Multimodal Large Language Models (MLLMs) typically process a large number of visual tokens, leading to considerable computational overhead, even though many of these tokens are redundant. Existing visual token pruning methods primarily focus on selecting the most salient tokens based on attention scores, resulting in the semantic incompleteness of the selected tokens. In this paper, we propose a novel visual token pruning strategy, called Saliency-Coverage Oriented token Pruning for Efficient MLLMs (SCOPE), to jointly model both the saliency and coverage of the selected visual tokens to better preserve semantic completeness. Specifically, we introduce a set-coverage for a given set of selected tokens, computed based on the token relationships. We then define a token-coverage gain for each unselected token, quantifying how much additional coverage would be obtained by including it. By integrating the saliency score into the token-coverage gain, we propose our SCOPE score and iteratively select the token with the highest SCOPE score. We conduct extensive experiments on multiple vision-language understanding benchmarks using the LLaVA-1.5 and LLaVA-Next models. Experimental results demonstrate that our method consistently outperforms prior approaches. Our code is available at https://github.com/kinredon/SCOPE.

Circuit discovery has gradually become one of the prominent methods for mechanistic interpretability, and research on circuit completeness has also garnered increasing attention. Methods of circuit discovery that do not guarantee completeness not only result in circuits that are not fixed across different runs but also cause key mechanisms to be omitted. The nature of incompleteness arises from the presence of OR gates within the circuit, which are often only partially detected in standard circuit discovery methods. To this end, we systematically introduce three types of logic gates: AND, OR, and ADDER gates, and decompose the circuit into combinations of these logical gates. Through the concept of these gates, we derive the minimum requirements necessary to achieve faithfulness and completeness. Furthermore, we propose a framework that combines noising-based and denoising-based interventions, which can be easily integrated into existing circuit discovery methods without significantly increasing computational complexity. This framework is capable of fully identifying the logic gates and distinguishing them within the circuit. In addition to the extensive experimental validation of the framework's ability to restore the faithfulness, completeness, and sparsity of circuits, using this framework, we uncover fundamental properties of the three logic gates, such as their proportions and contributions to the output, and explore how they behave among the functionalities of language models.

Circuit discovery has gradually become one of the prominent methods for mechanistic interpretability, and research on circuit completeness has also garnered increasing attention. Methods of circuit discovery that do not guarantee completeness not only result in circuits that are not fixed across different runs but also cause key mechanisms to be omitted. The nature of incompleteness arises from the presence of OR gates within the circuit, which are often only partially detected in standard circuit discovery methods. To this end, we systematically introduce three types of logic gates: AND, OR, and ADDER gates, and decompose the circuit into combinations of these logical gates. Through the concept of these gates, we derive the minimum requirements necessary to achieve faithfulness and completeness. Furthermore, we propose a framework that combines noising-based and denoising-based interventions, which can be easily integrated into existing circuit discovery methods without significantly increasing computational complexity. This framework is capable of fully identifying the logic gates and distinguishing them within the circuit. In addition to the extensive experimental validation of the framework's ability to restore the faithfulness, completeness, and sparsity of circuits, using this framework, we uncover fundamental properties of the three logic gates, such as their proportions and contributions to the output, and explore how they behave among the functionalities of language models.

Widely adopted evaluation metrics for sparse-view CT reconstruction, such as Structural Similarity Index Measure and Peak Signal-to-Noise Ratio, prioritize pixel-wise fidelity but often fail to capture the completeness of critical anatomical structures, particularly small or thin regions that are easily missed. To address this limitation, we propose a suite of novel anatomy-aware evaluation metrics designed to assess structural completeness across anatomical structures, including large organs, small organs, intestines, and vessels. Building on these metrics, we introduce CARE, a Completeness-Aware Reconstruction Enhancement framework that incorporates structural penalties during training to encourage anatomical preservation of significant structures. CARE is model-agnostic and can be seamlessly integrated into analytical, implicit, and generative methods.

No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via ensemble averaging (DASH), and machine-verify it with 305 Lean 4 theorems. We characterize the complete attribution design space: exactly two families of methods exist -- faithful-complete methods (unstable, with rankings that flip up to 50% of the time) and ensemble methods like DASH (stable, reporting ties for symmetric features) -- and no method lies outside this dichotomy. The impossibility is quantitative: the attribution ratio diverges as 1/(1-rho^2) for gradient boosting, is infinite for Lasso, and converges for random forests. DASH (Diversified Aggregation of SHAP) is provably Pareto-optimal among unbiased aggregations, achieving the Cramer-Rao variance bound with a tight ensemble size formula. In a survey of 77 public datasets, 68% exhibit attribution instability. Switching to conditional SHAP does not escape the impossibility when features have equal causal effects. The framework includes practical diagnostics -- a Z-test workflow and single-model screening tool -- and has direct consequences for fairness auditing: SHAP-based proxy discrimination audits are provably unreliable under collinearity. The design space theorem, diagnostics, and impossibility are mechanically verified in Lean 4 (305 theorems from 16 axioms, 0 sorry) -- to our knowledge, the first formally verified impossibility in explainable AI.

The main XAI attribution methods for deep neural networks -- GradCAM, SHAP, LIME, Integrated Gradients -- operate on separate theoretical foundations and are not formally comparable. We present GRALIS (Gradient-Riesz Averaged Locally-Integrated Shapley), a mathematical framework establishing a representation theory for attributions: every additive, linear, and continuous attribution functional on L^2(Q,mu) admits a unique canonical representation (Q, w, Delta), proved necessary by the Riesz Representation Theorem. This class encompasses SHAP, IG, LIME and linearized GradCAM, but excludes nonlinear functionals such as standard GradCAM or attention maps. Seven formal theorems provide simultaneous guarantees absent in any individual method: (T1) necessary canonical form; (T2) exact completeness; (T3) Monte Carlo convergence O(1/sqrt(m))+O(1/k); (T4) exact Shapley Interaction Values; (T5) Hoeffding ANOVA decomposition; (T6) Sobol sensitivity generalization; (T7) multi-scale extension (MS-GRALIS) with minimum-variance weights. An algebraic appendix justifies the GRALIS-SIV correspondence via the Mobius transform without circularity. GRALIS satisfies 13.5/14 axiomatic properties vs. 2.5-6/14 for individual methods, including completeness, sensitivity, locality, order-k interactions and optimal multi-scale aggregation simultaneously. Preliminary validation on BreaKHis (1,187 histology images, DenseNet-121) reports deletion faithfulness AUC +0.015 (malignant), 96% class-conditional consistency, SAL = 0.762+/-0.109 and sparsity index 0.39. Extended comparison with baseline XAI methods is planned for a companion paper.

We present a novel theoretical framework, Q-MMR, for off-policy evaluation in finite-horizon MDPs. Q-MMR learns a set of scalar weights, one for each data point, such that the reweighted rewards approximate the expected return under the target policy. The weights are learned inductively in a top-down manner via a moment matching objective against a value-function discriminator class. Notably, and perhaps surprisingly, a data-dependent finite-sample guarantee for general function approximation can be established under only the realizability of $Q^π$, with a dimension-free bound -- that is, the error does not depend on the statistical complexity of the function class. We also establish connections to several existing methods, such as importance sampling and linear FQE. Further theoretical analyses shed new light on the nature of coverage, a concept of fundamental importance to offline RL.

Many real-world data can be modeled as 3D graphs, but learning representations that incorporates 3D information completely and efficiently is challenging. Existing methods either use partial 3D information, or suffer from excessive computational cost. To incorporate 3D information completely and efficiently, we propose a novel message passing scheme that operates within 1-hop neighborhood.

One common task in many data sciences applications is to answer questions about the effect of new interventions, like: 'what would happen to Y if we make X equal to x while observing covariates Z = z?'. Formally, this is known as conditional effect identification, where the goal is to determine whether a post-interventional distribution is computable from the combination of an observational distribution and assumptions about the underlying domain represented by a causal diagram. A plethora of methods was developed for solving this problem, including the celebrated do-calculus [Pearl, 1995]. In practice, these results are not always applicable since they require a fully specified causal diagram as input, which is usually not available. In this paper, we assume as the input of the task a less informative structure known as a partial ancestral graph (PAG), which represents a Markov equivalence class of causal diagrams, learnable from observational data.