Selected work

Representative Papers

A Compositional Theory of Curvature in Probabilistic Circuits

Aug 13, 2026

This work addresses the limitations of global sharpness-aware regularization in probabilistic circuits, which induces depth bias and underfitting by disregarding the compositional curvature structure of the loss landscape. The study reveals, for the first time, that the trace of the Hessian in probabilistic circuits admits a decomposable form, precisely factorizing into the product of circuit flows and local sharpness terms. Building on this insight, the authors propose an adaptive sharpness-aware regularization method grounded in local intrinsic curvature. This approach preserves the closed-form updates of the EM algorithm while effectively balancing model generalization and training stability. Empirical results demonstrate that the proposed method substantially recovers the generalization performance sacrificed by global regularization, without compromising the robustness inherent to sharpness-aware learning.

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A linear upper bound on the number of moves required for independent set reconfiguration with two sliding tokens

Aug 13, 2026

This work addresses the problem of determining the minimum number of sliding moves required to reconfigure one pair of non-adjacent labeled vertices on a graph into another such pair. Focusing on the two-token independent set reconfiguration problem, the authors combine graph-theoretic analysis with combinatorial reasoning to devise path-construction and state-transition strategies. They establish, for the first time, that in any connected component of the reconfiguration graph induced by $n$-vertex graphs, any feasible reconfiguration between two valid states can be accomplished in at most $4n$ steps. This result provides a linear upper bound, resolving an open question posed by Briański et al. at MFCS 2021 and marking a significant theoretical advance in the study of token reconfiguration problems.

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A Probabilistic Circuit-Induced Pseudo-Metric for Out-of-Distribution Detection

Aug 10, 2026

Existing out-of-distribution (OOD) detection methods based on probabilistic circuits rely solely on the root node likelihood or its associated uncertainty, thereby neglecting the rich hierarchical structure inherent in the circuit and limiting detection performance. This work proposes Hierarchical Likelihood Vectors (HLVs) and Hierarchical Likelihood Distance (HLD), which, for the first time, leverage the internal hierarchy of probabilistic circuits to construct an unsupervised pseudo-metric for OOD detection. The approach enables efficient detection without retaining in-distribution data and precisely identifies the circuit nodes responsible for distributional shifts. By integrating integral probability metrics with analytical hypothesis testing, the method significantly outperforms baseline approaches—based on root likelihood, uncertainty, typicality, and kernel methods—on both tabular data and MNIST, achieving superior detection accuracy and enhanced interpretability.

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Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributions

Aug 05, 2026

Existing attribution methods struggle to simultaneously achieve diversity, plausibility, and feasibility in counterfactual explanations. This work proposes a tractable attribution distribution framework that, for the first time, explicitly models an individual’s feasible attribution space using a closed-form probability distribution. By integrating probabilistic circuits with exponential tilting, the approach enables explicit control over the proximity and sparsity of generated counterfactuals through tilting parameters—without requiring model retraining. The attribution distribution is constructed using a cost-aware function that accounts for both feature proximity and modification costs. Evaluated on standard benchmarks, the method achieves high diversity, plausibility, and feasibility while maintaining efficient rejection sampling. Visualizations on MNIST further demonstrate that the tilting strength offers a controllable trade-off between proximity and validity of counterfactual suggestions.

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Eternal Vertex Cover Problem on Halin Graphs

Jul 25, 2026

This study addresses the eternal vertex cover problem on Halin graphs, focusing on the ratio ρ between the minimum number of guards required for dynamic defense and the size of a classical minimum vertex cover. For 3-connected Halin graphs of treewidth 3, the authors establish the first nontrivial bounds within any biconnected graph class: 7/6 ≤ ρ ≤ 3/2. These bounds are achieved through the construction of specific graph families and the design of two distinct defense strategies. The paper further demonstrates that certain subclasses, such as caterpillar-like Halin graphs, attain ρ = 4/3. A 1.5-approximation algorithm is proposed to effectively approach the upper bound, and a family of graphs is constructed for which ρ approaches 7/6, thereby proving that the ratio strictly lies between 1 and 2.

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Recent publications

Latest Papers

A Compositional Theory of Curvature in Probabilistic Circuits

Aug 13, 2026

This work addresses the limitations of global sharpness-aware regularization in probabilistic circuits, which induces depth bias and underfitting by disregarding the compositional curvature structure of the loss landscape. The study reveals, for the first time, that the trace of the Hessian in probabilistic circuits admits a decomposable form, precisely factorizing into the product of circuit flows and local sharpness terms. Building on this insight, the authors propose an adaptive sharpness-aware regularization method grounded in local intrinsic curvature. This approach preserves the closed-form updates of the EM algorithm while effectively balancing model generalization and training stability. Empirical results demonstrate that the proposed method substantially recovers the generalization performance sacrificed by global regularization, without compromising the robustness inherent to sharpness-aware learning.

0 citationsRead paper

A linear upper bound on the number of moves required for independent set reconfiguration with two sliding tokens

Aug 13, 2026

This work addresses the problem of determining the minimum number of sliding moves required to reconfigure one pair of non-adjacent labeled vertices on a graph into another such pair. Focusing on the two-token independent set reconfiguration problem, the authors combine graph-theoretic analysis with combinatorial reasoning to devise path-construction and state-transition strategies. They establish, for the first time, that in any connected component of the reconfiguration graph induced by $n$-vertex graphs, any feasible reconfiguration between two valid states can be accomplished in at most $4n$ steps. This result provides a linear upper bound, resolving an open question posed by Briański et al. at MFCS 2021 and marking a significant theoretical advance in the study of token reconfiguration problems.

0 citationsRead paper

A Probabilistic Circuit-Induced Pseudo-Metric for Out-of-Distribution Detection

Aug 10, 2026

Existing out-of-distribution (OOD) detection methods based on probabilistic circuits rely solely on the root node likelihood or its associated uncertainty, thereby neglecting the rich hierarchical structure inherent in the circuit and limiting detection performance. This work proposes Hierarchical Likelihood Vectors (HLVs) and Hierarchical Likelihood Distance (HLD), which, for the first time, leverage the internal hierarchy of probabilistic circuits to construct an unsupervised pseudo-metric for OOD detection. The approach enables efficient detection without retaining in-distribution data and precisely identifies the circuit nodes responsible for distributional shifts. By integrating integral probability metrics with analytical hypothesis testing, the method significantly outperforms baseline approaches—based on root likelihood, uncertainty, typicality, and kernel methods—on both tabular data and MNIST, achieving superior detection accuracy and enhanced interpretability.

0 citationsRead paper

Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributions

Aug 05, 2026

Existing attribution methods struggle to simultaneously achieve diversity, plausibility, and feasibility in counterfactual explanations. This work proposes a tractable attribution distribution framework that, for the first time, explicitly models an individual’s feasible attribution space using a closed-form probability distribution. By integrating probabilistic circuits with exponential tilting, the approach enables explicit control over the proximity and sparsity of generated counterfactuals through tilting parameters—without requiring model retraining. The attribution distribution is constructed using a cost-aware function that accounts for both feature proximity and modification costs. Evaluated on standard benchmarks, the method achieves high diversity, plausibility, and feasibility while maintaining efficient rejection sampling. Visualizations on MNIST further demonstrate that the tilting strength offers a controllable trade-off between proximity and validity of counterfactual suggestions.

0 citationsRead paper

Eternal Vertex Cover Problem on Halin Graphs

Jul 25, 2026

This study addresses the eternal vertex cover problem on Halin graphs, focusing on the ratio ρ between the minimum number of guards required for dynamic defense and the size of a classical minimum vertex cover. For 3-connected Halin graphs of treewidth 3, the authors establish the first nontrivial bounds within any biconnected graph class: 7/6 ≤ ρ ≤ 3/2. These bounds are achieved through the construction of specific graph families and the design of two distinct defense strategies. The paper further demonstrates that certain subclasses, such as caterpillar-like Halin graphs, attain ρ = 4/3. A 1.5-approximation algorithm is proposed to effectively approach the upper bound, and a family of graphs is constructed for which ρ approaches 7/6, thereby proving that the ratio strictly lies between 1 and 2.

0 citationsRead paper