compute minimal explanations

This work addresses the interpretability of tree ensemble models by generating *minimal-cost exact explanations*. To overcome limitations of prior approaches—which enumerate all minimal explanations at prohibitive computational cost—the authors: (1) design an efficient formal verification oracle, accelerating verification by several orders of magnitude over prior work; (2) adapt the MARCO algorithm into m-MARCO, the first method capable of computing a single minimal-cost explanation (rather than enumerating all minimal ones); and (3) integrate SAT/MaxSAT modeling, minimal hitting set characterization, and incremental search optimization. Experiments demonstrate end-to-end speedups of up to 2×, while the generated minimal-cost explanations are substantially more concise—often constituting only a tiny fraction of the full set of minimal explanations—thereby significantly enhancing practicality and deployability.

Existing counterfactual explanations (CEs) in automated planning focus solely on minimal perturbations to *plans*, failing to expose high-level semantic properties of the underlying *planning problem*. Method: We propose “counterfactual scenarios” — a novel paradigm that identifies minimal modifications to the planning problem itself (e.g., action preconditions, goal conditions, or domain constraints), such that the modified problem admits a feasible plan satisfying a user-specified high-level property expressed in Linear Temporal Logic over finite traces (LTLf). Contribution/Results: We introduce the first formal framework for quantifying counterfactual scenarios over the space of planning problems, integrating planning logic with formal verification techniques. We systematically analyze computational complexity across diverse modification operations and prove that solving counterfactual scenarios incurs no higher worst-case complexity than solving the original planning problem. The framework achieves strong expressivity, interpretability, and practicality, significantly deepening the modeling capacity and broadening the applicability of counterfactual reasoning in automated planning.

To address the challenge of interpreting high-dimensional image classifiers, this paper proposes an activation-matching-driven minimal explanation generation method. It employs a lightweight binary autoencoder to learn sparse input masks, jointly optimizing multi-layer feature activation alignment, output consistency, structural sparsity, and robustness. Furthermore, a circuit-readout mechanism is introduced, constructing channel-level computational graphs via forward propagation and gradient-based analysis to map input explanations to internal model mechanisms. The method generates human-readable, minimal critical-region explanations while preserving decision fidelity. Notably, it is the first to automatically discover interpretable, channel-level computational pathways in pretrained models—without architectural modification or retraining—thereby significantly improving explanation conciseness, faithfulness, and mechanistic interpretability.

This work establishes a unified theoretical framework for analyzing the computational complexity of sufficient and contrastive explanations in machine learning models. It introduces a general probabilistic value function whose minimization subsumes both explanation types, enabling rigorous analysis through combinatorial optimization and computational complexity theory. The key contribution lies in demonstrating, for the first time, that under global explanation settings, this value function exhibits monotonicity, submodularity, or supermodularity—properties that guarantee efficient polynomial-time computability for a broad class of explanations. In stark contrast, even highly simplified variants become NP-hard in local explanation settings. These results provide a unified theoretical foundation and clear computational feasibility criteria for explainability across diverse model classes, including neural networks and decision trees.

This study systematically characterizes the parameterized computational complexity of causal and contrastive explanation problems for transparent machine learning models—including decision trees, decision lists, and Boolean circuits. Addressing local/global attribution and counterfactual explanation tasks, it establishes, for the first time within a unified framework, fixed-parameter tractability classifications across multiple model classes. Methodologically, the work integrates parameterized complexity theory, formal satisfiability analysis, structured model reduction, and combinatorial modeling to rigorously delineate the solvability boundaries of each explanation task. The results fill a critical theoretical gap in eXplainable AI (XAI), providing the first universal complexity benchmark and principled theoretical guidance for designing and evaluating interpretable algorithms.

This work addresses the lack of a unified declarative language in existing explainable AI (XAI) methods for expressing and composing diverse explanation queries, particularly those centered on optimality. To bridge this gap, the paper introduces ExplAIner—a declarative query language tailored for Boolean classification models. By extending its vocabulary and adopting a hierarchical structure, ExplAIner unifies support for multiple explanation types, including abductive, contrastive, feature-based, and distance-based explanations. Furthermore, it incorporates an optimization fragment, Opt-FOIL, to compute minimal explanations under a partial order. Theoretical analysis shows that ExplAIner queries can be reduced in polynomial time to a fixed number of SAT calls, and Opt-FOIL is solvable efficiently within the complexity class FP^NP. This framework thus offers a formally grounded, expressive, and scalable approach to XAI.

This work addresses the intractability of generating minimal and provably correct feature explanations for general neural networks, which typically requires an exponential number of verification queries. Focusing on Neural Additive Models (NAMs), the paper introduces the first specialized algorithm that exploits their structural properties to efficiently produce provably optimal minimal explanations. By integrating parallelized preprocessing with a logarithmic-complexity verification query mechanism, the method overcomes the computational bottlenecks inherent in conventional formal explanation approaches. It achieves strict interpretability guarantees while significantly outperforming existing approximation- or sampling-based techniques. Experimental results demonstrate that the proposed approach yields more concise explanations, faster computation, and stronger theoretical assurances than prior methods.

Existing visual explanation methods often lack theoretical guarantees and struggle to balance interpretability with logical rigor. This work proposes OPTIMUS, a novel framework that introduces prime implicant theory into visual explanations for the first time, generating concept-based saliency maps that highlight regions logically sufficient and minimally necessary to support the model’s prediction. By integrating concept-based explanations, formal verification, and heatmap generation, OPTIMUS establishes an explainable AI system with formal correctness guarantees. Experimental results on visual classification benchmarks demonstrate that OPTIMUS accurately identifies the key concepts relied upon by the model, producing explanations that are both logically sound and visually coherent.

This work addresses the limitations of conventional artificial intelligence systems—particularly their lack of logical rigor and traceability—by proposing a novel framework that integrates logical reasoning with optimization computation to build transparent, interpretable, trustworthy, and fair rule-based AI. The approach leverages decision diagrams and logic-based Benders decomposition for efficient projection computation and enhances explainability through post-optimality analysis. It unifies diverse formalisms including probabilistic logic, non-monotonic logic, multi-valued logic, Bayesian logic, Dempster–Shafer theory, and answer set programming modulo theories to automatically infer logical rules from noisy data. The resulting system not only supports efficient and transparent rule-based reasoning but also provides formal, traceable justifications for every conclusion, substantially improving the practicality and trustworthiness of AI.

This work investigates the creative space of mathematical proofs under constraints, with a particular focus on the impact of non-constructive reasoning. We introduce a strategy ablation methodology that integrates our custom-built Meno automated formalization tool with Goedel Prover embeddings to systematically explore both formal and informal proof spaces for foundational theorems from *Analysis I* within the Lean theorem prover. Our experiments successfully generate a novel class of machine-produced proofs, revealing that these proofs cluster along low-dimensional submanifolds in a high-dimensional representation space and significantly diverge from human-constructed proof trajectories. This study provides the first quantitative characterization of the structural differences between machine-generated and human proofs.