evaluate the complexity of computing explanations, across three model types representing the extremes of the interpretability spectrum: (1) linear models; (2) decision trees; and (3) neural networks. Our findings offer insights into both the local and global interpretability of these models. For instance, under standard complexity assumptions such as P != NP, we prove that selecting global sufficient subsets in linear models is computationally harder than selecting local subsets. Interestingly, with neural networks and decision trees, the opposite is true: it is harder to carry out this task locally than globally. We believe that our findings demonstrate how examining explainability through a computational complexity lens can help us develop a more rigorous grasp of the inherent interpretability of ML models.

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.